(page) Jazz Harmony for Guitar By Tom Small NOTE: This is SJH-M4B.txt, available at popcorncinema.com as a free download. This is the first part of an unfinished work. Readers of my earlier work K7-mas8D, are no doubt expecting something about chords of 2 voices, but my investigation of 4-voice chords have lead me in a different direction. And I thought it best to present it in any form feasible to my resources. Hence, the illustrations are put off for now. Greetings to my visitors on the World-Wide Web! --Tom Small, St. Louis Park, Minnesota, June, 2009. Your postcards are always welcome at: 8 Dearborn Square Kankakee, Illinois 60901 USA (new page) T A B L E O F C O N T E N T S Part 1 HARMONY AND SCALE THE MAJOR SCALE THE CLOCK DERIVATION SEQUENCE THE TRITONE INTERVAL PERFECT INTERVALS MAJOR AND MINOR INTERVALS THE SEVENTH AND NINTH INTERVALS MAJOR SEVENTH AND MINOR NINTH CHORD NAMES RULES FOR CHORD NAMES TRIADS AND TETRADES HOW MANY ARE THERE? CATALOGUE SEQUENCE WHIP LIST EXCLUDED FORMS Part 2 FOUR-VOICE HARMONY VOICING IN PRACTICE A SERIES OF CHORDS BASS VOICE INDEX SUBSTITUTE AND CADENCE CHORD CONTRAST VOICE LEADING STANDARD JAZZ HARMONY CLOSE KEYS DEFINED PRECESSION LIST PRIMES SERIES 28 SERIES 101 Appendix AUGMENTED TUNING (page 1) FORWARD We experience and so believe in musical beauty; there's no logical explanation. But musicians, faced with music's endless possibilities, have always responded with rules to simplify their choices. We take some measure of consonance and dissonance, but from what do they result? Chords can be harsh or pretty, and here, the reason why is ultimately unanswered. But there will be a certainty about dissonance: it is the minor second, and its octave, the minor ninth. Perhaps the oldest idea of harmony is that of a "passing tone". Harmony in a formal sense defines consonance and dissonance. A passing tone is a tone that is dissonant for the moment, but becomes consonant in retrospect -- for having been used properly. (It resolves to a "resting tone"). In Jazz as I conceive it, the only passing tone that really matters is the flat seventh because that means the chord cannot be a "tonic chord". People looking through my book will see that it has a lot of numbers in it, and say I have brought mathematics to music. But this is not so. Mathematics is about proving whether something is true; music has no proofs. Musical methods, of which this is one, are a mental construction whose only worth is their practical value to musicians (and, in some cases, to their audience.) Where math has proof, music has utility. I have tired to show at each step, why my method is sensible, and the most practical approach. The first part of "Jazz Harmony for Guitar" is about the names of musical chords. The second part is about chord progression. But the first part has almost nothing to do with guitars. And how can there be Jazz without rhythm? I call my chords "Jazz" because if I didn't, that's still how people would describe them. My ideas seemed to have a life of their own. If they survive me, thanks are due to the musicians still using them. And although I wrote for guitar, I would hope that my readers will find something of interest for any instrument, and any style of music. The Mind of a Musician Jazz is based on Classical music, but also on improvisation. Of course, classical musicians also improvised, but unlike most players today, the also composed. To "compose" is to write it down. A "solo" is improvised; a "song" is composed. A "score" is the paper it's written on. And usually, a "score" means music on a five-line staff. For Jazz, there is the "lead sheet", which has the melody, and perhaps a few other notes, on the staff, with chord symbols. It's hard to say what's going through the mind of a musician playing music, but it does not seem to be words or numbers. So you might think you're better off without any sort of music theory, and pursue instead a purely intuitive approach. But musicians who improvise or compose face two problems. The first one is: How are you going to be sure when you're repeating yourself? Now you might want to repeat some little thing you just played (perhaps with variation), or you might not want to. The point is, you don't want to repeat yourself unintentionally. It's not always easy to recognize the difference between two chords. Or between what you're playing now and what you played last year (except that the times have changed). So as to the question of whether a musician should read and write, as well as play, I think it's better to have it down on paper. No surprise, there. My solution to music's first problem is knowing the names of chords, and having a standard way to write music using chord symbols. And for guitar, a different kind of tablature than what has been most often used. Having names for chords helps remember them. It also helps in a band. For example, a bass player could play along just knowing the chord symbols, because they suggest the fundamental tones. Chord names are also helpful for transposing instruments. Only chord symbols need to be transposed, not the whole score. Finding Inspiration The second problem of music is finding a starting point -- an inspiration for creating new music. With Jazz, there's some song you've heard, and you do it in your own style, and with improvisation. Maybe, there is a score to read from. So what's the problem? I think new songs often start out as something that has been done before. And only a fool would call his own music completely original. But nevertheless, "originality" is something all artists want. And if you start with an old song, then isn't whatever you do with it always related, however distantly, to what someone else did first? It's a philosophical question; maybe for you, there is no "second problem of music". Looking through this book, the reader will have noticed long lists of chords. These musical lists are my gift to the world! Using them, I hope you will find musical inspiration. And please consider any results to be your own creation, not mine. A piece of music belongs to the spirit that brought it forth. But a list of chords results from procedures that anyone could follow. I think what I've done is create, for harmony, a kind of rhyming dictionary (such as is used for song lyrics). I've suggested how chords can be paired, and that's sort of like saying how words can be rhymed. And my computer program, the Chord Line Editor, which goes along with this text, is my gift to the world! art@ forward (page) Part 1 HARMONY AND SCALE "Harmony" means more than one note sounding at a time, and a pleasing progression of chords. To speak with clarity about this, we're going to need some specialized vocabulary. Touch a vibrating string at midpoint, and a higher note results. This is the "octave" above the first. The frequency of vibration is twice that of the first. When men and women sing the same melody, they are actually singing in octaves. No doubt, this is how it got its proper name, the "Perfect Octave" The distance between two notes is their "interval". The octave is divided into twelve, equal intervals called "semitones" or "half steps". A "whole step" is two semitones. The "chromatic scale" is the scale of all the semitones, and music with lots of half steps is sometimes called, "chromatic". A "pitch" is a note at any of its octaves. A chord with two pitches is a "dyad". A "triad" is a chord of three pitches, and a "tetrad" is a four-pitch chord. Consider the three notes, C, E, and G (which in Solfege notation are called: do, mi, sol). Played together, we call it a "C major chord." And you have probably seen such notes referred to as: "1, 3 and 5." You may not think of yourself as a practitioner of music theory, but if you have called those notes a "C major chord", you are. Here we will make the distinction of calling a group of pitches a "chord form". This is in contrast to a "chord inversion" -- a particular arrangement of notes. All the intervals of a group of notes are its "intervallic". To "transpose" a chord (or a song) is simply to raise or lower the intervallic, which changes each note the same. Figured-bass Harmony Modern music theory holds that it makes sense to call C, E and G, a "major chord" because the quality of the sound is similar no matter at which octave a note is sounded. The "root" of the chord is represented by "1", as for example "C" in C major. The other notes of a chord are named by their distance from the root. This was not always common practice. Musicians in the time of J.S. Bach described a group of notes according to the interval from the bass. For example, having the E in the bass (i.e, as the lowest note), with G and C above it, was called the "6/3 chord." (This was "bass figured" harmony.) Here are all the inversions of a C major chord, with bass-figures. fig@ bass figured chords, open chords We no longer use this system, but it is easy enough for us to specify the bass note by putting a letter after a slash, as in C major /G. "Tonality" means that there is a pitch from which the other notes of a chord or scale seem to derive. If the root is perceived as the tonal center, then there is "tonality". Otherwise, there is "atonality". I will specify chords that have either of two pitches as root. These are "enharmonic chords", which is ambiguous tonality. Musical scales A "scale" means one note after the other, instead of simultaneously. The tonal center of a scale (of a piece of music based on the scale) is the "tonic". If music has a tonic, then that note sounds right as the last note. Or, if the tonic is not the last note, the effect is of music ending in an unfinished way. From the standpoint of harmony, a melody is a thing that passes between the pitches of a chord. In Jazz, it's a question of what scale goes over what chords. One approach is to have for a scale all the pitches of two chords. Then a passing note of the one chord will be a resting tone to the other. What is wanted is a pleasing affect not only at a moment in time, but with what notes came before and will come after. In Classical music, this is called, "counterpoint"; in Jazz it's called "voice leading". ................................................ VOCABULARY REVIEW octave interval whole step / half step / semitone chromatic scale pitch dyad / triad / tetrad C major chord chord form chord inversion root / tonic tonal center / tonality / atonality enharmonic chords intervallic / transpose ................................................ THE MAJOR SCALE There may be no logical explanation for it, but there's no denying that the major scale sounds "happy". In a way, this scale and the major triad are the foundation of both classical and jazz harmony. The "major scale" is used to name musical intervals. An example of the major scale are the notes C, D, E, F, G, A, B, and C, which is the "C major scale". This is expressed with numbers as 1, 2, 3, 4, 5, 6, h7, and 1. (The octave of the 1 is an 8). The basic Jazz chords are made by adding a note of the major scale to the major chord. When a "2" is added to the 1, 3, and 5, it is written as "9", and called a ninth chord; for example: C,E,G,D. When a "4" is added, it is written as "11", and called an eleventh chord; for example, C,F,G,E. Of course musicians of the classical tradition (composers of "regular harmony") knew and used all the intervals. But for them, the ninth and certain other intervals, like the fourth, were passing tones. (The fourth is temporarily "suspended" above the third, and etc.) In Jazz harmony, these are consonant, resting tones. A scale with five pitches is called "pentatonic". The six-note scale of all whole steps is the "whole tone scale". A seven-note scale other than the major scale is a "minor scale". Music consisting entirely of the seven notes with few or no accidentals is "diatonic music" (as opposed to chromatic). The "relative minor" scale has the "6" of the major scale as a tonal center. The scale, A, B, C, D, E, F, G, and A, is represented using numbers as 1, 2, b3, 4, 5, b6, b7. (If you know key signatures, the key of A has an F#, C# and G#; the b3, b6 and b7 correspond to F, C and G.) Like notes in the score, letters on the page take sharps (#) and flats (b) to raise or lower a semitone; the "natural sign" then returns the pitch to its unaltered value. Numbers also use the plus sign (+) for sharps. Two names for the same pitch, like C# and Db, are "enharmonic". In type, the letter "h" takes the place of the natural sign. In the key of C, Bb is represented by "7" and B is represented by "M7" or "h7". This is necessary because "7" also means the "seventh chord". (The G7 chord has the notes GBDF, and the numbers 1, 3, 5, b7). So with a chord name like "Ab7", we know that the flat sign refers to the "A", not the "7". FIVE-LINE STAFF A lot of guitarists don't use the 5-line staff (the treble clef), but anybody ought to know at least a little bit about it. This is a world language, known in all corners of the world. Higher on the page means higher in pitch. Five horizontal lines and the spaces between are the musical staff. Beginning at the left is the clef sign, which specifies the letter names. Then comes the key signature and the meter, or a "C" which means the 4/4 ("four-four") meter. Piano music has a treble clef for the right hand and a bass clef for the left hand. The treble clef is remembered by knowing the letters F, A, C, and E in the spaces, and the bass clef with A, C, E and G in the spaces. There's two kinds of tempo, with beats of three or four. Half notes get two beats, eighth notes get a half beat. Got that? fig@ treble, bass clef with eighth, half notes Above or below the five lines go the short ledger lines; note how the pitch C is represented in five octaves. fig@ C on the 5-line staff The "Solfege System" uses the singable syllables, do ("doe"), re ("ray"), mi ("me"), fa, sol, la, and ti in place of the letters C thru B. To "change the key" of a piece of music is to transpose it. Transposition on the staff is accomplished by key signatures. The key of C has no key signature. The key of F has one flat, which is Bb, and the key of G has one sharp, which is F#. In other words, the letters, FGABbCDEF, or GBCDEF#G are also major scales. key of: accidentals: C none F Bb Bb Bb, Eb Eb Bb, Eb, Ab Ab Bb, Eb, Ab, Db G F# D F#, C# A F#, C#, G# E F#, C#, G#, D# Continuing the process, called "the circle of fifths", arrives at the enharmonic keys, Fb and G#. But keys with more than four accidentals are less often used. fig@ 9 key sigs with labels Some instruments are "transposing instruments", and with good reason. Suppose a horn player has learned letter associations for the valves that are to be pressed. Now someone invents another horn exactly the same except for its size. There's no point learning different letter names for the same valves. So in order to play with other musicians, the music he reads from is transposed -- the key signature is changed appropriately. The C at the middle of a piano keyboard is "middle C", and is represented by a note written one ledger line below the treble clef staff. Guitar is a transposing instrument; middle C for guitar is on the second space from the top. This is properly noted by the treble clef sign that includes a little number eight below it. fig@ treble clef with 8 But using an ordinary treble clef sign serves guitarists in a different way because if you want to have guitar music played on piano, you probably want it raised an octave. The piano is more clear at that octave. Guitar is well-suited to be a transposing instrument, and not just to the octave. We can tighten or loosen the strings and get a different kind of sound out of them. To make best use of the 5-line staff, guitarists need to understand about transposing instruments. Here are some conventions for guitar staff notation. Numbers 1 to 4 indicate which finger to stop the string with. A number in a circle identifies the string, and a Roman numeral identifies the fret. A little diamond shape calls for the harmonic, and a quarter or eighth note with a hollow note head means to sustain that string. fig@ guitar staff notations art@ gregorian chant staff (page) art@ clock pattern, "the 7b5 chord" THE CLOCK The clock is a visual way of understanding chords. The face of a clock is a tool for musical harmony because there are twelve hours in a day and twelve semitones in an octave. We should thank the ancient world for this, for surely they would have seen the connection. But their knowledge was lost, and the practical value of representing music in this manner is little known today. fig@ clock with arrow to clock with letters The numbers of the clock correspond to fret numbers on a guitar. At noon is the twelfth fret or open string. At the seventh hour, the perfect fifth interval. For representing chords, we put the root at the noon hour. With letters, we put the "C" on top and show a chord in the key of C. But numbers are arranged with the 1 at any hour. fig@ clock with arrow to chord part numbers These "chord part numbers" will be used in chord names: 9 this is an octave above "2" b3 the minor third. 3 the major third 11 this is an octave above the "4" b5 "flat five" or, more properly, the "diminished fifth" 5 the perfect fifth, or simply, "the fifth" +5 "aug five". (The b6 is not used.) 6 the sixth 7 the 7 by itself means b7, the flat 7 M7,h7 the major seven. Sometimes, the "b3" is referred to as "+9" (augmented ninth), and the "b5" as the "+4" (augmented fourth). An empty circle goes in place of each hour, and if that pitch sounds, the circle is filled in. In this way, a visual pattern describes the chord. For example, here is the C major triad. fig@ clock with Cmaj To take advantage of this technique, you need to be able to look at the face of a clock and imagine it symbolically -- with letters or chord part numbers. For each pitch that sounds, a "spot" is filled in. What if you play some notes and want to know the chord symbol for them? If you know the letter names, you can make a pattern on the clock. Imagine the pattern being rotated around the face of a clock, with each note in turn at the top. Then you can see what the chord part numbers are, and recognize the chord symbol. fig@ clock F maj in 3 positions Or instead of rotating the pattern, learn to rotate the chord numbers, and so examine each note as root. fig@ clock F maj with numbers As another example, what is the chord symbol of this pattern? fig@ clock for minor seventh = sixth chord For the major sixth and minor seventh chords, the solution is enharmonic, with two roots. fig@ clock with ami7=c6 Which root is the best choice? If one of the roots of an enharmonic chord does not belong to the major scale of the tonic, the best choice is the other one. THE MAJOR Here is the major scale represented on a clock. The seven "degrees of the major scale" are often shown by Roman Numerals. The V has a special name: the "dominant". The IV is the "subdominant". fig@ clock with major scale The names of musical intervals are based on the major scale. They refer to either the value of a note compared to its tonic, or the equivalent distance between any two notes. minor second (a half step) major second (a whole step) minor third major third perfect fourth diminished fifth (or augmented fourth) perfect fifth minor sixth major sixth minor seventh major seventh A major or perfect interval increased by a semitone becomes "augmented", and a minor or perfect interval decreased by a semitone becomes "diminished". Chord Pairs A pair of chords can be represented by putting one clock inside the other. For example, here is the F major chord inside the C major chord. fig@ clock with F maj to C maj It is easy to see that these two chords share a pitch, and to see how, in a progression, all the ways the other notes might change. We could also show this by writing the chords on a staff, but then we would be describing specific chord inversions. Only the clock can show a pairing of chord forms. Here, for example, are all the possible pairings of two major triads. We will be making more such comparisons in seeking the best way for jazz chords to connect. fig@ clocks for 11 major triad pairs Here is a drawing of an inner clock and outer clock with only the numbers present. The chord parts for F are aligned with the chord parts for C. fig@ paired clocks for F This diagram can be helpful in figuring out ways that a chord with the root F changes to a chord with the root C. Diagrams for this and other jumps are found in the appendix. Clock notation Musicians can be vague about whether "interval" refers to one note or to two because a note is named for its interval from the root or tonic. The interval between two notes neither of which is the "1" might be called a "step interval" when the distinction needs be made. Expressing an interval in minutes avoids this problem because it's clearly a step interval that's being described. Let clock intervals be noted with "cl"; for example, "5cl" means a semitone. The usual way for musicians to understand intervals and transpose music is to memorize the letter associations for each key. In other words, to measure the difference between two notes by saying the value of one in the key signature of the other. This has the advantage of not needing numbers, and being easy enough once you've learned how. The disadvantage is that, for most musicians, key signatures with a lot of sharps or flats are a little harder to work with then the more familiar keys. Using a clock, this is not a problem. My advise is to use both approaches. art@ modern clock gears art@ cu/ sundial (page) DERIVATION SEQUENCE I am going to derive all possible chord forms of less than five different pitches. I will do this in an order that places the largest interval of the intervallic at the start of the sequence of dyads, triads or tetrades. In this way, one can see that all the possibilities have been presented. I will show the clock pattern for each. I will interpret the chord parts using each pitch as the root, and one or two will be selected as root. Each form will be given a chord name and chord symbol. Chord symbols are 4 characters long or less. Triad chord symbols are usually 3 characters long or less. There will be seventy forms. Thirteen of them are "excluded forms". Forms are excluded if they have more than one half step. There are eight forms with less than three pitches, eighteen forms of three pitches, and thirty-one forms of four pitches. Following the derivation sequence, I will arrange the fifty-seven non-excluded forms in a way that groups similar chord names together, the "Catalogue Sequence". So a chord form will have both a derivation number and a catalogue sequence number. Form number one is silence. The point of beginning this way is that, for any form, you can reverse each dot as to being silent or sounded. For example, the pattern on a clock representing a piano's black keys, reversed, would represent the white keys. So each form has a unique counterpart, and the counterpart to form number one is all the pitches sounding at once. (I do not know its number.) Form number two is a single pitch: the octave. When two voices come together, it's called a "unison". THE TRITONE INTERVAL fig@ clock 30cl The largest interval for the 2-pitch forms is 30cl, so this is form number three. It has the special name, "tritone". The chord parts, 1 and b5, are the same for either pitch as root. The tritone is an enharmonic form, usually called a diminished fifth. The diminished chord and 7b5 chord have two tritones in them. Also, dividing the octave into six equal whole steps produces the "whole-tone scale". (The augmented chord divides the octave into three equal parts.) fig@ aug, dim, 7b5, whole tone The only completely symmetrical chords are the diminished chord and the augmented triad. These and the whole tone scale are totally atonal, and music including them is sometimes called "atonal music". You can experience atonality by improvising notes from the whole tone scale. You will observe that it is difficult to reach a musical conclusion. This is not the case with the major scale. Musical tonality is like spacial asymmetry. One has a sense of being in a particular place because of the irregular layout. In regular harmony, the tritone is a passing tone; the notes that comprise it resolve to a perfect interval. In Jazz, a tritone can do that, or resolve to another tritone (typically by half step). The diminished fifth is a restless, unfinished sound. PERFECT INTERVALS The next form is the perfect fourth and fifth. For example, the note C above a G makes the interval of a fourth, and the G above the C makes the interval of a fifth. There is one chord form, and it has two inversions. fig@ clock 25cl This form is not enharmonic, because the root is always the lower of the fifth or the upper of the fourth. (Only in chords of more pitches does the root sometimes have a fourth above it.) The name "perfect" was used centuries ago. It's still appropriate for these two intervals with their forceful sound. What is the practical difference between the perfect fourth and the perfect fifth? The fifth occurs as a harmonic of the open string; the fourth does not. Therefore we hear the G as coming from the C, but not vice versa. Lightly put your finger on the string at the seventh fret and you will hear the fifth of the open string as a "harmonic". Besides vibrating on the whole of its length, and the half of it (the octave), the string vibrates on a third of its length, which produces the perfect fifth. The inversion of the fourth is certainly more dissonant than the inversion of the fifth. With C in the bass, the G above it matches the overtone of the C. But with the G in the bass, the C above it clashes, because the G has a D as its harmonic at the seventh fret. In regular harmony, a chord of G going to a chord of C is a "full cadence", and from F to C, a "half cadence". But with jazz harmony, the chord on G more often sounds like a substitute for the tonic chord. In Jazz, going from F to C is the stronger change because the F is dissonant to the overtones of C; this is the "subdominant progression". A progression of any two forms where the "F" of IV goes to the "E" of root C is certainly subdominant. It's also subdominant if the tonal center sounds like F going to C. 3-Chord Harmony It has become contemporary practice to use chords from these three roots of the scale as a kind of simplified, 3-chord harmony. In other words, C, F, and G as the roots of the major triads or substitutes for them. The virtue is simplicity. And this is an effective technique for jazz chords, which offer great variation on the major triad. Three-chord harmony makes sense because it shows how the major triad can express the two half steps of the major scale. Please make a mental note of these typical jumps as an F major triad progresses to a C major triad: The F of IV falls to the E of C; the C holds for both chords. For the G major triad going to a C major triad: The B of V rises to the C of the tonic; the G holds for both chords. fig@ open 3-chord harmony MAJOR AND MINOR INTERVALS fig@ clocks 20cl, 15cl The next two forms are the major third and minor third, 20cl and 15cl. Inverted, they make the minor sixth and major sixth. It's a pleasant effect to go up and down the major scale playing every other note. What you are hearing is an alternation of major and minor thirds (or sixths). This is a chief attraction to regular harmony, then as now. In the classical tradition, such as in the time of J.S. Bach, consecutive perfect intervals were considered old-fashioned. Before him, as with the music called Gregorian Chant, consecutive perfect fifths were sung almost to exclusion. In contrast to the classical tradition of Bach, is what today is called, "parallel change" or "parallel harmony". To illustrate, what if we had the bass going from C to D, and wanted to put another voice above it? Regular harmony might add an E above the C and then an F above the D; this makes a major third followed by a minor third. With parallel harmony, if the note above the C were E, then the note above D would be F#; both major thirds. It is a question of whether a note is thought of having derived from a scale or from a chord. Because parallel harmony has parallel perfect intervals, it can be viewed as a re-appearance, in the context of jazz and folk music, of a musical practice from long ago. Parallel changes are forceful and clear. THE SEVENTH AND NINTH INTERVALS fig@ clock 10cl The seventh form has the intervals of 10cl (a whole step), which inverted is 50cl, a flat seventh interval. It's better to call this a "flat seventh", because "minor seventh" is the name of a chord. In harmony, the major second interval is called a "ninth", (70cl), which is how it's more often used. (An interval with an octave added to it is sometimes called a "displaced interval".) The ninth has a feeling of being suspended between its neighbors, the third and the root. Chords with a flat seventh often have the major third also, which creates a tritone between the 3 and b7. The ninth and flat seventh intervals have their own personalities. The ninth has an indecisive feeling, the seventh has an unfinished feeling. Chords with a flat seven sound strong with the major third under them, weak when the minor third is, and bad if neither. The ninth is one of the two intervals that characterize Jazz harmony. Tonic chords There are a couple rules I need for Jazz harmony, and one of them is that a chord with a b7 cannot have the tonic for a root. It just doesn't sound right. The ninth chord, on the other hand, sounds good with the root as tonic. A chord form suitable for the root as tonic is a "tonic chord". (The others, like G7, are the "dominant chords".) My chord lists focus on tonic chords. MAJOR SEVENTH AND MINOR NINTH fig@ clock 5cl The major seventh, like the major ninth, characterizes jazz harmony. The eighth form is 5cl, the minor second or half step. The inversion of this is the major seventh. In regular harmony, the major seventh exists only to rise a half step to the tonic; jazz harmony never does this. The major seventh and the perfect intervals are the only non- enharmonic dyads. The sound of the major seventh on its own seems a little harsh. But the presence of the major third (of which it is the perfect fifth) brings out its beauty. For example, as in the chord, C, E and B. On a guitar, which has short strings and a limited range, this chord sounds lovely. But in the biggest pipes of a church organ, it would sound awful. Or on a bass guitar, it would not sound too good either, at least as a chord. Delicate tones sound better in the higher registers. The reason for this is that a musical note has many vibrations at once. These are the "overtones" of the sound (and they characterize the timbre of an instrument). At a low frequency, the overtones of an interval like the major seventh clash more heavily. So it must fairly be admitted, since this is one of the two essential jazz intervals, that the kind of Jazz I'm talking about belongs to the higher registers. Well, the major seventh does, but the bass still has the ninth. In this text, we are concerned with arrangements of pitches, not the timbre of an instrument. The b9 Prohibited The other interval of this, the eighth form, is the minor ninth. Although it has often been used in chord names in the past, it cannot be allowed in the method I will describe. There are two reasons for this prohibition. Besides listing all the chord forms, we are going to consider all the inversions of those forms. How many inversions are there? Since three pitches can be arranged in six different ways, and four pitches in twenty-four different ways, it would seem we are faced with 18 x 6 plus 31 x 24, or 768 inversions. (We are not concerned with displaced intervals). But a form with a half step has only half as many possibilities. Since we require such an interval to be expressed as a major seventh and not as a minor ninth, a triad with a half step has only three inversions, and a tetrad with a half step has only twelve inversions. Eight of the eighteen triads have half steps and twenty-one of the thirty-one tetrades have half steps. So our task is much simplified. There is also a philosophical reason for excluding the minor ninth. Jazz is based on classical music, and the concept of dissonance and consonance is part of this tradition. With Jazz, we want everything included. But how can Jazz still be based on classical music if it has no dissonance? Clearly, of all the intervals, it is the minor second that is most dissonant in harmony. (In melody, the most pleasant.) This then, will be our one true dissonance, and we will not allow its use in chord names. Excluded forms The "excluded forms" of the derivation sequence are simply the forms with more than one half step. Excluded forms are notated "N01" thru "N13". There are thirteen excluded forms, and some of their inversions are worthwhile. Since a form with 5cl must have 55cl in the inversion, and since we don't include inversions as large as two octaves, such forms can be expressed only by having the two major sevenths overlap. Useful inversions of the excluded forms are named in the appendix. CHORD NAMES A chord's name is the name of the form. Inversions themselves don't have names, they must be specified fully. (But a chord's bass note can be specified after a slash, like G7/D.) A five-part chord can be shown with the extra pitch in parentheses added to the end of a chord symbol. Chords are generally named for their highest chord numbers because they often contribute most to sound quality. In chord names, the minor third is shown with "mi"; the "M" refers to the major seventh. The "7" by itself means the minor seventh. The chord parts of b7 and 6 appearing together are called a "thirteenth" chord (like G13). A 4 and 3 together are called an "eleventh chord" (like F11). If the form has a half step, this is evident in the name. These are the half-steps used in chord names: the major seventh (1, h7), the thirteenth (b7, 6), the minor ninth (b3, 9), the eleventh (4, 3); the five aug-four (5, +4), and the augmented ninth (3, +9). These half-steps are not used in chord names: 1 and b9; b9 and 9; 4 and b5; 5 and +5; +5 and 6; and b7 and h7. In naming triads, where there would be confusion with the name already supplied for the 4-pitch chord, either a hyphen or a capital "T" after the name of the triad will distinguish it. Specifically, this is required for the 96-, 3+9-, 5+4-, and 97- chords. The hyphen looks better, but sometimes the "T" is more legible. "Triad" must also be used in the full chord name (the spoken name) for the miM, 9M, MbT, 7bT, and di, because the same name is used for a tetrade. Handwritten, a delta sign (a little triangle) is conveniently indicates the major seventh, and a degree mark (a little circle) indicates a diminished fifth. Enharmonic Chords Since chord parts don't always define a root, why bother with enharmonic chords at all? Some chords, like the diminished chord, are completely atonal. Other chords, the kind we hear more often, clearly belong to a key. But there is a third kind of tonality, ambiguous tonality, even if it can't be definitely defined. My method is a way of defining it inexactly. And my method makes enharmonic chords easier to remember. All chord symbols with a 6, but not with a 96, are enharmonic, and the 6 is the root of the other chord. This accounts for seven of the ten (non-symmetrical) forms. The others are: 93=97T, 96T=75, and 94=mi97. For these three, the 9 of the first-mentioned chord is the root of the enharmonic. (And the b7 of the second-mentioned chord is the root of the other chord.) enharmonic forms 93=97T 96T=75 63=min 65=7b3 aug 7b5 6=mi7 mi6=dim7 6+9=mi5+4 M76=mi9 miM6=dim9 94=97 dim When the 6 becomes a 1, all the other part numbers go to the next higher part numbers too. For example, a 7 goes to a 9, a 1 to a 3, a 3 to a 5. And when the 1 becomes a 6, they go the other way. So of an enharmonic pair, it can be said that one of them has the "high numbers" and the other the "low numbers". The reason we have enharmonic chords is because they define ambiguous tonality. Enharmonic chord symbols define certain chords with either of two pitches as root. RULES FOR CHORD NAMES If a form has a half step, the lower pitch cannot be the root of the chord. The half-step below a tonal center is consonant, but the half-step above, is dissonant. Exclude a chord name interpretation with a 4 unless the major third is present. Exclude an +5 unless the major third is present with the exception of the augmented nine-six chord. Note the use of an exception in the previous rule. I try to go by the rules, but I have to make exceptions. Here, I am saying that, except for the 96+5, the root must have a major third if it is also to have a 4 or +5. Exclude a chord name interpretation that has more than one fifth in it, except for the 5+4 chord (1,3,5,+4), the minor 5+4 chord, and the 5+4 triad. An interpretation with the b5 but no b3 is excluded with these four exceptions: the 7b5 chord (1,3,b5,b7), the 7b5 triad, the major 7b5 chord, and the major 7b5 triad. Those are the four basic rules, but more exceptions must be made. (For the following entries, the number at the left is the derivation number.) These tetrad interpretations are excluded for simplicity, and because they do not seem necessary: 40. 1,b3,3,b5 in favor of the 13b5 chord: 1,b5,6,b7. 62. 1,b3,3,+5 in favor of the M7+5: 1,3,+5,h7. 64. 1,3,4,+5 in favor of the miM7: 1,b3,5,h7. 33. 1,5,6,h7 in favor of the enharmonic pair 94 and mi97 (this is the only form that would have three interpretations). These are excluded because the alternative interpretations are well-known chords: 65. 1,3,4,6 in favor of the M7 chord: 1,3,5,h7. 50. 1,5,h7,9 in favor of the 11 chord: 1,4,3,5. 63. 1,3,+5,9 in favor of the 7+5: 1,3,+5,b7. 52. 1,5,b7,9 in favor of the 96: 1,3,6,9. A triad with a half step has only three inversions, so it seems better to exclude these interpretations: 15 1,4,3 in favor of the M75: 1,5,h7. 10 1,h7,6 in favor of the 9b3: 1,b3,9. 11. 1,6,b7 in favor of the 9M: 1,h7,9. 21. 1,b3,6 in favor of the diminished triad: 1,b3,b5. This completes the procedure for naming chord forms and identifying some of them as enharmonic pairs. There are forty-nine non-excluded triad and tetrad forms, and ten of them have two names. To summarize, here are the rules for naming them: 1. No chord is named with a minor ninth as one of its parts. 2. No chord has more than one of +5,5 or b5, except for the five aug-four chords. 3. No chord has a b5 without a b3 except for the seven flat-five chords. 4. No chord has a 4 or +5 unless the 3 is present, except for the augmented nine-six. The typical problem is to come up with a name given a bunch of notes. Keep these tips in mind: 1. This system does not apply to chords of more than four pitches. 2. If the pattern has a half step, the upper pitch is not the root. 3. If the form has a fourth, the upper pitch is probably not the root. Only three forms include the perfect fourth, the 11, 74 and 94. They each have the 3 as well. TRIADS AND TETRADES The following list I call the "derivation sequence". It shows the chord forms in an order listing the space intervals from largest to least. The triads run from form number nine to form 27, and the tetrades from form 28 (form 33 starts with the 94), to form number 70 (the diminished chord). Here is an excerpt from the derivation sequence that will illustrate its design. Example derivation entry ........................................... 9. 50, 5, 5 (excluded) [N01] 10. 45, 10, 5 WH-- R17 R:9M (11) SJH 1, 6, h7 9b3: b3, 1, 9 b9, b7, 1 The above says that form number 9 has the intervals 50cl, 5cl and 5cl. It is an excluded form notated as "N01". Form number 10 has the intervals 45cl, 10cl, and 5cl. With the first note as root, the chord parts are 1, 6 and h7. With the second note as root, the chord parts are b3, 1 and 9. This is the preferred choice, and the chord symbol is 9b3. "WH-- R17" means that this form contains a whole step and a half step, as explained below. "R:9M" means that if you laid out this series of intervals in a counter-clockwise direction, the result would be the nine major seven triad, which has derivation number 11. "SJH" stands for "Standard Jazz Harmony", which is explained in Part 2. The pattern resulting from reversing the order of intervals in a chord form I call the "retort" of the form. "Retrograde" already refers to reversing the order of notes in a melody, but this is a little different. Looking at the derivation list, it seems that the chords that we use more often tend to be towards the end of it. This must be because forms with large intervals have the other notes close together. HOW MANY ARE THERE? There are forty-nine named three or four-part chords. Eighteen are triads and thirty-one are tetrades. How many inversions are there? Since three pitches can be arranged in six different ways, and four pitches in twenty-four different ways, it would seem we are faced with 18 x 6 plus 31 x 24, or 852 inversions. But our task is easier because we exclude inversions with a minor ninth. A form with a half step has only half the possibilities. But three chords are enharmonic by symmetry: The augmented chord has only 2 inversions, the diminished chord has 6, and the 7b5 has 12. For the 9 other triads without half steps, and the 8 triads that do have half steps, add 78. For the 8 other tetrads without half steps, and the 21 tetrades that do have half steps, add 444. The grand total is 542. Following the Derivation Sequence is the Catalogue Sequence, which associates forms according to their chord symbols, and gives their full, spoken names. DERIVATION OF TRIAD CHORD FORMS 9. 50, 5, 5 (excluded) [N01] 10. 45, 10, 5 WH-- (17) R: 9M (11) SJH 9b3 1, b3, 9 nine flat three 1, 6, h7 9b3: b3, 1, 9 b9, b7, 1 C9b3: C Eb D 11. 45, 5, 10 WH-- (17) R: 9b3 (10) SJH 9M 1, h7, 9 nine major seven triad 1, 6, b7 b3, 1, b9 9M: 9, h7, 1 C9M: C B D 12. 40, 15, 5 -H-- (18) R: miM (14) 3+9- 1, 3, +9 the three aug-nine 1, +5, h7 3+9T: h3, 1, b3 b9, 6, 1 C3+9T: C E D# 13. 40, 10, 10 W--- (2) SJH 93 1, 3, 9 the nine-three 97- 1, b7, 9 the nine-seven triad 1, +5, b7 93: 3, 1, 9 97T: 9, b7, 1 C93: C E D D97T: D C E 14. 40, 5, 15 -H-- (18) R: 3+9T (12) miM 1, b3, h7 the minor-major triad 1, +5, 6 3, 1, b9 miM: b3, h7, 1 CmiM: C Eb B 15. 35, 20, 5 -H-P (16) R: M73 (18) SJH M75 1, 5, h7 major seven-five M75: 1, 5, h7 4, 1, 3 b9, +5, 1 CM75: C G B 16. 35, 15, 10 W--P (15) R: 65 (17) SJH 96- 1, 6, 9 the nine-six triad 75 1, 5, b7 the seven-five 75: 1, 5, b7 4, 1, b3 96T: 9, 6, 1 C96T: C A D D75: D A C 17. 35, 10, 15 W--P (15) R: 96T (16) SJH 65 1, 5, 6 the six-five 7b3 1, b3, b7 the seven flat-three 65: 1, 5, 6 4, 1, 9 7b3: b3, b7, 1 C7b3: C Eb G Eb65: Eb B C 18. 35, 5, 20 -H-P (16) R: M75 (15) SJH M73: 1, 3, h7 major seven-three 1, 5, +5 4, 1, b9 M73: 3, h7, 1 CM73: C E B 19. 30, 25, 5 -HIP (20) R: 5+4T (20) SJH MbT 1, b5, h7 major seven flat five triad MbT: 1, b5, h7 b5, 1, 4 b9, 5, 1 CMbT: C Gb B 20. 30, 20, 10 W-I- (19) R: 73 (22) SJH 7bT 1, b5 b7 seven flat five triad 7bT: 1, b5, b7 b5, 1, 3 9, +5, 1 C7bT: C Gb Bb 21. 30, 15, 15 --I- (13) SJH di: 1, b3, b5 diminished triad 1, b5, 6 di: b5, 1, b3 b3, 6, 1 C dim: C Eb Gb 22. 30, 10, 20 W-I- (19) R: 7bT (20) SJH 73 1, 3, b7 the seven-three 1, b5, +5 b5, 1, 9 73: 3, b7, 1 C73: C E Bb 23. 30, 5, 25 -HIP (20) R: MbT (19) 5+4- 1, +4, b5 five aug-four triad 5+4T: 1, b5, h5 b5, 1, b9 4, h7, 1 C5+4: C G F# 24. 25, 25, 10 W--P (1) SJH 95 1, 5, 9 the nine-five 1, 4, b7 5, 1, 4 95: 9, 5, 1 C95: C G D 25. 25, 20, 15 ---P (14) R: min (26) SJH maj 1, 3, 5 the major chord 1, 4, 6 maj: 5, 1, 3 b3, +5, 1 C maj: C E G 26. 25, 15, 20 ---P (14) R: maj (25) SJH 63 1, 3, 6 the six-three min 1, b3, 5 the minor chord 1, 4, +5 min: 5, 1, b3 63: 3, 6, 1 C63: C E A A min: A C E 27. 20, 20, 20 ----- (4) SJH aug 1, 3, b5 the augmented chord aug: 1, 3, +5 C aug: C E #G DERIVATION OF TETRADE CHORD FORMS 28. 45, 5, 5, 5 (excluded) [N02] 29. 40, 10, 5, 5 (excluded) [N03] 30. 40, 5, 10, 5 (excluded) [N04] 31. 40, 5, 5, 10 (excluded) [N05] 32. 35, 15, 5, 5 (excluded) [N06] 33. 35, 10, 10, 5 WH-P (31) R: 9M7 (36) SJH 94 1, 4, 3, 9 the nine-four mi97 1, b3, b7, 9 the minor nine-seven 1, 5, 6, h7 94: 4, 1, 9, 3 mi97: b3, b7, 1, 9 b9, +5, b7, 1 C94: C F D E Bmi97: D F C E 34. 35, 10, 5, 10 WH-P (11) 96M7 1, 6, h7, 9 nine six major seven 1, 5, 6, b7 4, 1, 9, b3 b3, b7, 1, b9 96M7: 9, 6, h7, 1 C96M7: C A B D 35. 35, 5, 15, 5 [N07] 36. 35, 5, 10, 10 WH-P (31) R: 94 (33) SJH 9M7 1, 9, 3, h7 nine major seven 1, 5, +5, b7 4, 1, b9, b3 9M7: 3, h7, 1, 9 9, 6, b7, 1 C9M7: C E B D 37. 35, 5, 5, 15 (excluded) [N08] 38. 30, 20, 5, 5 (excluded) [N09] 39. 30, 15, 10, 5 WHIP (27) R: mi13 (46) mi96 1, 9, b3, 6 minor nine-six chord 1, b5, 6, h7 b5, 1, b3, 4 mi96: b3, 6, 1, 9 b9, 5, b7, 1 Cmi96: C Eb A D 40. 30, 15, 5, 10 WHI- (28) R: miM6 (43) 13b5 1, b5, 6, b7 thirteen flat-five 13b5: 1, b5, 6, b7 b5, 1, b3, h3 b3, 6, 1, b9 9, +5, h7, 1 C13b5: C Gb Bb A 41. 30, 10, 15, 5 WHIP (29) R: 96+5 (45) 7+9 1, b3, h3, b7 seven aug-nine 1, b5, +5, h7 b5, 1, 9, 4 7+9: h3, b7, 1, b3 b9, 5, 6, 1 C7+9: C E Bb D# 42. 30, 10, 10, 10 W-I- (12) SJH 97 1, 3, b7, 9 nine-seven chord 1, b5, +5, b7 b5, 1, 9, 3 97: 3, b7, 1, 9 9, +5, b7, 1 C97: C E Bb D 43. 30, 10, 5, 15 WHI- (28) R: 13b5 (40) miM6 1, b3, 6, h7 minor-major seven-six dim9 1, b3, b5, 9 diminished ninth chord 1, b5, +5, 6 dim9: b5, 1, 9, b3 3, b7, 1, b9 miM6: b3, 6, h7, 1 Cdim9: C Eb Gb D EbmiM6: Eb Gb C D 44. 30, 5, 20, 5 (excluded) [N10] 45. 30, 5, 15, 10 WHIP (29) R: 7+9 (41) 96+5 1, +5, 6, 9 augmented nine-six 1, b5, h5, b7 b5, 1, b9, 3 4, h7, 1, b3 96+5: 9, +5, 6, 1 C96+5: C A D G# 46. 30, 5, 10, 15 WHIP (27) R:mi96 (39) mi13 1, b3, 6, b7 minor thirteenth chord 1, b5, h5, 6 b5, 1, b9, b3 4, h7, 1, 9 mi13: b3, 6, b7, 1 Cmi13: C Eb Bb A 47. 30, 5, 5, 20 (excluded) [N11] 48. 25, 25, 5, 5 (excluded) [N12] 49. 25, 20, 10, 5 WHIP (26) R: 13 (61) SJH 5+4 1, 3, +4, 5 the five aug-four 1, 4, 6, h7 5+4: h5, 1, 3, b5 b3, +5, 1, 9 b9, b5, b7, 1 C5+4: C G E F# 50. 25, 20, 5, 10 WH-P (25) R: M76 (57) SJH 11 1, 4, 3, 5 the eleventh chord 1, 4, 6, b7 11: 5, 1, 3, 4 b3, +5, 1, b9 9, 5, h7, 1 C11: C F E G 51. 25, 15, 15, 5 -HIP (23) R: M7di (60) 6+9 1, 3, 6, +9 six aug-nine mi5+4 1, b3, +4, 5 minor five aug-four 1, 4, +5, h7 mi5+4: 5, 1, b3, b5 6+9: 3, 6, 1, b3 1, b9, b5, 6 C6+9: C E A D# A5+4: A C E D# 52. 25, 15, 10, 10 W--P (30) R: 9 (56) SJH 96 1, 3, 6, 9 the nine-six 1, 4, +5, b7 5, 1, b3, 4 96: 3, 6, 1, 9 9, 5, b7, 1 C96: C E A D 53. 25, 15, 5, 15 -H-P (9) 3+9 1, 3, 5, +9 the three aug-nine 1, 4, +5, 6 3+9: 5, 1, b3, h3 3, 6, 1, b9 b3, +5, h7, 1 C3+9: C E D# G 54. 25, 10, 20, 5 WHIP (24) R: M7b5 (59) SJH 74 1, 4, 3, b7 the seven-four 1, 4, 5, h7 5, 1, 9, b5 74: 4, b7, 1, 3 b9, b5, +5, 1 C74: C F E Bb 55. 25, 10, 15, 10 W--P (10) SJH 965 1, 5, 6, 9 the nine-six five 1, 4, 5, b7 5, 1, 9, 4 4, b7, 1, b3 965: 9, 5, 6, 1 C965: C D A G 56. 25, 10, 10, 15 W--P (30) R: 96 (52) SJH 9 1, 3, 5, 9 the ninth chord 1, 4, 5, 6 9: 5, 1, 9, 3 4, b7, 1, 9 b3, +5, b7, 1 C9: C E G D 57. 25, 10, 5, 20 WH-P (25) R: 11 (50) SJH M76 1, 3, 6, h7 the major seven-six mi9 1, b3, 5, 9 minor ninth chord 1, 4, 5, +5 mi9: 5, 1, 9, b3 4, b7, 1, b9 M76: 3, 6, h7, 1 CM76: C E A B Ami9: A C E B 58. 25, 5, 25, 5 (excluded) [N13] 59. 25, 5, 20, 10 WHIP (24) R: 74 (54) SJH M7b5: 1, 3, b5, h7 the major seven flat-five 1, 4, b5, b7 5, 1, b9, 4 M7b5: b5, h7, 1, 3 9, 5, +5, 1 CM7b5: C E Gb B 60. 25, 5, 15, 15 -HIP (23) R: 6+9 (51) M7di 1, b3, b5, h7 diminished major seven 1, 4, b5, 6 5, 1, b9, 3 M7di : b5, h7, 1, b3 b3, +5, 6, 1 CM7di: C Eb Gb B 61. 25, 5, 10, 20 WHIP (26) R: 5+4 (49) SJH 13 1, 3, 6, b7 thirteenth chord 1, 4, b5, +5 5, 1, b9, b3 b5, h7, 1, 9 13: 3, 6, b7, 1 C13: C Bb E A 62. 20, 20, 15, 5 -H-P (22) R: miM7 (64) M7+5 1, 3, +5, h7 major seven aug-five M7+5: 1, 3, +5, h7 +5, 1, 3, 5 h3, +5, 1, b3 1, b9, 4, 6 CM7+5: C E G# B 63. 20, 20, 10, 10 W-I- (7) SJH 7+5 1. 3. +5, b7 seven aug-five 7+5 1, 3, +5, b7 +5, 1, 3, b5 3, +5, 1, 9 9, b5, b7, 1 C7+5: C E G# Bb 64. 20, 20, 5, 15 -H-P (22) R: M7+5 (62) miM7 1, b3, 5, h7 minor major seven 1, 3, +5, 6 +5, 1, 3, 4 3, +5, 1, b9 miM7: b3, 5, h7, 1 CmiM7: C Eb G B 65. 20, 15, 20, 5 -H-P (5) SJH M7 1, 3, 5, h7 major seventh chord M7: 1, 3, 5, h7 +5, 1, b3, h5 4, 6, 1, 3 b9, 4, +5, 1 CM7: C E G B 66. 20, 15, 15, 10 W-IP (21) R: mi6 (69) SJH 7 1, 3, 5, h7 the seventh chord 7: 1, 3, 5, b7 +5, 1, b3, b5 4, 6, 1, b3 9, b5, 6, 1 C7: C E G Bb 67. 20, 15, 10, 15 W--P (8) SJH 6 1, 3, 5, 6 the six chord mi7 1, b3, 5, b7 minor seventh chord 6: 1, 3, 5, 6 +5, 1, b3, 4 4, 6, 1, 9 mi7: b3, 5, b7, 1 C6: C E G A Ami7: A C E G 68. 20, 10, 20, 10 W-I- (6) SJH 7b5 1, 3, b5, b7 the seven flat-five chord 7b5: 1, 3, b5, b7 +5, 1, 9, b5 7b5: b5, b7, 1, 3 9, b5, +5, 1 C7b5: C E Gb Bb Gb7b5: Gb Bb C E 69. 20, 10, 15, 15 W-IP (21) R: 7 (66) SJH mi6 1, b3. 5, 6 the minor six chord dim7 1, b3, b5, b7 diminished seventh chord mi6: 1, b3, 5, 6 6, 1, 3, b5 4, +5, 1, 9 dim7: b3, b5, b7, 1 Cmi6: C Eb G A Adim7: A C Eb G 70. 15, 15, 15, 15 --I- (13) SJH dim 1, b3, b5, 6 diminished chord dim: 1, b3, b5, 6 6, 1, b3, b5 b5, 6, 1, b3 b3, b5, 6, 1 C dim: C Eb Gb A art@ end of DS (page) CATALOGUE SEQUENCE OF CHORD FORMS Shows catalogue number, derivation number (), chord symbol, chord parts, and chord name. 1.(1) 0 silence 2.(2) 60cl 1 unison or octave 3.(3) 55cl 1,h7 major seven or minor second 4.(4) 50cl 1,b7 = 9,1 minor seventh or major second. 5.(5) 45cl 1,6 = b3,1 major sixth or minor third 6.(6) 40cl 1,3 = 3,+5 major third or minor sixth 7.(7) 35cl 1,5 perfect fifth or perfect fourth 8.(8) 30cl 1,b5 diminished fifth, or tritone 9.(25) maj 1,3,5 the major chord ---P R14 10.(24) 95 1,5,9 the nine-five W--P R1 11.(13) 93=97T W--- R2 1,3,9 = b7,9,1 the nine-three 1,b7,9 = 9,1,3 the nine-seven triad 12.(16) 96T=75 W--P R15 1,6,9 = b7,5,1 the nine-six triad 1,5,b7 = 9,6,1 the seven-five 13.(18) M73 1,3,h7 major seven-three -H-P R16 14.(15) M75 1,5,h7 major seven-five -H-P R16 15.(26) 63=min ---P R14 1,3,6 = b3,5,1 the six-three 1,b3,5 = 6,1,3 the minor chord 16.(10) 9b3 1,b3,9 nine flat three WH-- R17 17.(14) miM 1,b3,h7 minor-major triad -H-- R18 18.(17) 65=7b3 W--P R15 1,5,6 = b3,b7,1 the six-five 1,b3,b7 = 6,1,5 the seven flat-three 19.(22) 73 1,3,b7 the seven-three W-I- R19 20.(11) 9M 1,h7,9 nine maj. seven triad WH-- R17 21.(21) di 1,b3,b5 the diminished triad --I- R3 22.(27) aug 1,3,+5 the augmented chord ---- R4 23.(12) 3+9T 1,b3,3 three aug-nine triad -H-- R18 24.(19) MbT 1,b5,h7 maj.seven flat five triad -HIP R20 25.(20) 7bT 1,b5,b7 seven flat five triad W-I- R19 26.(23) 5+4- 1,+4,5 five aug-four triad -HIP R20 27.(66) 7 1,3,5,b7 the seventh chord W-IP R21 28.(65) M7 1,3,5,h7 major seventh chord -H-P R5 29.(64) miM7 1,b3,5,h7 minor-major seventh -H-P R22 30.(60) M7di 1,b3,b5,h7 diminished major seven -HIP R23 31.(68) 7b5 1,3,b5,b7 = b5,b7,1,3 W-I- R6 the seven flat-five chord 32.(59) M7b5 1,3,b5,h7 major seven flat-five WHIP R24 33.(63) 7+5 1,3,+5,b7 the seven aug-five W-I- R7 34.(62) M7+5 1,3,+5,h7 major seven aug-five -H-P R22 35.(67) 6=mi7 W--P R8 1,3,5,6 = b3,5,b7,1 the six chord 1,b3,5,b7 = 6,1,3,5 minor seventh chord 36.(69) mi6=dim7 W-IP R21 1,b3,5,6 = b3,b5,b7,1 the minor six chord 1,b3,b5,b7=6,1,b3,5 diminished seventh chord 37.(50) 11 1,3,4,5 the eleventh chord WH-P R25 38.(54) 74 1,3,4,b7 the seven-four WHIP R24 39.(61) 13 1,3,6,b7 thirteenth chord WHIP R26 40.(46) mi13 1,b3,6,b7 minor thirteenth chord WHIP R27 41.(40) 13b5 1,b5,6,b7 thirteen flat-five WHI- R28 42.(49) 5+4 1,3,b5,h5 the five aug-four WHIP R26 43.(51) 6+9=m5+4 -HIP R23 1,b3,3,6 = b3,b5,h5,1 the six aug-nine 1,b3,b5,h5 = 6,1,b3,3 minor five aug-four 44.(53) 3+9 1,b3,h3,5 the three aug-nine -H-P R9 45.(41) 7+9 1,b3,h3,b7 seven aug-nine WHIP R29 46.(56) 9 1,3,5,9 the ninth chord W--P R30 47.(57) M76=mi9 WH-P R25 1,3,6,h7=b3,5,1,9 the major seven-six 1,b3,5,9=6,1,3,h7 minor ninth chord 48.(43) miM6=dim9 WHI- R28 1,b3,6,h7=b3,b5,1,9 minor-major seven-six 1,b3,b5,9=6,1,b3,h7 diminished ninth chord 49.(52) 96 1,3,6,9 the nine-six W--P R30 50.(39) mi96 1,b3,6,9 minor nine-six chord WHIP R27 51.(55) 965 1,5,6,9 the nine-six five W--P R10 52.(45) 96+5 1,+5,6,9 augmented nine-six WHIP R29 53.(34) 96M7 1,6,h7,9 nine-six maj. seven WHIP R11 54.(36) 9M7 1,3,h7,9 nine maj. seven chord WH-P R31 55.(42) 97 1,3,b7,9 nine-seven chord W-I- R12 56.(33) 94=mi97 WH-P R31 1,3,4,9 = b7,9,b3,1 the nine-four 1,b3,b7,9=9,4,1,3 the minor nine-seven 57.(70) dim 1,b3,b5,6 diminished chord --I- R13 58.(9) N01 50,5,5 the first excluded form 59.(28) N02 45,5,5,5 65.(37) N08 35,5,5,15 60.(29) N03 40,10,5,5 66.(38) N09 30,20,5,5 61.(30) N04 40,5,10,5 67.(44) N10 30,5,20,5 62 (31) N05 40,5,5,10 68.(47) N11 30,5,5,20 63.(32) N06 35,15,5,5 69.(48) N12 25,25,5,5 64.(35) N07 35,5,15,5 70.(58) N13 25,5,25,5 art@ cat seq (page) WHIP LIST How shall we describe the sound qualities of a chord form? Words seem useless. We can, however, specify the intervals it contains. For example, does it have a tritone or not? Almost all forms have major and minor intervals. (Only the 965 and 95 do not.) Since we are trying to make distinctions among the forms, we ignore what they have in common. Thus, we have the "WHIP list". The four letters stand for whole note, half note, tritone and perfect interval. If a form has any of these intervals, its WHIP list word includes the letter for that interval. So a chord will have a derivation number, a catalogue number, and now, an "R number", which is its position on the WHIP list. Retorts determine creation of the WHIP list since a form and its retort go on the same line. (They have the same intervals.) The first thirteen entries are for forms that do not have a retort, and entries 14 thru 31 are for those that do. WHIP list for all forms (31) .......................................................... W--P R1 C10 D24 95 W--- R2 C11 D13 93=97T --I- R3 C21 D21 di ---- R4 C22 D27 aug -H-P R5 C28 D65 M7 W-I- R6 C31 D68 7b5 W-I- R7 C33 D63 7+5 W--P R8 C35 D67 6=mi7 -H-P R9 C44 D53 3+9 W--P R10 C51 D55 965 WH-P R11 C53 D34 96M7 W-I- R12 C55 D42 97 --I- R13 C57 D70 dim ---P R14 C9 D25 maj C15 D26 63=min W--P R15 C12 D16 96T=75 C18 D17 65=7b3 -H-P R16 C13 D18 M73 C14 D15 M75 WH-- R17 C16 D10 9b3 C20 D11 9M -H-- R18 C17 D14 miM C23 D12 3+9T W-I- R19 C19 D22 73 C25 D20 7bT -HIP R20 C24 D19 MbT C26 D23 5+4T W-IP R21 C27 D66 7 C36 D69 mi6=dim7 -H-P R22 C29 D64 miM7 C34 D62 M7+5 -HIP R23 C30 D60 M7di C43 D51 6+9=m5+4 WHIP R24 C32 D59 M7b5 C38 D54 74 WH-P R25 C37 D50 11 C47 D57 M76=mi9 WHIP R26 C39 D61 13 C42 D49 5+4 WHIP R27 C40 D46 mi13 C50 D39 mi96 WHI- R28 C41 D40 13b5 C48 D43 miM6=dim9 WHIP R29 C45 D41 7+9 C52 D45 96+5 W--P R30 C46 D56 9 C49 D52 96 WH-P R31 C54 D36 9M7 C56 D33 94=mi97 "W" = whole step, "H" = half step, "I" = tritone, and "P" = perfect fourth or perfect fifth .......................................................... WHIP list for all triads (11) .......................................................... W--P R1 C10 D24 95 W--- R2 C11 D13 93=97T --I- R3 C21 D21 di ---- R4 C22 D27 aug ---P R14 C9 D25 maj C15 D26 63=min W--P R15 C12 D16 96T=75 C18 D17 65=7b3 -H-P R16 C13 D18 M73 C14 D15 M75 WH-- R17 C16 D10 9b3 C20 D11 9M -H-- R18 C17 D14 miM C23 D12 3+9T W-I- R19 C19 D22 73 C25 D20 7bT -HIP R20 C24 D19 MbT C26 D23 5+4T .......................................................... WHIP list for all tetrades (20) .......................................................... -H-P R5 C28 D65 M7 W-I- R6 C31 D68 7b5 W-I- R7 C33 D63 7+5 W--P R8 C35 D67 6=mi7 -H-P R9 C44 D53 3+9 W--P R10 C51 D55 965 WH-P R11 C53 D34 96M7 W-I- R12 C55 D42 97 --I- R13 C57 D70 dim W-IP R21 C27 D66 7 C36 D69 mi6=dim7 -H-P R22 C29 D64 miM7 C34 D62 M7+5 -HIP R23 C30 D60 M7di C43 D51 6+9=m5+4 WHIP R24 C32 D59 M7b5 C38 D54 74 WH-P R25 C37 D50 11 C47 D57 M76=mi9 WHIP R26 C39 D61 13 C42 D49 5+4 WHIP R27 C40 D46 mi13 C50 D39 mi96 WHI- R28 C41 D40 13b5 C48 D43 miM6=dim9 WHIP R29 C45 D41 7+9 C52 D45 96+5 W--P R30 C46 D56 9 C49 D52 96 WH-P R31 C54 D36 9M7 C56 D33 94=mi97 .......................................................... art@ for whip list (page) EXCLUDED FORMS The excluded forms have so few inversions that it's not worth referring to them as chord forms. Since we don't want chords spanning more than two octaves, and intervals of 5cl can only be expressed as 55cl, forms with two 5cl in a row have no practical inversions. D9. N01 50, 5, 5 Too big. D28. N02 45,5,5,5 D29 N03 40,10,5,5 Too big. D30. N04 40,5,10,5 D31. N05 40,5,5,10 Too big. D32. N06 35,15,5,5 Too big. D35 N07 35,5,15,5 D37. N08 35,5,5,15 Too big. D38. N09 30,20,5,5 Too big. D44. N1O 30,5,20,5 D47. N11 30,5,5,20 Too big. D48. N12 25,25,5,5 Too big. D58. N13 25,5.25,5 Inversions possible for the remaining five excluded forms are derived from overlapping the major seventh intervals. C Db B C = 5,50,5 = N01 = not playable C D B C# = 10,45,10 = N02 = 2(42n 31n) C Eb B D = 15,40,15 = N04 = 3(32n 21n) C E B D# = 20,35,20 = N07 = 4(22n 11n) C F B E = 25,30,25 = N10 = 4(23n 12n) C Gb B F = 30,25,35 = N13 = 4(2n4 13n) C G B F# = 35,20,35 = N10 = 3(3n2 2n1) C Ab B G = 40,10,40 = N07 = 4(2n2 1n1) C A B G# = 45,10,40 = N04 = 4(2n3 1n2) C Bb B A = 50,5,50 = N02 = 4(2n4 1n3) C B Db C = 55,10,55 = N01 = not playable There are nine useful chords. The names suggest the inversion. For the M9+8, the 1,h7 is below the 9,+8. For the miM9, the sequence of intervals is 1, b3, h7, 9. the major nine aug-eight chord 1. C M9+8 1 9h7b9 C D B C# 2(42n 31n) b7 1 6h7 C D B C# b9b3 1 9 C D B C# h7b9b7 1 C D B C# the minor-major nine chord 2. C miM9 1b3h7 9 C EbB D 3(32n 21n) 6 1+5h7 C EbB D b9 3 1b3 C EbB D b7b9 6 1 C EbB D the major seven aug-nine chord 3. C M7+9 1 3h7b3 C E B D# 4(22n 11n) +5 1 5h7 C E B D# b9 4 1 3 C E B D# 6b9+5 1 C E B D# the major eleven chord 4. C M11 1 4h7 3 C F B E 4(23n 12n) 5 1b5h7 C F B E b9b5 1 4 C F B E +5b9 5 1 C F B E the major flat-five four 5. C Mb54 1b5h7 4 C F#B F 4(24n 13n) b5 1 4h7 C F#B F b9 5 1b5 C F#B F 5b9b5 1 C F#B F the eleven major seven chord 6. 1 5h7b5 C G B F# G 11M 4 1 3h7 C G B F# 3(3n2 2n1) b9+5 1 5 C G B F# b5b9 4 1 C G B F# the aug nine major seven chord 7. 1+5h7 5 C AbB G Ab+9M7 3 1b3h7 C AbB G 4(2n2 1n1) b9 6 1+5 C AbB G 4b9 3 1 C AbB G the minor nine major seven chord 8. 1 6h7+5 C A B Ab A mi9M b3 1 9h7 C A B Ab 4(2n3 1n2) b9b7 1 6 C A B Ab 3b9b3 1 C A B Ab the nine aug-8 major seven chord 9. 1b7h7 6 C BbB A Bb9+8M 9 1b9h7 C BbB A 4(2n4 1n3) b9h7 1b7 C BbB A b3b9 9 1 C BbB A (file: exclud2.6A) For the M7+9, the 1,h7 is below the 3,+9. For the M11, the 1,h7 is below the 4,3. For the Mb54, the 1,h7 is below the b5,4. For the 11M, the 4,3 is below the 1,h7. For the +9M7, the 3,+9 is below the 1,h7. For the mi9M, the sequence of intervals is b3,1,9,h7. For the 9+8M, the 9,+9 is below the 1,h7. The M9+8 and 9+8M are the only exceptions to our prohibition of 55cl or 5cl. And other rules for naming chords do not apply to the inversions of excluded forms. (page) art@ top of pt 2 PART 2 FOUR-VOICE HARMONY It's natural that guitar players would think differently about harmony than piano players do. For a guitarist, a chord is a tablature, and a tablature is something to be learned in the hand. Performers know a chord by how it feels -- a sensation more vivid with guitar than piano. Having read the first part of my book, my readers probably expect us to continue with forms of five and then six different pitches. But I have found that it is surprisingly difficult to pair up chords of more than four pitches so that most pitches change from one to the other. Say you think this chord sounds different than the chord that came before. But how different? The measure of this I call "chord contrast". And the basic measure of contrast is the number of notes that change. That's why for me, essential jazz harmony means chords of four pitches. Because they are capable of the greatest contrast. The fewer the pitches that sound at once in a piece of music, the greater the emphasis on melody. Therefore, I begin with chords of four pitches, because such music has the greatest harmonic significance. art@ cu/4-part score, inked A "voice" refers to choral music, and means that a note in the first chord changes to the corresponding note with melodic expression. The four voices of choral music are called the "bass" and "tenor" (and describe male voices), and the "alto" and "soprano" (which describe female voices). These names are used for instruments also. "Voice leading" is how Jazz brings melody to harmony. It basically means the voices move by a half step or whole step when they can. In a band, people won't always hear the separate strings of a guitar changing elegantly. There's only the one big sound. But needed or not, voiced chords sound better and are more fun to play. VOICING IN PRACTICE Here's how to figure out voicing for a pair of chords. Write the letter names of the notes of each chord side by side, and look at where the half-steps are. Draw a line connecting these notes. Next, do the same for the whole steps. Really the easiest, most versatile way to look at how two chords can fit together is a paper construction such that two clock diagrams pivot at their center. In the appendix, you'll find clock diagrams that can be cut out for this purpose. The smaller one rotates inside the larger. Musicians don't usually do this sort of thing. More likely, a musician would simply look at a piano keyboard, and observing which notes are close together, come up with the change. Another method is to simply look at how the notes could be written on the staff. But we'll start with handwriting. Write the letters of two chords, and observe how the voices can move. To illustrate using triads, suppose we had a chord of the pitches C, E and B, and we wanted to go to a chord of the pitches C, F and Bb. They both have a C, the E steps up to the F, and the B steps down to the Bb -- contrary motion. 1st chord, 2nd chord, CM73 Bb95 ------ ------ B Bb E F C C But in many cases, there is no clear-cut solution. A SERIES OF CHORDS The possibilities for chord change seem limitless. For each possible form pair, there are eleven possible changes of root. And then for each interval by which the roots can change, there is each inversion of one form compared to every inversion of the other. But we don't really care about all possible chord changes. What we want are the best chord changes, or, short of that, some good chord changes. The first step to a manageable solution is to limit the number of forms we will consider. And for each form we will select only some of the inversions. When we've got it short enough, we call it a "Series" and give it a name. Next, we limit our interest to only a few root interval jumps, or to only one. Then, seeking maximum chord contrast, we put our chords in pairs. We try for the best combinations by looking at voice leading. The "calling chord", at the top of the paragraph, is compared to the chords that go with it, the "called chords". Such a group of chord inversions is what I call a "precession". The calling chord tablatures have asterisks to make them stand out. I chose the word "precession" because it sounds clearly different than "progression". And to make the point that a musical exercise is not the same as "music", although it might be close. But such a series of chords and their changes is probably still too long to deal with at once. For practice and etc., the musician chooses only a few from the list -- this is the "prime" of the precession. So you can deal with a little piece of it. When you get to know them well enough to have favorites, you are playing the chords of jazz harmony. BASS VOICE INDEX "Series 35" is thirty-five inversions from eleven tetrad chord forms: M7, 6, mi6, 11, 9, mi9, M76, 7, 7b5, 13, and 97. The first seven are the tonic chords. The M76 is enharmonic to the mi9. They are illustrated with guitar tablatures for standard tuning. In standard tuning, the same inversion often has a different tablature depending on which strings are used; this requires another line. So the series is 74 lines long. The inversion number appears after the "#" sign. Enharmonic chord parts are also shown. Series 35, Thirty-Five Chords for Guitar in Standard Tuning ----------------------------------------------------------------- 1. A M7 1 5h7 3 A E AbDb 5(132 2xx) #1 Eb M7 1 5h7 3 EbBbD G 6(x13 23x) #1 F M7 1 5h7 3 F C E A 3(xx1 333) #1 G M7 3 5 1h7 B D G Gb 5(311 x3x) #2 Bb M7 3 5 1h7 D F BbA 3(x31 1x3) #2 Eb M7 5 1h7 3 BbEbD G 6(11x 23x) #3 G M7 5 1h7 3 D G GbB 5(x11 x33) #3 2. A 6 1 3 6 5 A DbGbE 4(211 x2x #4 b3 5 1 b7 D 6 1 3 6 5 D GbB A 4(x21 1x2) #4 b3 5 1 b7 F 6 3 6 5 1 A D C F 5(11x 12x) #5 5 1 b7 b3 A 6 3 6 5 1 DbGbE A 4(x11 x22) #5 5 1 b7 b3 Eb 6 5 3 6 1 BbG C Eb 4(3x2 21x) #6 b7 5 1 b3 G 6 5 3 6 1 D B E G 3(x3x 231) #6 b7 5 1 b3 Ab 6 6 1 5 3 F AbEbC 6(x31 3x3) #7 1 b3 b7 5 D 6 6 1 5 3 B D A Gb 5(313 x3x) #7 1 b3 b7 5 3. A mi6 1 6b3 5 A GbC E 4(2x1 22x) #8 b3 1 b5 b7 Eb mi6 1 6b3 5 EbC GbBb 5(x2x 132) #8 b3 1 b5 b7 F mi6 b3 6 5 1 AbD C F 4(12x 23x) #9 b5 1 b7 b3 A mi6 b3 6 5 1 C GbE A 3(x12 x33) #9 b5 1 b7 b3 F mi6 5b3 6 1 C AbD F 6(3x1 21x) #10 b7 b5 1 b3 G mi6 5b3 6 1 D BbE G 3(x3x 131) #10 b7 b5 1 b3 C mi6 6 5 1b3 A G C Eb 4(2x2 21x) #11 1 b7 b3 b5 Ab mi6 6 5 1b3 F EbAbB 7(x2x 231) #11 1 b7 b3 b5 4. C 11 1 4 3 5 C F E G 8(11x 21x) #12 D 11 1 4 3 5 D G GbA 5(x11 x31) #12 Eb 11 4 3 5 1 AbG BbEb 3(2x3 12x) #13 G 11 4 3 5 1 C B D G 3(x1x 211) #13 E 11 5 1 4 3 B E A Ab 7(111 x3x) #14 G 11 5 1 4 3 D G C B 5(x11 1x3) #14 5. C 9 1 3 9 5 C E D G 7(21x 12x) #15 Eb 9 1 3 9 5 EbG F Bb 5(x21 x22) #15 G 9 3 9 5 1 B A D G 7(1x1 12x) #16 Ab 9 3 9 5 1 C BbEbAb 3(x1x 122) #16 D 9 5 1 3 9 A D GbE 4(221 x2x) #17 F 9 5 1 3 9 C F A G 2(x22 1x2) #17 A 9 9 1 3 5 B A DbE 5(3x3 21x) #18 C 9 9 1 3 5 D C E G 3(x3x 331) #18 6. D mi9 1b3 9 5 D F E A 8(31x 23x) #19 6 1 h7 3 E mi9 1b3 9 5 E G GbB 5(x31 x33) #19 6 1 h7 3 F mi9 b3 9 5 1 AbG C F 4(1x2 23x) #20 1 h7 3 6 A mi9 b3 9 5 1 C B E A 3(x1x 233) #20 1 h7 3 6 F mi9 5 1b3 9 C F AbG 6(331 x3x) #21 3 6 1 h7 A mi9 5 1b3 9 E A C B 5(x33 1x3) #21 3 6 1 h7 7. F M76 6 1h7 3 D F E A 8(31x 23x) #19 1 b3 9 5 G M76 6 1h7 3 E G GbB 5(x31 x33) #19 1 b3 9 5 Ab M76 1h7 3 6 AbG C F 4(1x2 23x) #20 b3 9 5 1 C M76 1h7 3 6 C B E A 3(x1x 233) #20 b3 9 5 1 Ab M76 3 6 1h7 C F AbG 6(331 x3x) #21 5 1 b3 9 C M76 3 6 1h7 E A C B 5(x33 1x3) #21 5 1 b3 9 8. C 7 1 3b7 5 C E BbG 7(212 x2x) #22 E 7 1 3b7 5 E AbD B 6(x21 2x2) #22 A 7 3 5 1b7 DbE A G 7(311 x2x) #23 C 7 3 5 1b7 E G C Bb 5(x31 1x2) #23 G 7 5 3b7 1 D B F G 8(3x2 31x) #24 G 7 5 3b7 1 D B F G 3(x3x 241) #24 B 7 b7 3 1 5 A EbB Gb 4(23x 14x) #25 Eb 7 b7 3 1 5 DbG EbBb 4(x12 x13) #25 9. D 7b5 1 3b7b5 D GbC Ab 9(212 x1x) #26 D 7b5 1 3b7b5 D GbC Ab 4(x21 2x1) #26 Ab 7b5 3b7b5 1 C GbD Ab 7(23x 13x) #27 C 7b5 3b7b5 1 E BbGbC 7(x12 x12) #27 10. Bb 13 1b7 3 6 BbAbD G 6(1x1 23x) #28 D 13 1b7 3 6 D C GbB 5(x1x 133) #28 Bb 13 3b7 1 6 D AbBbG 8(341 x1x) #29 D 13 3b7 1 6 GbC D B 7(x34 1x1) #29 D 13 b7 6 1 3 C B D Gb 7(2x3 11x) #30 F 13 b7 6 1 3 EbD F A 5(x2x 321) #30 11. G 97 1b7 3 9 G F B A 3(1x1 2x3) #31 A 97 1 3 9b7 A DbB G 3(32x 2x1) #32 E 97 3b7 9 1 AbD GbE 4(121 x2x) #33 B 97 3b7 9 1 EbA DbB 6(x12 1x2) #33 C 97 b7 3 9 1 BbE D C 6(12x 2x3) #34 A 97 9 1 3b7 B A DbG 6(2x2 13x) #35 A 97 9 1 3b7 B A DbG 2(x1x 112) #35 (file: s35_6s.6S) -------------------------------------------------------- A variety of roots is used because it would be tiresome otherwise. This is the "series list"; when these chords appear subsequently, they will keep the same root. The letter name helps us remember the chord. How to combine these into progressions? A straight-forward technique for tetrades is the "bass voice index". The chords of a series that have the same chord part in the bass voice are listed together. Chords having the same chord part for the same bass note have the same root. So they can possibly be substituted for each other. Simply playing the chords from top to bottom on a bass voice index is good practice because you become aware of the chord parts. Fingering is shown by the numbers with colons. Series 35, bass voice index ---------------------------------------------------------------- 1. A M7 1 5h7 3 A E G#C# 5(132 2xx) #1 1:4:2:3 2. Eb M7 1 5h7 3 EbBbD G 6(x13 23x) #1 1:3:2:4 3. F M7 1 5h7 3 F C E A 3(xx1 333) #1 1:4:4:4 4. A 6 1 3 6 5 A C#F#E 4(211 x2x) #4 2:1:1:3 5. D 6 1 3 6 5 D F#B A 4(x21 1x2) #4 2:1:1:3 6. A mi6 1 6b3 5 A F#C E 4(2x1 22x) #8 2:1:3:4 7. Eb mi6 1 6b3 5 EbC GbBb 5(x2x 132) #8 2:1:4:3 8. C 11 1 4 3 5 C F E G 8(11x 21x) #12 1:2:4:3 9. D 11 1 4 3 5 D G F#A 5(x11 x31) #12 1:1:4:1 10. C 9 1 3 9 5 C E D G 7(21x 12x) #15 3:1:2:4 11. Eb 9 1 3 9 5 EbG F Bb 5(x21 x22) #15 2:1:3:4 12. D mi9 1b3 9 5 D F E A 8(31x 23x) #19 3:1:2:4 13. E mi9 1b3 9 5 E G F#B 5(x31 x33) #19 2:1:3:4 14. Ab M76 1h7 3 6 AbG C F 4(1x2 23x) #20 1:2:3:4 15. C M76 1h7 3 6 C B E A 3(x1x 233) #20 1:2:3:4 16. C 7 1 3b7 5 C E BbG 7(212 x2x) #22 2:1:3:4 17. E 7 1 3b7 5 E G#D B 6(x21 2x2) #22 2:1:3:4 18. D 7b5 1 3b7b5 D F#C G# 9(212 x1x) #26 3:1:4:2 19. D 7b5 1 3b7b5 D F#C G# 4(x21 2x1) #26 3:1:4:2 20. Bb 13 1b7 3 6 BbAbD G 6(1x1 23x) #28 1:1:2:4 21. D 13 1b7 3 6 D C F#B 5(x1x 133) #28 1:1:3:4 22. G 97 1b7 3 9 G F B A 3(1x1 2x3) #31 1:1:2:4 23. A 97 1 3 9b7 A C#B G 3(32x 2x1) #32 4:2:3:1 24. A 9 9 1 3 5 B A C#E 5(3x3 21x) #18 3:4:2:1 25. C 9 9 1 3 5 D C E G 3(x3x 331) #18 2:3:4:1 26. A 97 9 1 3b7 B A C#G 6(2x2 13x) #35 2:3:1:4 27. A 97 9 1 3b7 B A C#G 2(x1x 112) #35 1:2:3:4 28. F mi6 b3 6 5 1 AbD C F 4(12x 23x) #9 1:2:3:4 29. A mi6 b3 6 5 1 C GbE A 3(x12 x33) #9 1:2:3:4 30. F mi9 b3 9 5 1 AbG C F 4(1x2 23x) #20 1:2:3:4 31. A mi9 b3 9 5 1 C B E A 3(x1x 233) #20 1:2:3:4 32. A 7 3 5 1b7 C#E A G 7(311 x2x) #23 4:1:1:2 33. C 7 3 5 1b7 E G C Bb 5(x31 1x2) #23 4:1:1:2 34. G 9 3 9 5 1 B A D G 7(1x1 12x) #16 1:2:3:4 35. Ab 9 3 9 5 1 C BbEbAb 3(x1x 122) #16 1:2:3:4 36. Ab 7b5 3b7b5 1 C GbD Ab 7(23x 13x) #27 2:3:1:4 37. C 7b5 3b7b5 1 E BbGbC 7(x12 x12) #27 1:3:2:4 38. G M7 3 5 1h7 B D G F# 5(311 x3x) #2 3:1:1:4 39. Bb M7 3 5 1h7 D F BbA 3(x31 1x3) #2 3:1:1:4 40. Bb 13 3b7 1 6 D AbBbG 8(341 x1x) #29 3:4:1:1 41. D 13 3b7 1 6 F#C D B 7(x34 1x1) #29 3:4:1:1 42. Ab M76 3 6 1h7 C F AbG 6(331 x3x) #21 2:3:1:4 43. C M76 3 6 1h7 E A C B 5(x33 1x3) #21 2:3:1:4 44. E 97 3b7 9 1 G#D F#E 4(121 x2x) #33 1:3:2:4 45. B 97 3b7 9 1 D#A C#B 6(x12 1x2) #33 1:3:2:4 46. F 6 3 6 5 1 A D C F 5(11x 12x) #5 1:2:3:4 47. A 6 3 6 5 1 C#F#E A 4(x11 x22) #5 1:2:3:4 48. Eb 11 4 3 5 1 AbG BbEb 3(2x3 12x) #13 2:4:1:3 49. G 11 4 3 5 1 C B D G 3(x1x 211) #13 1:4:2:3 50. F mi6 5b3 6 1 C AbD F 6(3x1 21x) #10 4:1:2:1 51. G mi6 5b3 6 1 D BbE G 3(x3x 131) #10 3:1:4:1 52. F mi9 5 1b3 9 C F AbG 6(331 x3x) #21 2:3:1:4 53. A mi9 5 1b3 9 E A C B 5(x33 1x3) #21 2:3:1:4 54. Eb M7 5 1h7 3 BbEbD G 6(11x 23x) #3 1:1:2:4 55. G M7 5 1h7 3 D G F#B 5(x11 x33) #3 1:1:3:4 56. D 9 5 1 3 9 A D F#E 4(221 x2x) #17 2:3:1:4 57. F 9 5 1 3 9 C F A G 2(x22 1x2) #17 2:3:1:4 58. Eb 6 5 3 6 1 BbG C Eb 4(3x2 21x) #6 4:2:3:1 59. G 6 5 3 6 1 D B E G 3(x3x 231) #6 3:2:4:1 60. E 11 5 1 4 3 B E A G# 7(111 x3x) #14 1:1:1:4 61. G 11 5 1 4 3 D G C B 5(x11 1x3) #14 1:1:1:4 62. G 7 5 3b7 1 D B F G 8(3x2 31x) #24 3:2:4:1 63. G 7 5 3b7 1 D B F G 3(x3x 241) #24 3:2:4:1 64. Ab 6 6 1 5 3 F AbEbC 6(x31 3x3) #7 2:1:3:4 65. D 6 6 1 5 3 B D A F# 5(313 x3x) #7 2:1:3:4 66. C mi6 6 5 1b3 A G C Eb 4(2x2 21x) #11 2:3:4:1 67. Ab mi6 6 5 1b3 F EbAbB 7(x2x 231) #11 2:3:4:1 68. F M76 6 1h7 3 D F E A 8(31x 23x) #19 3:1:2:4 69. G M76 6 1h7 3 E G F#B 5(x31 x33) #19 2:1:3:4 70. D 13 b7 6 1 3 C B D F# 7(2x3 11x) #30 2:3:1:1 71. F 13 b7 6 1 3 EbD F A 5(x2x 321) #30 2:4:3:1 72. C 97 b7 3 9 1 BbE D C 6(12x 2x3) #34 1:2:3:4 73. B 7 b7 3 1 5 A D#B F# 4(23x 14x) #25 2:3:1:4 74. Eb 7 b7 3 1 5 DbG EbBb 4(x12 x13) #25 1:3:2:4 (file: s35bv_6s.6S) ---------------------------------------------------------------- Now suppose we want to create a progression of the tonic to the subdominant in the key of C, and the first bass note is "C". Then the first chord will have a "1" in the bass and the second chord will have a "5" in the bass (because the fifth of F is C). Looking at the bass voice index, the first chord could be any of the inversions from lines 1 to 23, and second chord could be any of the inversions from lines 50 to 63. In this way, 3-chord harmony can be expressed. The chord part of the bass is determined by the tonic, subdominant or dominant major triads. Then a jazz chord from the index can be substituted for them. The same technique would apply to the melody voice, but harmonizing a melody with tetrades is unwieldy. Usually for harmony, the bass is the most important voice, because its overtones interact with all the notes above it. A workable approach to start with a bass line. Harmonize each note with one of the major triads of 3-chord harmony. For notes not in the major scale, play the major chord three ways on it, and pick the one you like. Then, using a bass voice index, replace the simple triads with Jazz chords. fig@ harmonize the major scale with major triads With the bass voice index, we have a wide choice of chords. Progressions will sound OK with this approach. But there's usually no voice leading, and some pairs have more than one pitch in common. How can we find the best chord changes? SUBSTITUTE AND CADENCE The idea of "substitute chords" is an old jazz tradition. They add color and variation to simple harmony by using jazz chords to express the same tonality. A "cadence" is another word for chord change, but it also suggests a strong change. Whereas a substitute extends the tonality, a cadence changes it. But whether a pair of chords sounds like a cadence or substitution depends on the composition -- on how the change comes across in performance. It's not necessarily a question of harmony at all. So I prefer to focus more on the concept of chord contrast. What we are trying to accomplish is a musical phrase of 4-pitch chords. These chord pairs would more often be extending a tonality, and so could be thought of as substitutes. And the end of the phrase would typically have a cadence. In any case, a musical phrase stays in one key. A progression is as strong as the contrast of its changes. A composer sometimes wants high contrast and sometimes not. But the question for us is: How to have a maximum of chord contrast? CHORD CONTRAST The most clear-cut measure of chord contrast is how many notes change. A pair of chords with only one voice changing has little contrast, and a pair with all but one voice changing has high contrast. There are eight pitches in a pair of tetrades -- a choice of eight out of twelve. It's surprisingly seldom that a tetrad pair has no pitches in common. So I call it "high contrast" when one or no voices change. A second factor contributing to chord contrast is a variation of chord part between the two chords. Simply put, contrast is decreased if the same voice is the root of both chords (or if a "1" is paired to a "6"). This is why Jazz chords that sound good together may also sound good when one of them is raised or lowered; the contrast of chord parts persists no matter what the change of roots. Parallel Change Parallel change, or "parallel movement" is simply achieved, for example, by moving every note in a chord a half step down. A parallel change is typically a cadence, because the change of root is clear. Going up a half step is just as good. And so are other intervals, except that on certain jumps, notes will overlap. If the parallel jump matches an interval within the form, not all the notes will change. When the voices move independently, it is called "contrapuntal" movement. Parallel movement can scarcely exist except in a context of the contrapuntal. With parallel movement, there is no change of form. Parallel changes are another old tradition of Jazz, and of folk music, and one not quite normal to the classical tradition. VOICE LEADING The basic idea of voice leading is that the voices move in small jumps. The origins are the harmonies created by medieval church choirs. It is difficult to sing a melody that jumps by a seventh or a ninth. Such a change of pitch is better expressed as a whole step or half step. Singing a tritone is also difficult. Most singers could accomplish these, but with some unsteadiness; the musical effect would be less definite, less assured. Therefore we say, voice leading increases chord contrast. The other basis of classical counterpoint is that two voices a perfect interval apart should not move to the same perfect interval in the other chord. Parallel fifths and fourths were perceived as lacking variety. Although it would be impractical to exclude parallel perfect jumps from 4-part Jazz harmony, we still recognize that a chord change sounds better when a voice proceeds by a half or whole step, rather than jumping a seventh or ninth. Contrast is also decreased when a voice jumps a tritone. Of course two four-pitch forms often have a pitch that is a half step from either of two pitches of the other chord. In the inversion, it should take a whole step or half step to one of them. Voiced harmony is especially strong with half-steps. And contrast is further enhanced by "contrary motion", when one voice goes up as another goes down. And this is even more effective with stepwise movement. Here are three or four subdominants for each of the Series 35 tonic chords, chosen this time for contrast and voice leading. In some cases the root is bVII instead of the IV. The fifth of Bb is F (in the key of C), and if the F goes to the third of C, it has the effect of a subdominant even though the root is Bb. Subdominants of Series 35 --------------------------------------------------------------- 1. A M7 1 5h7 3 A E G#C# 5(132 2**) #1 D 6 5 3 6 1 A F#B D 3(3x2 21x) #6 b7 5 1 b3 D mi6 5b3 6 1 A F B D 3(3x1 21x) #10 b7 b5 1 b3 G 6 3 6 1 5 B E G D 5(331 3xx) 2. Eb M7 1 5h7 3 EbBbD G 6(*13 23*) #1 Ab 6 5 3 6 1 EbC F Ab 4(x3x 231) #6 b7 5 1 b3 Ab mi6 5b3 6 1 EbB F Ab 4(x3x 131) #10 b7 b5 1 b3 Db 6 3 6 1 5 F BbDbAb 6(x33 14x) 3. F M7 1 5h7 3 F C E A 3(**1 333) #1 Bb 6 5 3 6 1 F D G Bb 6(x3x 231) #6 b7 5 1 b3 Bb mi6 5b3 6 1 F DbG Bb 6(x3x 131) #10 b7 b5 1 b3 Bb 9 5 9 3 1 F C D Bb 3(xx1 314) Eb 97 9b7 1 3 F DbEbG 8(x14 11x) 4. G M7 3 5 1h7 B D G F# 5(311 *3*) #2 C 9 1 9 5 3 C D G E 5(411 x1x) C 97 b7 9 1 3 BbD C E 5(21x 11x) F 7 5b7 3 1 C EbA F 6(312 x1x) F 97 3b7 9 1 A EbG F 5(121 x2x) 5. Bb M7 3 5 1h7 D F BbA 3(*31 1*3) #2 Eb 9 1 9 5 3 EbF BbG 3(x41 1x1) Eb 97 b7 9 1 3 DbF EbG 3(x21 x21) Ab 7 5b7 3 1 EbGbC Ab 4(x31 2x1) Ab 97 3b7 9 1 C GbBbAb 3(x12 1x2) 6. Eb M7 5 1h7 3 BbEbD G 6(11* 23*) #3 Ab 9 9 5 3 1 BbEbC Ab 4(33x 2x1) Ab 7b5 3 1b5b7 C AbD Gb 6(3x1 22x) Ab 97 9 1 3b7 BbAbC Gb 5(2x2 13x) #35 7. G M7 5 1h7 3 D G F#B 5(*11 *33) #3 C 9 9 5 3 1 D G E C 5(x11 x14) C 7b5 3 1b5b7 E C GbBb 5(x3x 132) C 97 9 1 3b7 D C E Bb 5(x1x 112) #35 8. A 6 1 3 6 5 A C#F#E 4(211 *2*) #4 b3 5 1 b7 D 6 5 1 3 6 A D F#B 4(221 1xx) D mi6 5 1 6b3 A D B F 4(22x 13x) D 7 5b7 3 1 A C F#D 3(312 x1x) 9. D 6 1 3 6 5 D GbB A 4(*21 1*2) #4 b3 5 1 b7 G 6 5 1 3 6 D G B E 4(x22 12x) G mi6 5 1 6b3 D G E Bb 5(x11 x12) G 7 5b7 3 1 D F B G 3(x31 2x1) G 97 1b7 3 9 G F B A 3(1x1 2x3) 10. F 6 3 6 5 1 A D C F 5(11* 12*) #5 5 1 b7 b3 Bb 6 1 3 6 5 BbD G F 5(211 x2x) #4 b3 5 1 b7 Bb 7 b7 3 1 5 AbD BbF 3(23x 14x) #25 Bb 97 b7 3 9 1 AbD C Bb 4(12x 2x3) #34 11. A 6 3 6 5 1 C#F#E A 4(*11 *22) #5 5 1 b7 b3 D 6 1 3 6 5 D F#B A 4(x21 1x2) #4 b3 5 1 b7 D 9 1 3 9 5 D F#E A 4(x21 x22) #15 D 7 b7 3 1 5 C F#D A 3(x12 x13) #25 D 97 b7 3 9 1 C F#E D 8(12x 2x3) #34 12. Eb 6 5 3 6 1 BbG C Eb 4(3*2 21*) #6 b7 5 1 b3 Ab 9 9 1 3 5 BbAbC Eb 4(3x3 21x) #18 Ab M76 1h7 3 6 AbG C F 4(1x2 23x) #20 1 h7 3 6 Ab 13 1b7 3 6 AbGbC F 4(1x1 23x) #28 13. G 6 5 3 6 1 D B E G 3(*3* 231) #6 b7 5 1 b3 C 9 9 1 3 5 D C E G 3(x3x 331) #18 C M76 1h7 3 6 C B E A 3(x1x 233) #20 1 h7 3 6 C 13 1b7 3 6 C BbE A 3(x1x 133) #28 14. Ab 6 6 1 5 3 F AbEbC 6(*31 3*3) #7 1 b3 b7 5 Db M76 3 6 1h7 F BbDbC 6(x33 1x3) #21 3 6 1 h7 Db 7 3 5 1b7 F AbDbB 6(x31 1x2) #23 Gb 6 1 3 6 5 GbBbEbDb 8(x21 1x2) Gb 9 1 9 5 3 GbAbDbBb 6(x41 1x1) 15. D 6 6 1 5 3 B D A F# 5(313 *3*) #7 1 b3 b7 5 G M76 3 6 1h7 B E G F# 5(331 x3x) #21 3 6 1 h7 G 7 3 5 1b7 B D G F 5(311 x2x) #23 C 6 1 3 6 5 C E A G 7(211 x2x) C 97 b7 9 1 3 A#D C E 5(21x 11x) 16. A mi6 1 6b3 5 A F#C E 4(2*1 22*) #8 b3 1 b5 b7 D 6 5 3 6 1 A F#B D 3(3x2 21x) #6 b7 5 1 b3 D mi6 5b3 6 1 A F B D 3(3x1 21x) #10 b7 b5 1 b3 G M7 1h7 3 5 G GbB D 3(1x2 21x) G 97 9b7 3 1 A F B G 3(3x1 2x1) 17. Eb mi6 1 6b3 5 EbC GbBb 5(*2* 132) #8 b3 1 b5 b7 Ab 6 5 3 6 1 EbC F Ab 4(x3x 231) #6 b7 5 1 b3 Ab mi6 5b3 6 1 EbB F Ab 4(x3x 131) #10 b7 b5 1 b3 Db M7 1h7 3 5 DbC F Ab 4(x1x 231) Db 13 1b7 3 6 DbB F Bb 4(x1x 133) 18. F mi6 b3 6 5 1 AbD C F 4(12* 23*) #9 b5 1 b7 b3 Eb 6 3 1 6 5 G EbC Bb 3(14x 3x4) Eb 11 4 1 5 3 AbEbBbG 3(24x 1x1) Eb 13 3b7 6 1 G DbC Eb 3(12x 32x) 19. A mi6 b3 6 5 1 C GbE A 3(*12 *33) #9 b5 1 b7 b3 G 9 3 1 5 9 B G D A 7(14x 14x) G mi6 5 1 6b3 D G E Bb 5(x11 x12) G 7 3b7 5 1 B F D G 2(x12 x22) G 13 3b7 6 1 B F E G 2(x12 x42) 20. F mi6 5b3 6 1 C AbD F 6(3*1 21*) #10 b7 b5 1 b3 Bb 11 1 4 3 5 BbEbD F 6(11x 21x) #12 Bb M76 1h7 3 6 BbA D G 6(1x2 23x) #20 b3 9 5 1 Bb 13 1b7 3 6 BbAbD G 6(1x1 23x) #28 21. G mi6 5b3 6 1 D BbE G 3(*3* 131) #10 b7 b5 1 b3 C 11 1 4 3 5 C F E G 3(x11 x31) #12 C M76 1h7 3 6 C B E A 3(x1x 233) #20 b3 9 5 1 C 13 1b7 3 6 C BbE A 3(x1x 133) #28 22. C mi6 6 5 1b3 A G C Eb 4(2*2 21*) #11 1 b7 b3 b5 F M7 3 1 5h7 A F C E 5(14x 11x) F M7 3 1 5h7 A F C E 3(3x1 33x) F mi6 b3 1 5 6 AbF C D 3(2x1 31x) F M76 3 1 6h7 A F D E 5(14x 31x) 23. Ab mi6 6 5 1b3 F EbAbB 7(*2* 231) #11 1 b7 b3 b5 Db mi6 b3 1 5 6 E DbAbBb 6(x2x 141) Db M76 3 1 6h7 F DbBbC 8(x14 x41) Gb 9 1 5 9 3 GbDbAbBb 6(x4x 141) Gb 13 b7 6 1 3 E EbGbBb 6(x2x 321) 24. C 11 1 4 3 5 C F E G 8(11* 21*) #12 F 6 5 1 6 3 C F D A 5(44x 3x1) F M76 6 1h7 3 D F E A 8(31x 23x) #19 F 7 5 1b7 3 C F EbA 8(11x 13x) F 97 3 1b7 9 A F EbG 5(14x 44x) 25. D 11 1 4 3 5 D G F#A 5(*11 *31) #12 G 6 5 1 6 3 D G E B 5(x11 x13) G M76 6 1h7 3 E G F#B 5(x31 x33) #19 G 7 5 1b7 3 D G F B 5(x11 x23) G 97 3 1b7 9 B G F A 5(3x1 x21) 26. Eb 11 4 3 5 1 AbG BbEb 3(2*3 12*) #13 Ab 13 1b7 3 6 AbGbC F 4(1x1 23x) #28 Db 11 5 4 1 3 AbGbDbF 4(1x1 33x) Db 13 b7 3 6 1 B F BbDb 6(233 1xx) Db 97 1 3b7 9 DbF B Eb 3(x21 22x) 27. G 11 4 3 5 1 C B D G 3(*1* 211) #13 C mi6 1 6b3 5 C A EbG 2(x2x 132) #8 C M76 1h7 3 6 C B E A 3(x1x 233) #20 C 7 1b7 3 5 C BbE G 3(x1x 131) C 13 1b7 3 6 C BbE A 3(x1x 133) #28 28. E 11 5 1 4 3 B E A G# 7(111 *3*) #14 A 6 3 5 1 6 C#E A F# 7(311 x1x) A mi6 b3 5 1 6 C E A F# 7(211 x1x) A M76 3 6 1h7 C#F#A G# 7(331 x3x) #21 A 97 9 1 3b7 B A C#G 6(2x2 13x) #35 29. G 11 5 1 4 3 D G C B 5(*11 1*3) #14 C 6 3 5 1 6 E G C A 5(x31 1x1) C mi6 b3 5 1 6 EbG C A 5(x21 1x1) C M76 3 6 1h7 E A C B 5(x33 1x3) #21 C 7 3 5 1b7 E G C Bb 5(x31 1x2) #23 30. C 9 1 3 9 5 C E D G 7(21* 12*) #15 F 13 1b7 6 3 F EbD A (1x1 x35) F 97 1b7 3 9 F EbA G (1x1 2x3) #31 Bb M7 1 5 3h7 BbF D A 5(24x 3x1) Bb mi6 b3 5 1 6 DbF BbG 8(211 x1x) 31. Eb 9 1 3 9 5 EbG F Bb 5(*21 *22) #15 Ab 6 5 1 6 3 EbAbF C 6(x11 x13) Ab mi6 5 1 6b3 EbAbF B 6(x11 x12) Ab 11 5 1 4 3 EbAbDbC 6(x11 1x3) #14 Ab 9 5 1 3 9 EbAbC Bb 5(x22 1x2) #17 32. G 9 3 9 5 1 B A D G 7(1*1 12*) #16 C 11 1 4 3 5 C F E G 8(11x 21x) #12 C 13 b7 6 3 1 BbA E C 5(2x3 x14) C 97 b7 3 9 1 BbE D C 6(12x 2x3) #34 F mi6 5b3 6 1 C AbD F 6(3x1 21x) 33. Ab 9 3 9 5 1 C BbEbA 3(*1* 122) #16 Db mi6 1 6b3 5 DbBbE Ab 3(x2x 132) #8 Db 11 1 4 3 5 DbGbF Ab 4(x11 x31) #12 Db 9 1 3 9 5 DbF EbAb 3(x21 x22) #15 34. D 9 5 1 3 9 A D F#E 4(221 *2*) #17 G 6 3 5 1 6 B D G E 5(311 x1x) G mi6 b3 5 1 6 BbD G E 5(211 x1x) G 9 9 5 1 3 A D G B 4(222 1xx) G 97 9 1b7 3 A G F B 5(1x1 x23) 35. F 9 5 1 3 9 C F A G 2(*22 1*2) #17 Bb 6 3 5 1 6 D F BbG 3(x31 1x1) Bb mi6 b3 5 1 6 DbF BbG 3(x21 1x1) Bb 9 9 5 1 3 C F BbD 3(x11 11x) 36. A 9 9 1 3 5 B A C#E 5(3*3 21*) #18 D M7 1 5h7 3 D A C#F# 10(132 2xx) #1 D 6 6 5 1 3 B A D F# 7(1x1 11x) D 11 4 5 1 3 G A D F# 7(x41 11x) 37. C 9 9 1 3 5 D C E G 3(*3* 331) #18 F M7 1 5h7 3 F C E A 8(x13 23x) #1 F 6 6 5 1 3 D C F A 5(x1x 121) F 11 4 5 1 3 BbC F A 10(x41 11x) F M76 6 1h7 3 D F E A 3(x31 x33) #19 38. D mi9 1b3 9 5 D F E A 8(31* 23*) #19 6 1 h7 3 G 11 5 1 4 3 D G C B 10(111 x3x) #14 G 9 5 1 3 9 D G B A 9(221 x2x) #17 G 97 1b7 3 9 G F B A 3(1x1 2x3) #31 C M7 1 5 3h7 C G E B 7(24x 3x1) 39. E mi9 1b3 9 5 E G F#B 5(*31 *33) #19 6 1 h7 3 A mi6 5 1 6b3 E A F#C 7(x11 x12) A 11 5 1 4 3 E A D C# 7(x11 1x3) #14 A 9 5 1 3 9 E A C#B 6(x22 1x2) #17 A 97 1b7 3 9 A G C#B 5(1x1 2x3) #31 40. F mi9 b3 9 5 1 AbG C F 4(1*2 23*) #20 1 h7 3 6 Bb mi6 1 6b3 5 BbG DbF 5(2x1 22x) #8 Bb 11 1 4 3 5 BbEbD F 6(11x 21x) #12 Bb 13 b7 6 3 1 AbG D Bb 4(1x2 4x3) Bb 13 b7 6 3 1 AbG D Bb 3(2x3 x14) Bb 97 b7 3 9 1 AbD C Bb 4(12x 2x3) #34 41. A mi9 b3 9 5 1 C B E A 3(*1* 233) #20 1 h7 3 6 D mi6 1 6b3 5 D B F A 4(x2x 132) #8 D 11 1 4 3 5 D G F#A 5(x11 x31) #12 D 13 b7 6 3 1 C B F#D 8(1x2 4x3) D 13 b7 6 3 1 C B F#D 7(2x3 x14) D 97 b7 3 9 1 C F#E D 8(12x 2x3) #34 42. F mi9 5 1b3 9 C F AbG 6(331 *3*) #21 3 6 1 h7 Bb 6 3 5 1 6 D F BbG 8(311 x1x) Bb mi6 b3 5 1 6 DbF BbG 8(211 x1x) Bb 9 9 5 1 3 C F BbD 7(222 1xx) Bb 97 9 1b7 3 C BbAbD 8(1x1 x23) 43. A mi9 5 1b3 9 E A C B 5(*33 1*3) #21 3 6 1 h7 D 6 3 5 1 6 F#A D B 7(x31 1x1) D mi6 b3 5 1 6 F A D B 7(x21 1x1) D 9 9 5 1 3 E A D F# 7(x11 11x) 44. F M76 6 1h7 3 D F E A 8(31* 23*) #19 1 b3 9 5 Bb 9 3 5 9 1 D F C Bb 8(313 x4x) Bb 7b5 3 1b5b7 D BbE Ab 8(3x1 22x) Bb 97 3 1 9b7 D BbC Ab 10(141 4xx) 45. G M76 6 1h7 3 E G F#B 5(*31 *33) #19 1 b3 9 5 C 9 3 5 9 1 E G D C 5(x31 3x4) C 7b5 3 1b5b7 E C GbBb 5(x3x 132) F 7 b7 3 1 5 EbA F C 6(x12 x13) 46. Ab M76 1h7 3 6 AbG C F 4(1*2 23*) #20 b3 9 5 1 Db 11 5 4 1 3 AbGbDbF 4(1x1 33x) Db 9 5 9 1 3 AbEbDbF 4(13x 33x) Db 7b5 1b5b7 3 DbG B F 9(121 2xx) Db 7b5 1b5b7 3 DbG B F 4(x12 13x) 47. C M76 1h7 3 6 C B E A 3(*1* 233) #20 b3 9 5 1 F 11 5 4 1 3 C BbF A 3(x1x 143) F 9 5 9 1 3 C G F A 3(x13 x43) F 7b5 1b5b7 3 F B EbA 8(x12 13x) 48. Ab M76 3 6 1h7 C F AbG 6(331 *3*) #21 5 1 b3 9 Db 9 1 3 5 9 DbF AbEb 6(431 3xx) Db 9 1 3 5 9 DbF AbEb (x43 14x) Gb mi6 5 1b3 6 DbGbA Eb 2(x33 13x) Gb 97 3b7 9 1 BbE AbGb 6(121 x2x) 49. C M76 3 6 1h7 E A C B 5(*33 1*3) #21 5 1 b3 9 F 9 1 3 5 9 F A C G 5(x43 14x) F 9 1 3 5 9 F A C G (xx3 213) Bb mi6 5 1b3 6 F BbDbG 6(x33 13x) Bb 97 3b7 9 1 D AbC Bb 5(x12 1x2) (files: s35-iv1.6S and s35-iv2.6S ---------------------------------------------------------------- STANDARD JAZZ HARMONY I will create a larger series, which will be of more general significance. This is "Series 140", for guitar in augmented tuning. An advantage of augmented tuning is that all the strings are the same interval apart, so a tablature does not need to be shown on different combinations of strings. Inversions are selected that are playable on strings a major third apart. There are 34 forms and 140 inversions. I call the triads of Series 140, "Series 28", because there are that many tonic chords. But there are 39 triad chords total. Then Series 101 has chords numbered 40 to 140. The nine 4-part tonic chords have the 3 or b3. The mi6 is called a tonic chords even though it has a tritone. The next six tetrades have a 3 and b7. The dim and 965 chords are included for their unusual shape and clear sound. The diminished chord has four minor third intervals, and the 965 has two perfect fifths. The last two forms, the M7b5 and 5+4, may seem an odd choice, but I have found them to be useful and expressive. They belong as part of Standard Jazz Harmony so that the retort of any of its forms is also in the group. Regular harmony has passing tones, Standard Jazz harmony will have "passing forms". For the triad forms, only the 3+9T and 5+4T are excluded. Excluded tetrad forms are: miM7, M7di, M7+5, mi13, 13b5, 6+9=m5+4, 3+9, 7+9, miM6=dim9, mi96, 96+5, and 96M7. Standard Jazz Harmony Triads 1. 93 1,3,9 the nine-three (=97T: b7,9,1) W--- 2. M73 1,3,h7 major seven-three -H-P 3. 9b3 1,b3,9 nine flat three WH-- 4. 95 1,5,9 the nine-five W--P 5. M75 1,5,h7 major seven-five -H-P 6. 65 1,5,6 the six-five (=7b3: b3,b7,1) W--P 7. maj 1,3,5 the major chord ---P 8. min 1,b3,5 the minor chord (=63: 6,1,3) ---P 9. 9M 1,h7,9 nine major seven triad WH-- 10. 96T 1,6,9 nine-six triad (=75: b7,5,1) W--P 11. 73 1,3,b7 the seven-three W-I- 12. di 1,b3,b5 the diminished triad --I- 13. aug 1,3,+5 the augmented chord ---- 14. 7bT 1,b5,b7 seven flat five triad W-I- 15. MbT 1,b5,h7 major seven flat five triad -HIP Standard Jazz Harmony Tetrades 16. M7 1,3,5,h7 major seventh chord -H-P 17. 6 1,3,5,6 the six chord (=mi7: b3,5,b7,1) W--P 18. mi6 1,b3,5,6 minor six chord (=dim7:b3,b5,b7,1) W-IP 19. 11 1,3,4,5 the eleventh chord WH-P 20. 9 1,3,5,9 the ninth chord W--P 21, mi9 1,b3,5,9 minor ninth chord (=M76: 6,1,3,h7) WH-P 22. 96 1,3,6,9 the nine-six W--P 23. 9M7 1,3,h7,9 nine major seven chord WH-P 24. 94 1,3,4,9 the nine-four (=mi97: b7,9,b3,1) WH-P 25. 7 1,3,5,b7 the seventh chord W-IP 26. 7b5 1,3,b5,b7 seven flat-five chord W-I- 27. 7+5 1,3,+5,b7 the seven aug-five W-I- 28. 13 1,3,6,b7 thirteenth chord WHIP 29. 74 1,3,4,b7 the seven-four WHIP 30. 97 1,3,b7,9 nine-seven chord W-I- 31. dim 1,b3,b5,6 diminished chord --I- 32. 965 1,5,6,9 the nine-six five W--P 33. M7b5 1,3,b5,h7 the major seven flat-five WHIP 34. 5+4 1,3,b5,h5 the five aug-four WHIP It would be too much to compare each of 34 forms to all the others. Our first simplification is to ignore the pairing of 3-part and 4- part chords. In performing, it is not hard for a musician to add or take away a note. In a case where both chords have tritones, the first consideration is: How does the tritone change? Having the tritone descend a half step has the best contrast. And this follows the example of regular harmony, where the chord D7 goes to G7, and the interval F#,C# descends to F natural,C natural. Having the tritone move a whole step or a minor third are the other two possibilities. So it is simpler to talk about the tritone forms separately, and this divides our tetrad series in half. We will mainly look at how the tonic chords connect to each other, and how a tonic chord connects to one or a few tritone chords. And we will look at variations of tritone forms. CLOSE KEYS DEFINED Within a musical phrase, we need to keep the same key. Tonality is defined as the "distance" of a second note from the root or tonic. This a real quantity, because we perceive it musically, but it is not directly measured by the interval between the pitches. Tonal distance is measured by the difference of major scale notes between the major keys of the two pitches. My approach is to have four root jump intervals. From C to: D, F, G or Bb. My reasoning is based on key signatures. To illustrate: In the key of C, if the C rises to a Db, the change of key is "remote", because there are five accidentals in key of Db and none in the key of C. Continuing: Db 5 accidentals remote D 2 accidentals close Eb 3 accidentals distant E 4 accidentals distant F 1 accidental close Gb 6 accidentals remote G 1 accidental close Ab 4 accidentals distant A 3 accidentals distant Bb 2 accidentals close B 5 accidentals remote C no accidentals In the text that follows, we focus on root pairs whose keys are close. Note the variety of root progressions these four changes suggest. A perfect fourth exists between both the I and IV, and II and V, and a whole step exists between both the I and II, and IV and V; there are a lot of ways to combine these! PRECESSION LIST A precession might have aesthetic value, but its purpose is to invite variation. No matter if it sounds a little dull -- it's only a tool. Anyway, musicians sometimes prefer musical exercises. The calling chord, with asterisks, is at the top of each paragraph. The chords below, the called chords, are in the close keys. Chords are paired when they have voiced harmony, especially with contrary motion. The triad pairs have mostly two voices changing, and the tetrades mostly three. For a given inversion, there will not always be examples from each of II, IV, V and bVII. For the tetrades, all called chords are also calling chords. This is not always so for the triad precession. To add or delete a chord pairing in the tetrad precession, take care to find both occurrences of it. Aesthetic Choice Although it was my wish to avoid arbitrary selection so far as possible, the selection of inversions for a series must partly be an aesthetic choice. Although Series 140 has a roughly equal representation of each form, some forms result in playable guitar tablatures more readily than others. The table below shows which form pairs were omitted with the current version of the Series 101 precession: M7 6 11 9 mi9 mi6 96 9M7 94 7 ----------------------------------------------------------- M7 x x x x x x x x x x 6 x no x x x no no x no x 11 x x x x x x x x x x 9 x x x no x x no x x x mi9 x x x x no x x x x x mi6 x no x x x no x x no x 96 x no x no x x no x x no 9M7 x x x x x x x x x x 94 x no x x x no x x x x 7 x x x x x x no x x no ----------------------------------------------------------- PRIMES The basic idea is that a chord is paired with its calling chord. But it's also worthwhile playing the called chords with each other. This is a way of learning the precession. Essential Jazz practice is to know the subdominant. I like choosing chords for a prime that has the roots: II, V, I, IV, bVII. This way, the roots advance by subdominants. But choose any sequence you like. With a pair of chords, what difference does it make in which order they are played? It seems to me that it's the subdominant that is the forward direction of Jazz harmony, and for some pairs, this is the direction in which they sound best. Here is a plan for learning the chords of a series. Play them first in series order, and then in bass voice index order. Try to know what the chord parts are, or at least, which note is the root. Then use the bass voice index to create little progressions based on 3-chord harmony. Next, use voice leading to form chord changes that interest you. You "understand" the calling chord when you can play substitutes for it. Cadences can be invented by altering the root jump (altering the tablature position) of precession chords. Series 140 is a plain text file, included in the download of the Chord Line Editor, with a name like "QMAS-7". The calling chords are searchable three ways. Search for the letter "Q" followed by the chord symbol. Or search by the series number, which is preceded by the pound sign ("#"). You can also search using the inversion's chord parts. For this to be efficient, each chord part is represented by a single keystroke. The major seven has an "M", the augmented fifth has a "U", the diminished fifth (or augmented fourth) has an "I", and the flat three (or augmented ninth) as an "N". (The flat nine would have a "V") art@ primes (page) Series 28 1. A 93 1 3 9 A C#B 8(n33 nn1) 1 C 93 3 9 1 E D C 7(3nn 1n3) 2 D 93 9 1 3 E D Gb 5(n1n 33n) 3 2. Eb M73 1 3h7 EbG D 3(n22 n1n) 4 G M73 1h7 3 G GbB 7(n2n n12) 5 C M73 3 1h7 E C B 8(2n2 nn1) 6 3. G 9b3 1b3 9 G BbA 6(n32 nn1) 7 C 9b3 b3 1 9 EbC D 3(n2n 31n) 8 D 9b3 b3 9 1 F E D 9(2nn 1n3) 9 4. G 95 1 5 9 G D A 6(n3n 2n1) 10 C 95 5 9 1 G D C 7(n2n 1n3) 11 Eb 95 9 1 5 F EbBb 6(n1n 3n2) 12 5. F M75 1 5h7 F C E 5(n2n 11n) 13 C M75 1h7 5 C B G 4(2nn 1n1) 14 6. G 65 1 5 6 G D E 5(n4n 31n) 15 C 65 5 1 6 G C A 8(n12 n3n) 16 A 65 6 5 1 GbE A 7(n1n 34n) 17 7. F maj 1 5 3 F C A 5(n2n 1n2) 18 D maj 3 1 5 GbD A 6(n2n 2n1) 19 Bb maj 5 3 1 F D Bb 6(n1n 2n2) 20 8. F min 1 5b3 F C Ab 5(n2n 1n1) 21 D min b3 1 5 F D A 6(n1n 2n1) 22 A min 5b3 1 E C A 5(n1n 1n2) 23 9. E 9M 1 9h7 E GbEb 3(n31 n2n) 24 Bb 9M 9 1h7 C BbA 3(3nn 1n4) 25 10. F 96T 1 6 9 F D G 6(n1n 23n) 26 A 96T 6 9 1 GbB A 7(n12 n4n) 27 C 96T 9 1 6 D C A 3(n1n 3n4) 28 11. D 73 1b7 3 D C Gb 5(3nn 13n) 29 Bb 73 3 1b7 D BbAb 5(3n3 nn1) 30 A 73 b7 3 1 G DbA 4(nn1 3n3) 31 12. D di 1b5b3 D AbF 5(3n1 n2n) 32 D di 1b5b3 D AbF 7(13n 4nn) 32 D di b3 1b5 F D Ab 6(n1n 24n) 33 13. D aug 1+5 3 D BbGb 3(n1n 1n1) 34 14. D 7bT 1b7b5 D C Ab 3(n1n 3n3) 35 A 7bT b5 1b7 EbA G 6(3n1 n3n) 36 A 7bT b7b5 1 G EbA 6(n3n 3n1) 37 15. A MbT 1b5h7 A EbAb 8(n3n 12n) 38 D MbT b5 1h7 AbD Db 7(n3n 1n4) 39 Series 101 16. F M7 1 3 5h7 F A C E 5(n22 11n) 40 C M7 1 5 3h7 C G E B 5(14n n14) 41 Eb M7 1 3h7 5 EbG D Bb 8(114 n4n) 42 C M7 1h7 3 5 C B E G 4(2nn 121) 43 D M7 1 5h7 3 D A DbGb 6(2n1 12n) 44 A M7 3 1 5h7 DbA E Ab 5(2n2 n11) 45 Bb M7 3 5 1h7 D F BbA 6(212 nn1) 46 G M7 5 1 3h7 D G B Gb 7(122 n1n) 47 F M7 5 1h7 3 C F E A 5(12n n12) 48 17. A 6 1 3 5 6 A DbE Gb 7(n44 31n) 49 D 6 1 3 6 5 D GbB A 7(112 n4n) 50 C 6 1 5 3 6 C G E A 4(2n1 n23) 51 F 6 1 5 6 3 F C D A 7(4n3 14n) 52 Bb 6 3 1 5 6 D BbF G 4(4n4 n31) 53 A 6 3 5 1 6 DbE A Gb 5(212 n3n) 54 C 6 3 6 1 5 E A C G 8(232 n1n) 55 Bb 6 3 6 5 1 D G F Bb 6(23n n12) 56 A 6 5 1 3 6 E A DbGb 5(n12 23n) 57 F 6 5 3 6 1 C A D F 5(1n2 32n) 58 C 6 5 6 1 3 G A C E 5(n42 11n) 59 G 6 5 6 3 1 D E B G 5(314 n4n) 60 C 6 6 1 3 5 A C E G 8(n32 21n) 61 F 6 6 1 5 3 D F C A 6(214 nn1) 62 Eb 6 6 3 1 5 C G EbBb 4(2n1 n14) 63 D 6 6 5 1 3 B A D Gb 4(1n3 44n) 64 18. F mi6 1b3 5 6 F AbC D 3(n43 31n) 65 C mi6 1 5b3 6 C G EbA 4(2n1 n13) 66 D mi6 1 6b3 5 D B F A 6(2n3 n11) 67 Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) 68 C mi6 b3 6 1 5 EbA C G 8(132 n1n) 69 G mi6 b3 5 6 1 BbD E G 8(n44 21n) 70 A mi6 5 1b3 6 E A C Gb 5(n12 13n) 71 F mi6 5b3 6 1 C AbD F 5(1n1 32n) 72 G mi6 5 6b3 1 D E BbG 5(313 n4n) 73 Bb mi6 6 1b3 5 G BbDbF 6(n32 11n) 74 Eb mi6 6 5 1b3 C BbEbGb 5(1n3 43n) 75 F mi6 6b3 5 1 D AbC F 3(n13 34n) 76 19. C 11 1 4 3 5 C F E G 4(23n n21) 77 D 11 1 4 5 3 D G A Gb 6(231 n2n) 78 C 11 4 1 3 5 F C E G 8(3n2 21n) 79 F 11 4 1 5 3 BbF C A 3(14n 3n4) 80 Eb 11 4 5 1 3 AbBbEbG 7(n31 22n) 81 F 11 4 3 5 1 BbA C F 3(1n4 34n) 82 G 11 5 1 4 3 D G C B 7(123 nn2) 83 Eb 11 5 4 1 3 BbAbEbG 3(1n3 n22) 84 20. C 9 1 3 5 9 C E G D 11(n33 2n1) 85 D 9 1 3 9 5 D GbE A 3(n11 n34) 86 Eb 9 1 5 9 3 EbBbF G 4(n14 n31) 87 C 9 1 9 5 3 C D G E 11(n31 2n3) 88 A 9 3 1 5 9 DbA E B 6(1n1 4n3) 89 G 9 3 1 9 5 B G A D 10(n3n 312) 90 Bb 9 3 5 9 1 D F C Bb 5(32n 1n3) 91 A 9 3 9 5 1 DbB E A 2(n1n 345) 92 G 9 5 1 3 9 D G B A 3(n12 2n4) 93 Eb 9 5 3 1 9 BbG EbF 2(2n3 n31) 94 F 9 5 9 1 3 C G F A 4(2n1 n33) 95 A 9 5 9 3 1 E B DbA 6(4n3 1n1) 96 Bb 9 9 1 3 5 C BbD F (n1n 332) 97 D 9 9 3 1 5 E GbD A 3(n31 n14) 98 A 9 9 5 1 3 B E A Db (n01 22n) 99 Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) 100 21. D mi9 1b3 5 9 D F A E 5(322 n1n) 101 C mi9 1b3 9 5 C EbD G 4(21n 4n1) 102 A mi9 b3 1 9 5 C A B E 4(2n3 12n) 103 Eb mi9 b3 5 1 9 GbBbEbF 6(n22 31n) 104 Bb mi9 b3 5 9 1 DbF C Bb 5(22n 1n3) 105 F mi9 5 1b3 9 C F AbG 5(121 n4n) 106 G mi9 5b3 1 9 D BbG A 6(2n2 n31) 107 22. F 96 1 3 6 9 F A D G 6(n11 23n) 108 C 96 1 3 9 6 C E D A 5(11n 3n2) 109 Bb 96 1 6 9 3 BbG C D 3(1n2 31n) 110 A 96 3 1 6 9 DbA GbB 6(1n1 n23) 111 Eb 96 3 6 1 9 G C EbF 6(n34 31n) 112 F 96 6 1 3 9 D F A G 6(211 n3n) 113 G 96 6 9 1 3 E A G B 8(23n n11) 114 A 96 9 1 3 6 B A DbGb 4(1n3 34n) 115 C 96 9 6 1 3 D A C E 5(3n2 11n) 116 F 96 9 3 6 1 G A D F 6(n31 21n) 117 23. Eb 9M7 1 3h7 9 EbG D F 6(33n 21n) 118 A 9M7 9 1 3h7 B A DbAb 4(1n3 3n2) 119 C 9M7 3 1 9h7 E C D B 7(3n3 1n2) 120 F 9M7 1 9h7 3 F G E A 4(n31 n23) 121 24. C 94 9 4 1 3 D F C E 5(32n 11n) 122 D 94 1 4 9 3 D G E Gb 7(12n 31n) 123 A 94 4 1 3 9 D A DbB 6(2n1 1n3) 124 25. F 7 1 3 5b7 F A C Eb 4(n33 21n) 125 D 7 1 3b7 5 D GbC A 5(33n 1n2) 126 Eb 7 1 5b7 3 EbBbDbG 14(n3n 213) 127 C 7 1b7 3 5 C BbE G 3(3nn 132) 128 Bb 7 3 1 5b7 D BbF Ab 5(3n3 n21) 129 A 7 3 5 1b7 DbE A G 4(323 nn1) 130 C 7 3b7 1 5 E BbC G 5(n13 14n) 131 Bb 7 3b7 5 1 D AbF Bb 5(3n1 n23) 132 A 7 5 1 3b7 E A DbG 4(n23 3n1) 133 F 7 5 1b7 3 C F EbA 4(23n n13) 134 G 7 5 3b7 1 D B F G 4(4nn 131) 135 C 7 5b7 1 3 G BbC E 5(n43 11n) 136 A 7 5b7 3 1 E G DbA 4(n21 3n3) 137 D 7 b7 3 1 5 C GbD A 5(13n 3n2) 138 Eb 7 b7 3 5 1 DbG BbEb 14(n13 23n) 139 C 7 b7 5 1 3 BbG C E 11(n1n 233) 140 Series 28, Melody Voice Index 1. B maj 5 3 1 F#D#B 7(n1n 2n2) 20 2. C 95 5 9 1 G D C 7(n2n 1n3) 11 3. C 93 3 9 1 E D C 7(3nn 1n3) 2 4. A 96T 6 9 1 F#B A 7(n12 n4n) 27 5. A min 5b3 1 E C A 5(n1n 1n2) 23 6. D 9b3 b3 9 1 F E D 9(2nn 1n3) 9 7. A 65 6 5 1 F#E A 7(n1n 34n) 17 8. A 73 b7 3 1 G C#A 4(nn1 3n3) 31 9. Ab aug +5 3 1 E C Ab 5(n1n 1n1) 34 10. A 7bT b7b5 1 G D#A 6(n3n 3n1) 37 11. F 96T 1 6 9 F D G 6(n1n 23n) 26 12. A 93 1 3 9 A C#B 8(n33 nn1) 1 13. G 95 1 5 9 G D A 6(n3n 2n1) 10 14. G 9b3 1b3 9 G BbA 6(n32 nn1) 7 15. C 9b3 b3 1 9 EbC D 3(n2n 31n) 8 16. D di 1b5b3 D AbF 7(13n 4nn) 32 17. F min 1 5b3 F C Ab 5(n2n 1n1) 21 18. D di 1b5b3 D AbF 5(3n1 n2n) 32 19. D 93 9 1 3 E D F# 5(n1n 33n) 3 20. G M73 1h7 3 G F#B 7(n2n n12) 5 21. E aug 1+5 3 E C G# 5(n1n 1n1) 34 22. D 73 1b7 3 D C F# 5(3nn 13n) 21 23. F maj 1 5 3 F C A 5(n2n 1n2) 18 24. D 7bT 1b7b5 D C Ab 3(n1n 3n3) 35 25. D di b3 1b5 F D Ab 6(n1n 24n) 33 26. D maj 3 1 5 F#D A 6(n2n 2n1) 19 27. D min b3 1 5 F D A 6(n1n 2n1) 22 28. Eb 95 9 1 5 F EbBb 6(n1n 3n2) 12 29. C M75 1h7 5 C B G 4(2nn 1n1) 14 30. C aug 3 1+5 E C G# 5(n1n 1n1) 34 31. G 65 1 5 6 G D E 5(n4n 31n) 15 32. C 65 5 1 6 G C A 8(n12 n3n) 16 33. C 96T 9 1 6 D C A 3(n1n 3n4) 28 34. A 7bT b5 1b7 EbA G 6(3n1 n3n) 36 35. Bb 73 3 1b7 D BbAb 5(3n3 nn1) 30 36. Eb M73 1 3h7 EbG D 3(n22 n1n) 4 37. E 9M 1 9h7 E F#D# 3(n31 n2n) 24 38. Bb 9M 9 1h7 C BbA 3(3nn 1n4) 25 39. C M73 3 1h7 E C B 8(2n2 nn1) 6 40. F M75 1 5h7 F C E 5(n2n 11n) 13 41. A MbT 1b5h7 A D#G# 8(n3n 12n) 38 42. D MbT b5 1h7 G#D C# 7(n3n 1n4) 39 Series 28, Sample Subdominants 1. A 93 1 3 9 A C#B 8(n33 nn1) 4(21x 1xx) D 95 5 1 9 A D E (23n nn1) 5(11x x1x) 2. C 93 3 9 1 E D C 7(3nn 1n3) 7(6xx 1x2) F 96T 1 6 9 F D G 6(n1n 23n) 7(x2x 12x) 3. D 93 9 1 3 E D F# 5(n1n 33n) 7(x1x 11x) G 9M 1 9h7 G A F# 6(n31 n2n) 7(x41 x1x) 4. Eb M73 1 3h7 EbG D 3(n22 n1n) 5(x21 3xx) Ab di b3 1b5 B AbD 3(2n3 n1n) 6(2x1 2xx) 5. G M73 1h7 3 G F#B 7(n2n n12) 5(xx1 x33) C M73 3 1h7 E C B 8(2n2 nn1) 5(x3x 1x3) 6. C M73 3 1h7 E C B 8(2n2 nn1) 5(x3x 1x3) F maj 1 5 3 F C A 5(n2n 1n2) 3(xx1 3x3) 7. G 9b3 1b3 9 G BbA 6(n32 nn1) 3(xx3 1x3) C 96T 9 1 6 D C A 3(n1n 3n4) 5(x1x 1x1) 8. C 9b3 b3 1 9 EbC D 3(n2n 31n) 3(x4x 31x) F 7bT b7b5 1 EbB F 4(n1n 13n) 4(x3x 13x) 9. D 9b3 b3 9 1 F E D 9(2nn 1n3) 8(x1x 2x3) C 93 1 9 3 C D E (n1n n31) 7(x41 xx1) 10. G 95 1 5 9 G D A 6(n3n 2n1) 5(xx1 3x1) C MbT b5 1h7 GbC B 7(n13 nn2) 4(xx1 2x4) 11. C 95 5 9 1 G D C 7(n2n 1n3) 7(x4x 1x2) F M75 1h7 5 F E C 9(2nn 1n1) 8(x1x 2x1) 12. Eb 95 9 1 5 F EbBb 6(n1n 3n2) 6(x3x 3x1) Ab di 1b5b3 AbD B 7(n3n 1n2) 6(xx1 2x2) 13. F M75 1 5h7 F C E 5(n2n 11n) 3(xx1 33x) Bb 65 5 1 6 F BbG 6(n12 n3n) 3(xx1 1x1) 14. C M75 1h7 5 C B G 4(2nn 1n1) 8(1x2 x1x) F maj 5 3 1 C A F (n1n 2n2) 6(3x2 x1x) 15. G 65 1 5 6 G D E 5(n4n 31n) 5(xx1 31x) C M75 5 1h7 G C B 8(n12 nn1) 5(xx1 1x3) 16. C 65 5 1 6 G C A 8(n12 n3n) 10(x11 x1x) F M73 1h7 3 F E A 5(n2n n12) 8(x1x 23x) 17. A 65 6 5 1 F#E A 7(n1n 34n) 4(xx1 x22) D min b3 1 5 F D A 6(n1n 2n1) 5(x4x 3x1) 18. F maj 1 5 3 F C A 5(n2n 1n2) 8(x13 x3x) Bb 96T 6 9 1 G C Bb 7(n23 nn1) 10(x11 x2x) 19. D maj 3 1 5 F#D A 6(n2n 2n1) 7(x3x 14x) G 9b3 1b3 9 G BbA 6(n32 nn1) 8(x31 x3x) 20. Bb maj 5 3 1 F D Bb 6(n1n 2n2) 6(x3x 2x1) Eb maj 3 1 5 G EbBb 7(n2n 2n1) 8(x3x 14x) 21. F min 1 5b3 F C Ab 5(n2n 1n1) 8(x13 x2x) Bb min 5b3 1 F DbBb 6(n1n 1n2) 6(x3x 1x1) 22. D min b3 1 5 F D A 6(n1n 2n1) 5(x4x 3x1) G 65 6 5 1 E D G 3(n3n n12) 7(x1x 12x) 23. A min 5b3 1 E C A 5(n1n 1n2) 5(x3x 1x1) D 65 1 6 5 D B A 6(2n3 nn1) 4(x2x 1x2) 24. E 9M 1 9h7 E F#D# 3(n31 n2n) 5(x41 x1x) A 93 9 1 3 B A C# 4(1n3 3nn) 7(2x2 1xx) 25. Bb 9M 9 1h7 C BbA 3(3nn 1n4 8(1x1 x3x) Eb 95 1 5 9 EbBbF 2(n3n 2n1) 6(x13 x1x) 26. F 96T 1 6 9 F D G 6(n1n 23n) 7(x2x 12x) Bb M75 5 1h7 F BbA 6(n12 nn1) 8(x11 x3x) 27. A 96T 6 9 1 F#B A 7(n12 n4n) 4(xx1 1x2) D 95 9 1 5 E D A 3(n3n n14) 5(x3x 3x1) 28. C 96T 9 1 6 D C A 3(n1n 3n4) 5(x1x 1x1) F 73 b7 1 3 EbF A 4(n1n n33) 5(x2x x21) 29. D 73 1b7 3 D C F# 5(3nn 13n) 29 Bb 73 3 1b7 D BbAb 5(3n3 nn1) 30 A 73 b7 3 1 G C#A 4(nn1 3n3) 31 30. D di 1b5b3 D AbF 5(3n1 n2n) 32 D di 1b5b3 D AbF 7(13n 4nn) 32 D di b3 1b5 F D Ab 6(n1n 24n) 33 31. D aug 1+5 3 D A#F# 3(n1n 1n1) 34 32. D 7bT 1b7b5 D C G# 3(n1n 3n3) 35 A 7bT b5 1b7 EbA G 6(3n1 n3n) 36 A 7bT b7b5 1 G EbA 6(n3n 3n1) 37 33. A MbT 1b5h7 A D#G# 8(n3n 12n) 38 D MbT b5 1h7 G#D C# 7(n3n 1n4) 39 Series 101, Bass Voice Index 1. Eb 9M7 1 3h7 9 EbG D F 6(33n 21n) #118 F 96 1 3 6 9 F A D G 6(n11 23n) #108 C 9 1 3 5 9 C E G D 3(332 n1n) #85 D mi9 1b3 5 9 D F A E 5(322 n1n) #101 2. Eb 9 1 5 9 3 EbBbF G 4(n14 n31) #87 C 9 1 9 5 3 C D G E 3(312 n3n) #88 F 6 1 5 6 3 F C D A 7(4n3 14n) #52 F 9M7 1 9h7 3 F G E A 4(n31 n23) #121 Eb 7 1 5b7 3 EbBbDbG 6(3n2 13n) #127 D 11 1 4 5 3 D G A Gb 6(231 n2n) #78 Bb 96 1 6 9 3 BbG C D 3(1n2 31n) #110 D M7 1 5h7 3 D A DbGb 6(2n1 12n) #44 D 94 1 4 9 3 D G E Gb 7(12n 31n) #123 3. C M7 1h7 3 5 C B E G 4(2nn 121) #43 C mi9 1b3 9 5 C EbD G 4(21n 4n1) #102 D 7 1 3b7 5 D GbC A 5(33n 1n2) #126 D mi6 1 6b3 5 D B F A 6(2n3 n11) #67 4. Eb M7 1 3h7 5 EbG D Bb 8(114 n4n) #42 C 7 1b7 3 5 C BbE G 3(3nn 132) #128 D 6 1 3 6 5 D F#B A 7(112 n4n) #50 D 9 1 3 9 5 D F#E A 3(n11 n34) #86 C 11 1 4 3 5 C F E G 4(23n n21) #77 5. C 6 1 5 3 6 C G E A 4(2n1 n23) #51 C mi6 1 5b3 6 C G EbA 4(2n1 n13) #66 C 96 1 3 9 6 C E D A 5(11n 3n2) #109 F mi6 1b3 5 6 F AbC D 3(n43 31n) #65 A 6 1 3 5 6 A C#E F# 7(n44 31n) #50 6. F 7 1 3 5b7 F A C Eb 4(n33 21n) #125 F M7 1 3 5h7 F A C E 5(n22 11n) #40 C M7 1 5 3h7 C G E B 5(14n n14) #41 7. G mi6 b3 5 6 1 BbD E G 8(n44 21n) #70 Bb 6 3 6 5 1 D G F Bb 6(23n n12) #56 Bb 9 3 5 9 1 D F C Bb 5(32n 1n3) #91 A 9 3 9 5 1 C#B E A 2(n1n 345) #92 Bb 7 3b7 5 1 D AbF Bb 5(3n1 n23) #132 Bb mi9 b3 5 9 1 DbF C Bb 5(22n 1n3) #105 8. A 96 3 1 6 9 C#A F#B 6(1n1 n23) #111 Eb 96 3 6 1 9 G C EbF 6(n34 31n) #112 Eb mi9 b3 5 1 9 GbBbEbF 6(n22 31n) #104 A 9 3 1 5 9 C#A E B 6(1n1 4n3) #89 9. C 7 3b7 1 5 E BbC G 5(n13 14n) #131 C mi6 b3 6 1 5 EbA C G 4(n13 2n1) #69 A mi9 b3 1 9 5 C A B E 4(2n3 12n) #103 G 9 3 1 9 5 B G A D 2(3n3 12n) #90 C 6 3 6 1 5 E A C G 8(232 n1n) #55 10. A 6 3 5 1 6 DbE A Gb 5(212 n3n) #54 Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) #68 Bb 6 3 1 5 6 D BbF G 4(4n4 n31) #53 11. A 7 3 5 1b7 DbE A G 4(323 nn1) #130 Bb 7 3 1 5b7 D BbF Ab 5(3n3 n21) #129 12. A M7 3 1 5h7 DbA E Ab 5(2n2 n11) #45 C 9M7 3 1 9h7 E C D B 7(3n3 1n2) #120 Bb M7 3 5 1h7 D F BbA 6(212 nn1) #46 13. A 94 4 1 3 9 D A C#B 6(2n1 1n3) #124 Eb 11 4 5 1 3 AbBbEbG 7(n31 22n) #81 F 11 4 3 5 1 BbA C F 3(1n4 34n) #82 C 11 4 1 3 5 F C E G 8(3n2 21n) #79 F 11 4 1 5 3 BbF C A 3(14n 3n4) #80 14. A mi6 5 1b3 6 E A C F# 5(n12 13n) #71 A 6 5 1 3 6 E A C#F# 5(n12 23n) #57 A 7 5 1 3b7 E A C#G 4(n23 3n1) #133 G M7 5 1 3h7 D G B F# 7(122 n1n) #47 15. G 6 5 6 3 1 D E B G 5(314 n4n) #60 G 7 5 3b7 1 D B F G 4(4nn 131) #135 F 6 5 3 6 1 C A D F 5(1n2 32n) #58 F mi6 5b3 6 1 C AbD F 5(1n1 32n) #72 G mi6 5 6b3 1 D E BbG 5(313 n4n) #73 A 7 5b7 3 1 E G C#A 4(n21 3n3) #137 A 9 5 9 3 1 E B C#A 6(4n3 1n1) #95 16. G mi9 5b3 1 9 D BbG A 6(2n2 n31) #107 Eb 9 5 3 1 9 BbG EbF 2(2n3 n31) #94 F mi9 5 1b3 9 C F AbG 5(121 n4n) #106 G 9 5 1 3 9 D G B A 6(233 nn1) #93 17. C 7 5b7 1 3 G BbC E 5(n43 11n) #136 C 6 5 6 1 3 G A C E 5(n42 11n) #59 F M7 5 1h7 3 C F E A 5(12n n12) #48 F 7 5 1b7 3 C F EbA 4(23n n13) #134 F 9 5 9 1 3 C G F A 4(2n1 n33) #95 Eb 11 5 4 1 3 BbAbEbG 3(1n3 n22) #85 G 11 5 1 4 3 D G C B 7(123 nn2) #83 20. A 9 9 5 1 3 B E A C# (n01 22n) #99 C 96 9 6 1 3 D A C E 5(3n2 11n) #116 D 9 9 3 1 5 E F#D A 3(n31 n14) #98 Bb 9 9 1 3 5 C BbD F (n1n 332) #97 Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) #100 A 9M7 9 1 3h7 B A C#G# 4(1n3 3n2) #119 A 96 9 1 3 6 B A C#F# 4(1n3 34n) #115 F 96 9 3 6 1 G A D F 6(n31 21n) #117 C 94 9 4 1 3 D F C E 5(32n 11n) #122 (files s101pt1.6a, s101pt3.6a, s101pt4.6a, s101pt5.6a, s101pt9.6a) art@ end of bvi's (page) QMAS-7 Series 140 of Standard Jazz Harmony Series 28 of Series 140 1. A 93 1 3 9 A C#B 8(*33 **1) #1 139 Q93 B 65 6 5 1 G#F#B 7(n3n n12) B min 5b3 1 F#D B 7(n1n 1n2) D 95 5 1 9 A D E (23n nn1) D M73 1h7 3 D C#F# 6(2nn 12n) D 73 1b7 3 D C F# 5(3nn 13n) D 73 3 1b7 F#D C 9(3n3 nn1) D 7bT b5 1b7 G#D C 7(n3n 1n3) E maj 3 1 5 G#E B 8(n2n 2n1) E min b3 1 5 G E B 8(n1n 2n1) E 9b3 b3 1 9 G E F# 7(n2n 31n) E 7bT 1b7b5 E D Bb 5(n1n 3n3) G M75 1 5h7 G D F# 7(n2n 11n) G 65 1 5 6 G D E 11(2n1 nn3) G MbT 1b5h7 G C#F# 6(n3n 12n) A 93 1 3 9 A C#B 8(n33 nn1) 1 2. C 93 3 9 1 E D C 7(3** 1*3) #2 391 Q93 D min b3 1 5 F D A 6(n1n 2n1) D di b3 1b5 F D Ab 5(n2n 3n1) F 96T 1 6 9 F D G 6(n1n 23n) F 73 b7 1 3 EbF A 4(n1n n33) F aug 1+5 3 F DbA 6(n1n 1n1) G 93 9 1 3 A G B 10(n1n 33n) G 96T 6 1 9 E G A 2(n43 1nn) G 7bT b7b5 1 F DbG 4(n3n 3n1) Bb 73 b7 3 1 AbD Bb 9(n13 n3n) Bb di b5b3 1 E DbBb 5(n1n 2n3) C 93 3 9 1 E D C 7(3nn 1n3) 2 3. D 93 9 1 3 E D F# 5(*1* 33*) #3 913 Q93 E M73 1h7 3 E D#G# 4(n2n n12) E 65 1 6 5 E C#B 5(n1n 2n4) G M73 1 3h7 G B F# 7(n22 n1n) G min b3 5 1 BbD G 11(n11 2nn) G 9M 1 9h7 G A F# 6(n31 n2n) G MbT 1b5h7 G C#F# 6(n3n 12n) A 95 5 9 1 E B A 4(n2n 1n3) A 96T 1 9 6 A B F# 7(n42 n1n) A M75 5 1h7 E A G# 5(n12 nn1) A 7bT b5 1b7 EbA G 6(3n1 n3n) C 95 1 9 5 C D G (n1n n34) C 9M 1 9h7 C D B 5(1nn 3n4) D 93 9 1 3 E D F# 5(n1n 33n) 3 4. Eb M73 1 3h7 EbG D 3(*22 *1*) #4 13M QM73 F 65 1 5 6 F C D 3(n4n 31n) F 73 b7 3 1 EbA F 4(n13 n3n) Ab maj 5 1 3 EbAbC 4(n12 2nn) Ab 65 5 1 6 EbAbF 4(n12 n3n) Ab di b3 1b5 B AbD 11(n2n 3n1) Bb 95 5 1 9 F BbC 5(n23 1nn) Bb 93 9 1 3 C BbD 11(n3n n11) Bb di b5 1b3 E BbDb 5(n13 2nn) Db 65 6 5 1 BbAbDb 11(n1n 34n) Db di b3b5 1 E G Db 4(n21 3nn) Eb M73 1 3h7 EbG D 3(n22 n1n) 4 5. G M73 1h7 3 G F#B 7(*2* *12) #5 1M3 QM73 A 95 1 5 9 A E B 9(n2n 14n) A 7bT b7b5 1 G EbA 8(n1n 13n) C M73 3 1h7 E C B 8(2n2 nn1) C 9M 1 9h7 C D B 5(1nn 3n4) C di b3b5 1 EbGbC 7(2nn n13) D 95 5 9 1 A E D 9(n2n 1n3) D 93 9 3 1 E F#D 9(1nn 3n3) D MbT b5 1h7 G#D C# 7(n3n 1n4) D 7bT b5 1b7 AbD C 7(n3n 1n3) F 95 9 1 5 G F C 6(n3n n14) F 96T 9 1 6 G F D 8(n1n 3n4) G M73 1h7 3 G F#B 7(n2n n12) 5 6. C M73 3 1h7 E C B 8(2*2 **1) #6 31M QM73 D 95 9 1 5 E D A 5(n1n 3n2) D min b3 1 5 F D A 6(n1n 2n1) F maj 1 5 3 F C A 5(n2n 1n2) F 9b3 1b3 9 F AbG 4(n32 nn1) F 73 b7 1 3 EbF A 4(n1n n33) F 7bT 1b7b5 F EbB 6(n1n 3n3) G 96T 6 1 9 E G A 4(n21 nn3) G 73 b7 1 3 F G B 6(n1n n33) G di 1b5b3 G DbBb 10(3n1 n2n) G 7bT b7b5 1 F DbG 4(n3n 3n1) Bb 95 5 9 1 F C Bb 5(n2n 1n3) Bb 65 5 6 1 F G Bb 6(n1n n32) C M73 3 1h7 E C B 8(2n2 nn1) 6 7. G 9b3 1b3 9 G BbA 6(*32 **1) #7 1N9 Q9b3 A 95 5 9 1 E B A 4(n2n 1n3) A 7bT b7b5 1 G EbA 6(n3n 3n1) C 93 9 1 3 D C E 15(n1n 33n) C 96T 9 1 6 D C A 15(n1n 3n4) C 7bT b5b7 1 GbBbC 7(n11 nn3) D M75 1h7 5 D C#A 6(2nn 1n1) D 7bT 1b7b5 D C Ab 3(n1n 3n3) D di b5 1b3 AbD F 6(n4n 21n) D aug 1+5 3 D A#F# 15(n1n 1n1) F MbT 1b5h7 F B E 4(n3n 12n) F 96T 9 1 6 G F D 8(n1n 3n4) F di b3b5 1 AbB F 6(n43 n1n) G 9b3 1b3 9 G BbA 6(n32 nn1) 7 8. C 9b3 b3 1 9 EbC D 3(*2* 31*) #8 N19 Q9b3 D 95 9 5 1 E A D 5(n12 3nn) D aug 3+5 1 F#A#D 7(n11 1nn) F 9b3 1b3 9 F AbG 4(n32 nn1) F 9M 1 9h7 F G E 4(n31 n2n) F 7bT b7b5 1 EbB F 4(n1n 13n) G M73 1 3h7 G B F# 7(n22 n1n) G 96T 6 9 1 E A G 5(n12 n4n) G 7bT b7b5 1 F DbG 4(n3n 3n1) Bb 95 5 9 1 F C Bb 5(n2n 1n3) Bb MbT b5 1h7 E BbA 3(n3n 1n4) C 9b3 b3 1 9 EbC D 3(n2n 31n) 8 9. D 9b3 b3 9 1 F E D 9(2** 1*3) #9 N91 Q9b3 E 95 9 1 5 F#E B 7(n1n 3n2) E min b3 1 5 G E B 8(n1n 2n1) G 93 1 3 9 G B A 6(n33 nn1) G 93 1 9 3 G A B 8(n1n n31) G 73 b7 1 3 F G B 6(n1n n33) G 7bT 1b7b5 G F Db 8(n1n 3n3) A 93 1 9 3 A B C# 10(n1n n31) A 96T 6 1 9 F#A B 6(n21 nn3) A 65 6 5 1 F#E A 5(n3n n12) C 65 5 6 1 G A C 8(n1n n32) C aug +5 3 1 G#E C 9(n1n 1n1) D 9b3 b3 9 1 F E D 9(2nn 1n3) 9 10. G 95 1 5 9 G D A 6(*3* 2*1) #10 159 Q95 A 95 9 5 1 B E A 4(1nn n23) A 65 6 5 1 F#E A 5(n3n n12) C 7bT b5 1b7 GbC Bb 5(n3n 1n3) C M75 5 1h7 G C B 8(n12 nn1) C di b5b3 1 GbEbC 7(n1n 2n3) C MbT b5 1h7 GbC B 7(n13 nn2) D 93 3 1 9 F#D E 5(n3n 31n) D 9M 9 1h7 E D C# 9(1n3 nn2) D 73 3 1b7 F#D C 9(3n3 nn1) D di b3 1b5 F D Ab 6(n1n 24n) D 7bT b5 1b7 AbD C 7(n3n 1n3) F M73 1h7 3 F E A 5(n2n n12) F MbT 1h7b5 F E B 6(n1n 4n3) G 95 1 5 9 G D A 6(n3n 2n1) 10 11. C 95 5 9 1 G D C 7(*2* 1*3) #11 591 Q95 D 96T 9 1 6 E D B 5(n1n 3n4) D 9b3 b3 1 9 F D E 5(n2n 31n) F 93 9 1 3 G F A 8(n1n 33n) F M75 1h7 5 F E C 9(2nn 1n1) F 7bT 1b7b5 F EbB 6(n1n 3n3) F di b3 1b5 AbF B 8(n2n 3n1) G 96T 1 6 9 G E A 8(n1n 23n) G M73 1h7 3 G F#B 7(n2n n12) G aug 1+5 3 G D#B 8(n1n 1n1) Bb 65 6 5 1 G F Bb 6(n3n n12) C 95 5 9 1 G D C 7(n2n 1n3) 11 12. Eb 95 9 1 5 F EbBb 6(*1* 3*2) #12 915 Q95 F maj 1 5 3 F C A 5(n2n 1n2) F 93 1 9 3 F G A 6(n1n n31) Ab 93 1 3 9 AbC Bb 7(n33 nn1) Ab 9b3 1b3 9 AbB Bb 7(n32 nn1) Ab di 1b5b3 AbD B 7(n3n 1n2) Bb 73 b7 3 1 AbD Bb 9(n13 n3n) Bb 96T 6 9 1 G C Bb 7(n23 nn1) Bb di b5b3 1 E DbBb 5(n1n 2n3) Db M73 3 1h7 F DbC 9(2n2 nn1) Db min b3 1 5 E DbAb 5(n1n 2n1) Eb 95 9 1 5 F EbBb 6(n1n 3n2) 12 13. F M75 1 5h7 F C E 5(*2* 11*) #13 15M QM75 G 93 1 3 9 G B A 6(n33 nn1) G 73 b7 3 1 F B G 6(n13 n3n) Bb 93 1 9 3 BbC D 3(1nn 31n) Bb M75 5 1h7 F BbA 6(n12 nn1) Bb 65 5 1 6 F BbG 6(n12 n3n) C 96T 6 1 9 A C D 7(n43 1nn) C 65 5 1 6 G C A 4(nn1 2n3) C di b5 1b3 GbC Eb 4(n4n 21n) Eb 93 9 3 1 F G Eb 4(n31 n1n) Eb aug 3+5 1 G B Eb 8(n11 1nn) F M75 1 5h7 F C E 5(n2n 11n) 13 14. C M75 1h7 5 C B G 4(2** 1*1) #14 1M5 QM75 D 95 1 5 9 D A E (n3n 2n1) D 65 1 6 5 D B A 6(2n3 nn1) F maj 5 3 1 C A F (n1n 2n2) F 93 1 3 9 F A G 4(n33 nn1) F 9b3 1b3 9 F AbG 4(n32 nn1) G 95 5 9 1 D A G 2(n2n 1n3) G 65 5 6 1 D E G 3(n1n n32) G di b5b3 1 DbBbG 2(n1n 2n3) Bb 95 9 1 5 C BbF (n1n 3n2) Bb 93 9 1 3 C BbD 11(n3n n11) Bb di b3 1b5 DbBbE 2(n1n 24n) C M75 1h7 5 C B G 4(2nn 1n1) 14 15. G 65 1 5 6 G D E 5(*4* 31n) #15 156 Q65 A 96T 6 1 9 F#A B 6(n21 nn3) A 73 b7 3 1 G C#A 6(n3n 1n1) C M75 5 1h7 G C B 8(n12 nn1) C 9M 1 9h7 C D B 5(1nn 3n4) C MbT b5 1h7 F#C B 5(n3n 1n4) D maj 3 1 5 F#D A 6(n2n 2n1) D 65 5 1 6 A D B 10(n12 n3n) D di b5 1b3 AbD F 6(n4n 21n) D 73 3 1b7 F#D C 9(3n3 nn1) F 95 9 5 1 G C F 8(n12 3nn) F M75 1 5h7 F C E 5(n2n 11n) F MbT 1b5h7 F B E 4(n3n 12n) G 65 1 5 6 G D E 5(n4n 31n) 15 16. C 65 5 1 6 G C A 8(*12 *3*) #16 516 Q65 D 95 9 1 5 E D A 5(n1n 3n2) D min b3 1 5 F D A 6(n1n 2n1) F M73 1h7 3 F E A 5(n2n n12) F 65 1 5 6 F C D 3(n4n 31n) F di 1b5b3 F B Ab 8(3n1 n2n) F di b3b5 1 AbB F 6(n43 n1n) G M75 1 5h7 G D F# 7(n2n 11n) G 65 1 5 6 G D E 5(n4n 31n) G MbT 1b5h7 G C#F# 6(n3n 12n) Bb M75 5 1h7 F BbA 6(n12 nn1) Bb 65 6 5 1 G F Bb 6(n3n n12) C 65 5 1 6 G C A 8(n12 n3n) 16 17. A 65 6 5 1 F#E A 7(*1* 34*) #17 651 Q65 B di b5b3 1 F D B 6(n1n 2n3) B 7bT b5 1b7 F B A 4(n3n 1n3) D M73 3 1h7 F#D C# 10(2n2 nn1) D min b3 1 5 F D A 6(n1n 2n1) D 65 6 1 5 B D A 4(1nn 4n3) E min b3 1 5 G E B 8(n1n 2n1) E 65 6 1 5 C#E B 5(2nn n14) E 73 b7 1 3 D E G# 5(3nn n11) G 95 1 5 9 G D A 6(n3n 2n1) G 93 1 3 9 G B A 6(n33 nn1) G di 1b5b3 G DbBb 6(n3n 1n2) A 65 6 5 1 GbE A 7(n1n 34n) 17 18. F maj 1 5 3 F C A 5(*2* 1*2) #18 153 Qmaj G 93 1 3 9 G B A 8(n11 n3n) G 7bT b7b5 1 F DbG 4(n3n 3n1) Bb 96T 6 9 1 G C Bb 7(n23 nn1) Bb 73 1 3b7 BbD Ab 11(n11 3nn) Bb MbT b5 1h7 E BbA 5(n13 nn2) C 95 9 1 5 D C G 3(n1n 3n2) C 65 5 1 6 G C A 8(n12 n3n) C 7bT b5 1b7 GbC Bb 5(n3n 1n3) Eb M75 1h7 5 EbD Bb 4(n1n 4n4) Eb 65 1 6 5 EbC Bb 7(2n3 nn1) F maj 1 5 3 F C A 5(n2n 1n2) 18 19. D maj 3 1 5 F#D A 6(*2* 2*1) #19 315 Qmaj E M73 1h7 3 E D#G# 4(n2n n12) E 65 1 6 5 E C#B 8(2n3 nn1) G 93 1 3 9 G B A 6(n33 nn1) G 96T 1 6 9 G E A 8(n1n 23n) G 9b3 1b3 9 G BbA 6(n32 nn1) A maj 5 3 1 E C#A 5(n1n 2n2) A 95 5 9 1 E B A 4(n2n 1n3) A 73 b7 3 1 G C#A 8(n13 n3n) C 95 5 9 1 G D C 7(n2n 1n3) C M75 5 1h7 G C B 8(n12 nn1) D maj 3 1 5 F#D A 6(n2n 2n1) 19 20. Bb maj 5 3 1 F D Bb 6(*1* 2*2) #20 531 Qmaj C 9b3 b3 9 1 EbD C 7(2nn 1n3) C 73 3 1b7 E C Bb 7(3n3 nn1) Eb maj 3 1 5 G EbBb 7(n2n 2n1) Eb 93 9 1 3 F EbG 6(n1n 33n) Eb 96T 9 1 6 F EbC 6(n1n 3n4) F maj 1 5 3 F C A 5(n2n 1n2) F 95 1 5 9 F C G 4(n3n 2n1) F 73 1b7 3 F EbA 4(n3n n13) Ab 73 b7 3 1 GbC Ab 7(n13 n3n) Ab 65 6 5 1 F EbAb 4(n3n n12) Bb maj 5 3 1 F D Bb 6(n1n 2n2) 20 21. F min 1 5b3 F C Ab 5(*2* 1*1) #21 15N Qmin G 65 6 5 1 E D G 3(n3n n12) G di b3b5 1 BbDbG 2(2nn n13) Bb min 5b3 1 F DbBb 6(n1n 1n2) Bb 9b3 b3 9 1 DbC Bb 5(2nn 1n3) Bb 73 1 3b7 BbD Ab 3(1nn n13) C 95 9 1 5 D C G 3(n1n 3n2) C min b3 1 5 EbC G 4(n1n 2n1) C 73 3 1b7 E C Bb 7(3n3 nn1) Eb 93 9 1 3 F EbG 4(n3n n11) Eb min b3 5 1 GbBbEb 7(n11 2nn) F min 1 5b3 F C Ab 5(n2n 1n1) 21 22. D min b3 1 5 F D A 6(*1* 2*1) #22 N15 Qmin E 95 9 1 5 GbE B 5(n3n n14) E 73 1b7 3 E D Ab 3(n3n n13) G 93 1 3 9 G B A 6(n33 nn1) G 9b3 1b3 9 G BbA 6(n32 nn1) G 65 6 5 1 E D G 3(n3n n12) A 95 5 9 1 E B A 4(n2n 1n3) A 65 6 5 1 GbE A 7(n1n 34n) A 7bT b7b5 1 G EbA 6(n3n 3n1) C 95 5 9 1 G D C 7(n2n 1n3) C MbT b5 1h7 GbC B 5(n3n 1n4) D min b3 1 5 F D A 6(n1n 2n1) 22 23. A min 5b3 1 E C A 5(*1* 1*2) #23 5N1 Qmin B 93 3 9 1 D#C#B 6(3nn 1n3) B aug 3 1+5 D#B G 4(n1n 1n1) D 93 9 1 3 E D F# 3(n3n n11) D 65 1 6 5 D B A 6(2n3 nn1) D 73 3b7 1 F#C D 7(n13 1nn) E min 1 5b3 E B G 4(n2n 1n1) E 65 1 6 5 E C#B 5(n1n 2n4) E 73 1b7 3 E D G# 3(n3n n13) G 95 5 1 9 D G A 3(n12 nn4) G 93 3 9 1 B A G 2(3nn 1n3) A min 5b3 1 E C A 5(n1n 1n2) 23 24. E 9M 1 9h7 E F#D# 3(*31 *2*) #24 19M Q9M F# 95 9 1 5 G#F#C# 9(n1n 3n2) F# 9b3 b3 1 9 A F#G# 9(n2n 31n) A 93 9 1 3 B A C# (n0n 22n) A 73 1b7 3 A G C# 8(n3n n13) A MbT 1h7b5 A G#D# (2nn 1n0) B 95 9 1 5 C#B F# 2(n1n 3n2) B M73 1h7 3 B A#D# 3(2nn 12n) B 65 1 5 6 B F#G# 3(2n1 nn3) D min b3 5 1 F A D 6(n11 2nn) D 65 6 5 1 B A D 2(3nn 12n) E 9M 1 9h7 E F#D# 3(n31 n2n) 24 25. Bb 9M 9 1h7 C BbA 3(3** 1*4) #25 91M Q9M Bb 9M 9 1h7 C BbA 5(1n3 nn2) C M75 1h7 5 C B G 4(2nn 1n1) C min 1b3 5 C EbG 4(2nn n11) Eb 95 1 5 9 EbBbF 2(n3n 2n1) Eb 93 1 9 3 EbF G 4(n1n n31) Eb aug 1+5 3 EbB G 4(n1n 1n1) F 93 9 1 3 G F A 8(n1n 33n) F 65 5 1 6 C F D (n12 n3n) F 73 1b7 3 F EbA 4(n3n n13) Ab min b3 5 1 B EbAb 4(1nn n12) Ab 65 6 5 1 F EbAb 4(n3n n12) Bb 9M 9 1h7 C BbA 3(3nn 1n4) 25 26. F 96T 1 6 9 F D G 6(*1* 23*) #26 169 Q96T G 96T 6 9 1 E A G 4(n23 nn1) G di b3b5 1 BbDbG 10(n21 3nn) Bb 95 5 9 1 F C Bb 5(n2n 1n3) Bb M73 1 3h7 BbD A 10(n22 n1n) Bb M75 5 1h7 F BbA 6(n12 nn1) C 93 3 9 1 E D C 9(1n3 nn1) C 9b3 b3 9 1 EbD C 7(2nn 1n3) C 7bT b5 1b7 GbC Bb 5(n3n 1n3) Eb 96T 9 1 6 F EbC 8(3nn 1n2) Eb min b3 1 5 GbEbBb 7(n1n 2n1) F 96T 1 6 9 F D G 6(n1n 23n) 26 27. A 96T 6 9 1 F#B A 7(*12 *4*) #27 691 Q96T B 93 3 1 9 D#B C# 2(n3n 31n) B di b5 1b3 F B D 6(n13 2nn) D 95 9 1 5 E D A 3(n3n n14) D 96T 9 6 1 E B D 3(n3n 21n) D 9b3 b3 1 9 F D E 5(n2n 31n) E 93 9 1 3 F#E G# 5(n3n n11) E M73 1h7 3 E D#G# 4(n2n n12) E 7bT 1b5b7 E A#D 5(n13 3nn) G 96T 1 6 9 G E A 8(n1n 23n) A 96T 6 9 1 F#B A 7(n12 n4n) 27 28. C 96T 9 1 6 D C A 3(*1* 3*4) #28 916 Q96T D 93 1 3 9 D F#E 3(n11 n3n) D M73 1h7 3 D C#F# 2(n2n n12) F 95 1 5 9 F C G 4(n3n 2n1) F 93 9 1 3 G F A 8(n1n 33n) F 73 b7 1 3 EbF A 4(n1n n33) G 93 1 3 9 G B A 8(n11 n3n) G 65 5 6 1 D E G 3(n1n n32) G 73 b7 3 1 F B G 6(n13 n3n) Bb min b3 5 1 DbF Bb 6(1nn n12) Bb MbT b5 1h7 E BbA 5(n13 nn2) C 96T 9 1 6 D C A 3(n1n 3n4) 28 Series 28 Dominant Chords 29. D 73 1b7 3 D C F# 5(3** 13*) #29 173 Q73 G maj 5 3 1 D B G 3(n1n 2n2) G min 5b3 1 D BbG 3(n1n 1n2) G 9M 9 1h7 A G F# (2nn 0n3) A 93 1 3 9 A C#B 8(n33 nn1) A 9M 1 9h7 A B G# 8(n31 n2n) C min b3 1 5 EbC G 4(n1n 2n1) D 73 1b7 3 D C F# 5(3nn 13n) 29 30. A 73 b7 3 1 G C#A 4(**1 3*3) #30 731 Q73 B 93 3 9 1 D#C#B 6(3nn 1n3) B maj 5 3 1 F#D#B 7(n1n 2n2) G M73 1 3h7 G B F# 7(n22 n1n) G M75 1 5h7 G D F# 7(n2n 11n) G 65 1 5 6 G D E 5(n4n 31n) D maj 3 1 5 F#D A 6(n2n 2n1) D 96T 9 1 6 E D B 5(n1n 3n4) A 73 b7 3 1 G C#A 4(nn1 3n3) 30 31. Bb 73 3 1b7 D BbAb 5(3*3 **1) #31 317 Q73 Eb 95 1 5 9 EbBbF 2(n3n 2n1) Eb 65 1 5 6 EbBbC (n4n 31n) Eb min 1 5b3 EbBbGb 3(n2n 1n1) F 93 1 3 9 F A G 4(n33 nn1) F 65 6 5 1 D C F 3(n1n 34n) Ab maj 5 3 1 EbC Ab 4(n1n 2n2) Bb 73 3 1b7 D BbAb 5(3n3 nn1) 31 32. D di 1b5b3 D AbF 5(3*1 *2*) #32 1iN Qdi D di 1b5b3 D AbF 7(13n 4nn) E 65 6 5 1 C#B E 6(1n3 4nn) G M73 3 1h7 B G Gb 3(2n2 nn1) G 73 3 1b7 B G F 2(3n3 nn1) A 95 9 1 5 B A E 4(1n3 n2n) A 65 5 1 6 E A Gb 9(12n 3nn) D di 1b5b3 D AbF 5(3n1 n2n) 32 33. D di b3 1b5 F D Ab 6(*1* 24*) #33 N1i Qdi E M75 1h7 5 E D#B 8(2nn 1n1) G 95 1 5 9 G D A 6(n3n 2n1) A M73 1 3h7 A C#G# 9(n22 n1n) A 95 5 9 1 E B A 4(n2n 1n3) C 93 3 9 1 E D C 7(3nn 1n3) D di b3 1b5 F D Ab 6(n1n 24n) 33 34. D aug 1+5 3 D A#F# 3(*1* 1*1) #34 1U3 Qaug E 9b3 b3 1 9 G E F# 7(n2n 31n) E M75 1 5h7 E B D# 4(n2n 11n) G 9b3 1b3 9 G BbA 6(n32 nn1) G 95 5 9 1 D A G 2(n2n 1n3) Ab 9b3 b3 9 1 B BbAb 3(2nn 1n3) Ab min 5b3 1 EbB Ab 8(1n1 n2n) D aug 1+5 3 D A#F# 3(n1n 1n1) 34 35. D 7bT 1b7b5 D C G# 3(*1* 3*3) #35 17i Q7bT G 93 1 3 9 G B A 6(n33 nn1) G 9b3 1b3 9 G BbA 6(n32 nn1) A M73 3 1h7 C#A G# 5(2n2 nn1) A 9b3 b3 9 1 C B A 4(2nn 1n3) A 95 5 9 1 E B A 4(n2n 1n3) D 7bT 1b7b5 D C Ab 3(n1n 3n3) 35 36. A 7bT b5 1b7 EbA G 6(3*1 *3*) #36 i17 Q7bT D 93 9 1 3 E D Gb 5(n1n 33n) D M73 1h7 3 D C#F# 2(n2n n12) D maj 1 5 3 D A F# 6(2n1 n2n) D 96T 1 6 9 D B E 3(n1n 23n) E 93 1 3 9 E G#F# 3(n33 nn1) E 95 1 5 9 E B F# 3(n3n 2n1) G 65 6 5 1 E D G 5(n1n 34n) A 7bT b5 1b7 EbA G 6(3n1 n3n) 36 37. A 7bT b7b5 1 G EbA 6(*3* 3*1) #37 7i1 Q7bT D M73 3 1h7 F#D C# 10(2n2 nn1) D 9b3 b3 1 9 F D E 5(n2n 31n) D min b3 1 5 F D A 6(n1n 2n1) E 9b3 b3 1 9 G E F# 7(n2n 31n) G M73 1h7 3 G F#B 7(n2n n12) G 9b3 1b3 9 G BbA 6(n32 nn1) A 7bT b7b5 1 G D#A 6(n3n 3n1) 37 38. A MbT 1b5h7 A D#G# 8(*3* 12*) #38 1iM QMbT B 93 1 3 9 B D#C# 10(n33 nn1) B 9b3 1b3 9 B D C# 10(n32 nn1) B 65 1 5 6 B F#G# 9(n4n 31n) D 65 5 1 6 A D B 10(n12 n3n) E 93 9 1 3 F#E G# 7(n1n 33n) E 65 5 1 6 B E C# 4(12n 3nn) A MbT 1b5h7 A D#G# 8(n3n 12n) 38 39. D MbT b5 1h7 G#D C# 7(*3* 1*4) #39 i1M QMbt E 9b3 b3 1 9 G E F# 7(n2n 31n) E min b3 1 5 G E B 8(n1n 2n1) E 96T 9 1 6 F#E C# 7(n1n 3n4) G M73 1h7 3 G F#B 7(n2n n12) G 95 1 5 9 G D A 6(n3n 2n1) A 95 1 5 9 A E B 8(n3n 2n1) A maj 1 5 3 A E C# 9(n2n 1n2) D MbT b5 1h7 G#D C# 7(n3n 1n4) 39 Series 101 of Series 140 Calling Chords of the Major Seventh 1. F M7 1 3 5h7 F A C E 5(*22 11*) #40 135M QM7 Bb 11 1 4 3 5 BbEbD F 2(23n n21) Bb 11 4 1 3 5 EbBbD F 4(n14 43n) Bb 9 9 1 3 5 C BbD F (n1n 332) Bb mi6 5 1b3 6 F BbDbG 6(n12 13n) Bb 7 5 1b7 3 F BbAbD 9(23n n13) Bb 7 5b7 1 3 F AbBbD 3(n43 11n) C 9 5 1 3 9 G C E D 8(n12 2n4) C 96 9 6 1 3 D A C E (n3n 211) C 7 5b7 1 3 G BbC E 5(n43 11n) Eb mi6 b3 5 6 1 GbBbC Eb 4(n44 21n) Eb 9 9 5 3 1 F BbG Eb 10(12n 3n3) Eb 9 9 5 1 3 F BbEbG 6(n12 33n) Eb 96 9 3 6 1 F G C Eb 4(n31 21n) F M7 1 3 5h7 F A C E 5(n22 11n) 40 2. C M7 1 5 3h7 C G E B 5(14* *14) #41 153M QM7 D 11 1 4 3 5 D G F#A 6(23n n21) D 9 1 3 9 5 D F#E A 3(n11 n34) D mi9 1b3 9 5 D F E A 6(21n 4n1) D 96 1 3 9 6 D GbE B 7(11n 3n2) D 7 b7 3 1 5 C F#D A 5(13n 3n2) F M7 5 1h7 3 C F E A 5(12n n12) F 6 5 6 1 3 C D F A 2(421 1nn) F 9 5 9 1 3 C G F A 4(2n1 n33) F 96 6 9 1 3 D G F A 6(23n n11) F 9M7 1 9h7 3 F G E A 4(n31 n23) G M7 5 1h7 3 D G F#B 7(12n n12) G 11 4 1 5 3 C G D B 5(14n 3n4) G 7 5 1b7 3 D G F B 6(23n n13) Bb 6 3 6 5 1 D G F Bb 6(23n n12) Bb 7 3b7 5 1 D AbF Bb 5(3n1 n23) C M7 1 5 3h7 C G E B 5(14n n14) 41 3. Eb M7 1 3h7 5 EbG D Bb 8(114 *4*) #42 13M5 QM7 Eb M7 1 3h7 5 EbG D Bb 4(n11 4n4) F 11 1 4 5 3 F BbC A 9(231 n2n) F 11 4 1 5 3 BbF C A 3(14n 3n4) F 9 1 9 5 3 F G C A 4(n31 2n3) Ab 6 5 1 3 6 EbAbC F 4(n12 23n) Ab 11 5 1 4 3 EbAbDbC 8(123 nn2) Ab 9 5 1 3 9 EbAbC Bb 4(n12 2n4) Ab 96 6 1 3 9 F AbC Bb 5(n21 1n3) Ab 7 5 1 3b7 EbAbC Gb 3(n23 3n1) Bb 9 5 9 3 1 F C D Bb 7(4n3 1n1) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Bb 9 9 5 1 3 C F BbD 9(nn1 233) Bb 7 5b7 3 1 F AbD Bb 5(n21 3n3) Db M7 3 5 1h7 F AbDbC 9(212 nn1) Db 6 3 5 1 6 F AbDbBb 5(n21 2n3) Db 9 9 5 1 3 EbAbDbF 4(n12 33n) Db mi6 b3 5 1 6 E AbDbBb 5(n11 2n3) Db 94 9 4 1 3 EbGbDbF 6(32n 11n) Db 7 3 5 1b7 F AbDbB 8(323 nn1) Eb M7 1 3h7 5 EbG D Bb 4(n11 4n4) 42 4. C M7 1h7 3 5 C B E G 4(2** 121) #43 1M73 QM7 D 11 4 5 1 3 G A D F# 6(n31 22n) D 9 1 5 9 3 D A E F# 3(n14 n31) D 96 1 6 9 3 D B E F# 3(n1n 231) D 94 1 4 9 3 D G E F# 7(12n 31n) D 7 b7 5 1 3 C A D F# (n1n 233) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 9 5 3 1 9 C A F G 4(2n3 n31) F 9M7 1 3h7 9 F A E G 4(n33 n21) F 7 5 3b7 1 C A EbF 2(4nn 131) G 96 9 3 6 1 A B E G 8(n31 21n) G 7 5 3b7 1 D B F G 4(4nn 131) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 6 3 1 5 6 D BbF G 4(4n4 n31) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) Bb 96 9 1 3 6 C BbD G (n1n 334) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) Bb 7 3 1 5b7 D BbF Ab 5(3n3 n21) C M7 1h7 3 5 C B E G 4(2nn 121) 43 5. D M7 1 5h7 3 D A C#F# 6(2*1 12*) #44 15M3 QM7 E 11 1 4 5 3 E A B G# 4(n23 1n2) E 9 1 3 5 9 E G#B F# 3(n33 2n1) E 96 1 3 6 9 E G#C#F# 5(n11 23n) E 7 b7 3 5 1 D G#B E 3(n13 23n) G M7 5 1 3h7 D G B F# 3(n12 2n1) G 6 5 6 3 1 D E B G 5(314 n4n) G 9 5 9 3 1 D A B G 4(4n3 1n1) A M7 5 1 3h7 E A C#G# 5(n12 2n1) A 11 4 1 3 5 D A C#E 3(n14 43n) A 9 5 1 3 9 E A C#B 5(n12 2n4) A 9 9 1 3 5 B A C#E 4(1n3 32n) A mi9 5 1b3 9 E A C B 5(n12 1n4) A 9M7 9 1 3h7 B A C#G# 4(1n3 3n2) A 7 5 1 3b7 E A C#G 4(n23 3n1) C 6 3 6 1 5 E A C G 4(n23 2n1) C mi6 b3 6 1 5 EbA C G 4(n13 2n1) C 9 9 3 1 5 D E C G 5(31n 14n) C 96 9 6 1 3 D A C E 5(3n2 11n) C 7 3b7 1 5 E BbC G 5(n13 14n) D M7 1 5h7 3 D A C#F# 6(2n1 12n) 44 6. A M7 3 1 5h7 C#A E G# 5(2*2 *11) #45 315M QM7 B M7 1h7 3 5 B A#D#F# 3(2nn 121) B 11 1 4 3 5 B E D#F# 3(23n n21) B 11 4 1 3 5 E B D#F# 5(n14 43n) B 9 9 1 3 5 C#B D#F# 6(1n3 32n) B 96 9 1 3 6 C#B D#G# 6(1n3 34n) B 7 1b7 3 5 B A D#F# 2(3nn 132) D 6 1 5 6 3 D A B F# 4(4n3 14n) D mi6 1 5b3 6 D A F B 6(2n1 n13) D 9 1 5 9 3 D A E F# 7(14n 31n) D 96 1 6 9 3 D B E F# 7(1n2 31n) D 7 1 5b7 3 D A C F# 5(3n2 13n) E 11 5 4 1 3 B A E G# 4(1n3 n22) E 9 5 9 1 3 B F#E G# 3(2n1 n33) E 96 6 9 1 3 C#F#E G# 5(23n n11) E 7 b7 5 1 3 D B E G# 7(1n2 33n) G 6 5 3 6 1 D B E G 7(1n2 32n) G mi6 5b3 6 1 D BbE G 7(1n1 32n) G 11 4 3 5 1 C B D G 5(1n4 34n) G 9 5 9 3 1 D A B G 4(4n3 1n1) G 7 5 3b7 1 D B F G 4(4nn 131) A M7 3 1 5h7 C#A E G# 5(2n2 n11) 45 7. Bb M7 3 5 1h7 D F BbA 6(212 **1) #46 351M QM7 C M7 1 3h7 5 C E B G 5(114 n4n) C 9 9 3 1 5 D E C G 5(31n 14n) C 7 1 3b7 5 C E BbG 3(33n 1n2) Eb mi6 1b3 5 6 EbGbBbC 5(433 1nn) Eb 9 1 9 5 3 EbF BbG 6(312 n3n) F M7 5 1h7 3 C F E A 5(12n n12) F 11 5 1 4 3 C F BbA 5(123 nn2) Ab 6 5 6 3 1 EbF C Ab 6(314 n4n) Ab mi6 5 6b3 1 EbF B Ab 6(313 n4n) Ab 7 5b7 3 1 EbGbC Ab 7(213 n3n) Bb M7 3 5 1h7 D F BbA 6(212 nn1) 46 8. G M7 5 1 3h7 D G B F# 7(122 *1*) #47 513M QM7 A 11 4 1 3 5 D A C#E 7(144 3nn) A 9 3 1 9 5 C#A B E 4(3n3 12n) A mi9 b3 1 9 5 C A B E 4(2n3 12n) A 7 3b7 1 5 C#G A E 6(131 4nn) C M7 1 5h7 3 C G B E 4(2n1 12n) C 6 6 5 1 3 A G C E 2(1n3 44n) C mi6 b3 5 1 6 EbG C A 8(112 n3n) C 9 9 5 1 3 D G C E 7(123 3nn) C 96 9 6 1 3 D A C E 5(3n2 11n) D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 11 1 4 5 3 D G A F# 6(231 n2n) D 9 1 9 5 3 D E A F# 5(312 n3n) D 9 1 5 9 3 D A E F# 7(14n 31n) D 9M7 1 9h7 3 D E C#F# 5(31n 23n) D 7 1 5b7 3 D A C F# 5(3n2 13n) F mi6 6b3 5 1 D AbC F 3(n13 34n) F 11 4 3 5 1 BbA C F 3(1n4 34n) F 9 3 9 5 1 A G C F 2(1n3 45n) F 7 b7 3 5 1 EbA C F 8(132 3nn) G M7 5 1 3h7 D G B F# 7(122 n1n) 47 9. F M7 5 1h7 3 C F E A 5(12* *12) #48 51M3 QM7 G 11 4 1 5 3 C G D B 5(14n 3n4) G 9 3 1 5 9 B G D A 4(1n1 4n3) G 96 3 1 6 9 B G E A 4(1n1 n23) G 7 3b7 5 1 B F D G 2(3n1 n23) Bb M7 1 5 3h7 BbF D A 3(14n n14) Bb M7 3 5 1h7 D F BbA 6(212 nn1) Bb mi6 b3 5 6 1 DbF G Bb 3(442 1nn) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) C M7 1 5 3h7 C G E B 5(14n n14) C 11 1 4 5 3 C F G E 4(231 n2n) Eb 6 6 3 1 5 C G EbBb 4(2n1 n14) Eb 96 6 9 1 3 C F EbG 4(23n n11) Eb 7 b7 3 1 5 DbG EbBb 6(13n 3n2) F M7 5 1h7 3 C F E A 5(12n n12) 48 Calling Chords of the Sixth 1. A 6 1 3 5 6 A C#E F# 7(*44 31*) #49 1356 Q6 B 11 4 1 3 5 E B D#F# 5(n14 43n) B 11 1 4 3 5 B E D#F# 3(23n n21) E 11 4 5 1 3 A B E G# 8(n31 22n) E mi9 b3 5 1 9 G B E F# 7(n22 31n) E 7 3b7 1 5 G#D E B 9(n13 14n) A 6 1 3 5 6 A C#E F# 7(n44 31n) 49 2. D 6 1 3 6 5 D F#B A 7(112 *4*) #50 1365 Q6 E 11 1 4 5 3 E A B G# 8(231 n2n) E 11 4 1 5 3 A E B G# 2(14n 3n4) E 9 1 9 5 3 E F#B G# 7(312 n3n) E 96 6 9 1 3 C#F#E G# 5(23n n11) A 9 3 5 9 1 C#E B A 4(32n 1n3) A mi9 b3 5 9 1 C E B A 4(22n 1n3) A 7 3b7 5 1 C#G E A 4(3n1 n23) D 6 1 3 6 5 D F#B A 7(112 n4n) 50 3. C 6 1 5 3 6 C G E A 4(2*1 *23) #51 1536 Q6 D 11 1 4 3 5 D G F#A 6(23n n21) D 9 1 3 9 5 D F#E A 7(11n 34n) D mi9 1b3 9 5 D F E A 6(21n 4n1) D 7 b7 3 1 5 C F#D A 5(13n 3n2) G 11 4 1 5 3 C G D B 5(14n 3n4) G 9 3 1 5 9 B G D A 4(1n1 4n3) G 96 3 1 6 9 B G E A 4(1n1 n23) C 6 1 5 3 6 C G E A 4(2n1 n23) 51 4. F 6 1 5 6 3 F C D A 7(4*3 14*) #52 1563 Q6 G 11 4 3 5 1 C B D G 5(1n4 34n) G 9 1 3 5 9 G B D A 6(n33 2n1) G mi9 1b3 5 9 G BbD A 6(n32 2n1) G 7 b7 3 5 1 F B D G 6(n13 23n) C M7 3 1 5h7 E C G B 8(2n2 n11) G 9 1 3 5 9 G B D A 6(n33 2n1) C mi9 b3 1 9 5 EbC D G 7(2n3 12n) C 9M7 3 1 9h7 E C D B 7(3n3 1n2) F 6 1 5 6 3 F C D A 7(4n3 14n) 52 5. Bb 6 3 1 5 6 D BbF G 4(4*4 *31) #53 3156 Q6 C M7 1h7 3 5 C B E G 4(2nn 121) C 11 1 4 3 5 C F E G 4(23n n21) C 11 4 1 3 5 F C E G 6(n14 43n) C 9 9 1 3 5 D C E G 7(1n3 32n) C 7 1b7 3 5 C BbE G 3(3nn 132) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 9 5 3 1 9 C A F G 4(2n3 n31) F 7 b7 3 1 5 EbA F C 8(13n 3n2) Bb 6 3 1 5 6 D BbF G 4(4n4 n31) 53 6. A 6 3 5 1 6 C#E A F# 5(212 *3*) #54 3516 Q6 B M7 1 3h7 5 B D#A#F# 4(114 n4n) B 9 9 3 1 5 C#D#B F# 4(31n 14n) B 96 9 3 6 1 C#D#G#B (n20 10n) B 7 1 3b7 5 B D#A F# 2(33n 1n2) E 11 5 1 4 3 B E A G# 4(123 nn2) E 9 5 1 3 9 B E G#F# 4(122 n4n) E mi9 5 1b3 9 B E G F# 4(121 n4n) G 96 9 3 6 1 A B E G 8(n31 21n) A 6 3 5 1 6 C#E A F# 5(212 n3n) 54 7. C 6 3 6 1 5 E A C G 8(232 *1*) #55 3615 Q6 D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 11 4 5 1 3 G A D F# 6(n31 22n) D 11 5 1 4 3 A D G F# 2(123 nn2) D 9 9 5 1 3 E A D F# 9(123 3nn) D 94 9 4 1 3 E G D F# 7(32n 11n) D 7 1 5b7 3 D A C F# 5(3n2 13n) F mi6 1b3 5 6 F AbC D 3(n43 31n) G 9 5 9 3 1 D A B G 4(4n3 1n1) C 6 3 6 1 5 E A C G 4(n23 2n1) 55 8. Bb 6 3 6 5 1 D G F Bb 6(23* *12) #56 3651 Q6 C M7 1 5 3h7 C G E B 5(14n n14) C 9 9 5 3 1 D G E C 7(12n 3n3) C 96 9 1 3 6 D C E A 7(1n3 34n) F 9 5 9 1 3 C G F A 4(2n1 n33) Ab 94 4 1 3 9 DbAbC Bb 5(2n1 1n3) Bb 6 3 6 5 1 D G F Bb 6(23n n12) 56 9. A 6 5 1 3 6 E A C#F# 5(*12 23*) #57 5136 Q6 B 11 4 1 3 5 E B D#F# 7(3n2 21n) B 9 3 1 9 5 D#B C#F# 6(3n3 12n) B mi9 b3 1 9 5 D B C#F# 6(2n3 12n) B 7 3b7 1 5 D#A B F# 4(n13 14n) E M7 1 3h7 5 E G#D#B 9(114 n4n) E 11 1 4 5 3 E A B G# 8(231 n2n) E 9 1 3 5 9 E G#B F# 7(332 n1n) E mi9 1b3 5 9 E G B F# 7(322 n1n) E 7 1 3b7 5 E G#D B 7(33n 1n2) A 6 5 1 3 6 E A C#F# 5(n12 23n) 57 10. F 6 5 3 6 1 C A D F 5(1*2 32*) #58 5361 Q6 G M7 3 1 5h7 B G D F# 3(2n2 n11) G 11 4 3 5 1 C B D G 5(1n4 34n) G 9 3 9 5 1 B A D G 4(1n3 45n) G 7 3 1 5b7 B G D F 2(3n3 n21) C 9 1 5 9 3 C G D E 5(14n 31n) F 6 5 3 6 1 C A D F 5(1n2 32n) 58 11. C 6 5 6 1 3 G A C E 5(*42 11*) #59 5613 Q6 D 11 4 5 1 3 G A D F# 6(n31 22n) D mi9 b3 5 1 9 F A D E 5(n22 31n) D 96 3 1 6 9 F#D B E 11(1n1 n23) G M7 1 5 3h7 G D B F# (03n n03) C 6 5 6 1 3 G A C E 9(421 1nn) 59 12. G 6 5 6 3 1 D E B G 5(314 *4*) #60 5631 Q6 A M7 3 5 1h7 C#E A G# 5(212 nn1) A 9 3 5 9 1 C#E B A 4(32n 1n3) A mi9 b3 5 9 1 C E B A 4(22n 1n3) A 9M7 3 1 9h7 C#A B G# 4(3n3 1n2) A 7 3 5 1b7 C#E A G 4(323 nn1) D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 9 1 9 5 3 D E A F# 5(312 n3n) D 9M7 1 9h7 3 D E C#F# 5(31n 23n) D 7 1 5b7 3 D A C F# 5(3n2 13n) G 6 5 6 3 1 D E B G 5(314 n4n) 60 13. C 6 6 1 3 5 A C E G 8(*32 21*) #61 6135 Q6 D 11 5 1 4 3 A D G F# 2(123 nn2) D 11 5 4 1 3 A G D F# 2(1n3 n22) D 96 1 6 9 3 D B E F# 7(1n2 31n) D 7 5b7 1 3 A C D F# 7(n43 11n) G 7 5 3b7 1 D B F G 4(4nn 131) C 6 6 1 3 5 A C E G 8(n32 21n) 61 14. F 6 6 1 5 3 D F C A 6(214 **1) #62 6153 Q6 G 11 5 1 4 3 D G C B 7(123 nn2) G 9 5 1 3 9 D G B A 7(122 n4n) G mi9 5 1b3 9 D G BbA 7(121 n4n) G 94 4 1 3 9 C G B A 4(2n1 1n3) G 7 5b7 3 1 D F B G 2(n21 3n3) C 9 9 3 1 5 D E C G 5(31n 14n) F 6 6 1 5 3 D F C A 6(214 nn1) 62 15. Eb 6 6 3 1 5 C G EbBb 4(2*1 *14) #63 6315 Q6 F M7 5 1h7 3 C F E A 5(12n n12) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 9 5 9 1 3 C G F A 4(2n1 n33) F 7 5 1b7 3 C F EbA 4(23n n13) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Db 94 1 4 9 3 DbGbEbF 6(12n 31n) Eb 6 6 3 1 5 C G EbBb 4(2*1 *14) 63 16. F 6 6 5 1 3 D C F A 7(1*3 44*) #64 6513 Q6 G 11 5 4 1 3 D C G B 7(1n3 n22) G 9 5 3 1 9 D B G A 6(2n3 n31) G mi9 5b3 1 9 D BbG A 6(2n2 n31) G 96 1 3 6 9 G B E A 8(n11 23n) G 9M7 1 3h7 9 G B F#A 6(n33 n21) G 7 5 3b7 1 D B F G 4(4nn 131) C M7 5 1 3h7 G C E B 8(n12 2n1) C 9 9 1 3 5 D C E G 7(1n3 32n) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) C 7 5 1 3b7 G C E Bb 7(n23 3n1) F 6 6 5 1 3 D C F A 7(1n3 44n) 64 Calling Chords of the Minor Sixth 1. F mi6 1b3 5 6 F AbC D 3(*43 31*) #65 1N56 Qmi6 G 96 6 1 3 9 E G B A 8(211 n3n) C M7 3 5 1h7 E G C B 8(212 nn1) C 11 4 5 1 3 F G C E 4(n31 22n) C mi9 b3 5 1 9 EbG C D 3(n22 31n) C 96 3 6 1 9 E A C D 3(n34 31n) C 7 3 5 1b7 E G C Bb 7(323 nn1) F mi6 1b3 5 6 F AbC D 3(n43 31n) 65 2. C mi6 1 5b3 6 C G EbA 4(2*1 *13) #66 15N6 Qmi6 D mi9 1b3 9 5 D F E A 6(21n 4n1) D 7 b7 3 1 5 C F#D A 5(13n 3n2) G M7 3 1 5h7 B G D F# 3(2n2 n11) G 11 4 1 5 3 C G D B 5(14n 3n4) G 96 3 1 6 9 B G E A 4(1n1 n23) G 7 3 1 5b7 B G D F 2(3n3 n21) C mi6 1 5b3 6 C G EbA 4(2n1 n13) 66 3. D mi6 1 6b3 5 D B F A 6(2*3 *11) #67 16N5 Qmi6 E 7 b7 5 1 3 D B E G# 7(1n2 33n) A 11 4 3 5 1 D C#E A 7(1n4 34n) A 7 3b7 5 1 C#G E A 4(3n1 n23) D mi6 1 6b3 5 D B F A 6(2n3 n11) 67 4. Bb mi6 b3 5 1 6 DbF BbG 6(112 *3*) #68 N516 Qmi6 C M7 1 3h7 5 C E B G 5(114 n4n) C 11 1 4 3 5 C F E G 4(23n n21) C 96 1 3 6 9 C E A D 5(112 3nn) C 96 9 3 6 1 D E A C 5(312 1nn) C 9M7 1 3h7 9 C E B D 3(33n 21n) C 7 1 3b7 5 C E BbG 3(33n 1n2) F M7 5 1 3h7 C F A E 5(122 n1n) F 11 5 1 4 3 C F BbA 5(123 nn2) F mi9 5 1b3 9 C F AbG 5(121 n4n) F 96 6 1 3 9 D F A G 6(211 n3n) F 7 5 1 3b7 C F A Eb 12(n23 3n1) Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) 68 5. C mi6 b3 6 1 5 EbA C G 8(132 *1*) #69 N615 Qmi6 D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 9M7 1 9h7 3 D E C#F# 5(31n 23n) D 7 1 5b7 3 D A C F# 5(3n2 13n) G 7 5b7 3 1 D F B G 6(213 n3n) C mi6 b3 6 1 5 EbA C G 4(n13 2n1) 69 6. G mi6 b3 5 6 1 BbD E G 8(*44 21*) #70 N561 Qmi6 A M7 1 3 5h7 A C#E G# 9(n22 11n) A 11 1 4 5 3 A D E C# 9(n23 1n2) A 96 1 3 9 6 A C#B F# 2(11n 3n2) A 7 1 3 5b7 A C#E G 8(n33 21n) D M7 5 1h7 3 A D C#F# 2(12n n12) D 7 5 1b7 3 A D C F# 13(23n n13) G mi6 b3 5 6 1 BbD E G 8(n44 21n) 70 7. A mi6 5 1b3 6 E A C F# 5(*12 13*) #71 51N6 Qmi6 B mi9 b3 1 9 5 D B C#F# 6(2n3 12n) B 7 3b7 1 5 D#A B F# 4(n13 14n) E M7 1 3 5h7 E G#B D# 4(n22 11n) E 11 1 4 5 3 E A B G# 8(231 n2n) E mi9 1b3 5 9 E G B F# 7(322 n1n) E 96 1 3 6 9 E G#C#F# 5(n11 23n) E 9M7 1 3h7 9 E G#D#F# 7(33n 21n) E 7 1 3 5b7 E G#B D 3(n33 21n) A mi6 5 1b3 6 E A C F# 5(n12 13n) 71 8. F mi6 5b3 6 1 C AbD F 5(1*1 32*) #72 5N61 Qmi6 G M7 3 1 5h7 B G D F# 3(2n2 n11) G 11 4 1 5 3 C G D B 5(14n 3n4) G 9M7 3 1 9h7 B G A F# 2(3n3 1n2) G 7 3 1 5b7 B G D F 2(3n3 n21) C 96 1 6 9 3 C A D E 5(1n2 31n) C 7 1 5b7 3 C G BbE 3(3n2 13n) F mi6 5b3 6 1 C AbD F 5(1n1 32n) 72 9. G mi6 5 6b3 1 D E BbG 5(313 *4*) #73 56N1 Qmi6 A M7 3 5 1h7 C#E A G# 5(212 nn1) A 11 4 5 1 3 D E A C# 5(312 2nn) A mi9 b3 5 9 1 C E B A 4(22n 1n3) A 7 3 5 1b7 C#E A G 4(323 nn1) G mi6 5 6b3 1 D E BbG 5(313 n4n) 73 10. Bb mi6 6 1b3 5 G BbDbF 6(*32 11*) #74 61N5 Qmi6 F 96 9 3 6 1 G A D F 6(n31 21n) F 7 b7 3 5 1 EbA C F 8(132 3nn) C 7 5b7 1 3 G BbC E 5(n43 11n) Bb mi6 6 1b3 5 G BbDbF 6(n32 11n) 74 11. Eb mi6 6 5 1b3 C BbEbGb 5(1*3 43*) #75 651N Qmi6 F mi9 5b3 1 9 C AbF G 4(2n2 n31) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) Eb mi6 6 5 1b3 C BbEbGb 5(1n3 43n) 75 12. F mi6 6b3 5 1 D AbC F 3(*13 34*) #76 6N51 Qmi6 G M7 5 1 3h7 D G B F# 7(122 n1n) G 11 5 1 4 3 D G C B 7(123 nn2) G 7 5 1 3b7 D G B F 2(n23 3n1) C 96 9 6 1 3 D A C E 5(3n2 11n) C 7 b7 5 1 3 BbG C E 3(1n2 33n) F mi6 6b3 5 1 D AbC F 7(133 4nn) 76 Calling Chords of the Eleventh 1. C 11 1 4 3 5 C F E G 4(23* *21) #77 1435 Q11 D 9 1 5 9 3 D A E F# 7(14n 31n) D 9 1 3 9 5 D F#E A 3(n11 n34) D mi9 1b3 9 5 D F E A 6(21n 4n1) D 7 b7 5 1 3 C A D F# 5(1n2 33n) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 11 5 1 4 3 C F BbA 5(123 nn2) F 9 5 1 3 9 C F A G 5(122 n4n) F 96 3 1 6 9 A F D G 2(1n1 n23) F 96 6 1 3 9 D F A G 6(211 n3n) F 94 4 1 3 9 BbF A G 2(2n1 1n3) F 7 5 1b7 3 C F EbA 4(23n n13) G 11 4 3 5 1 C B D G 5(1n4 34n) G 9 3 9 5 1 B A D G 4(1n3 45n) G 7 3b7 5 1 B F D G 2(3n1 n23) Bb M7 1 3 5h7 BbD F A 2(221 1nn) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 6 1 3 5 6 BbD F G 8(n44 31n) Bb 6 3 1 5 6 D BbF G 4(4n4 n31) Bb 6 1 5 3 6 BbF D G 2(2n1 n23) Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) Bb 9 3 9 5 1 D C F Bb 3(n1n 345) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) C 11 1 4 3 5 C F E G 4(23n n21) 77 2. D 11 1 4 5 3 D G A F# 6(231 *2*) #78 1453 Q11 E 9 1 3 5 9 E G#B F# 7(332 n1n) E mi9 1b3 5 9 E G B F# 7(322 n1n) E 96 6 1 3 9 C#E G#F# 5(211 n3n) G M7 5 1h7 3 D G F#B 7(12n n12) G M7 5 1 3h7 D G B F# 7(122 n1n) G 6 5 1 3 6 D G B E 7(122 3nn) G mi6 5 1b3 6 D G BbE 7(121 3nn) G 9M7 3 1 9h7 B G A F# 2(3n3 1n2) G 7 5 1 3b7 D G B F 6(233 n1n) A 7 3b7 1 5 C#G A E 6(131 4nn) C M7 1 3h7 5 C E B G 5(114 n4n) C M7 1 5h7 3 C G B E 4(2n1 12n) C 6 1 3 6 5 C E A G 5(112 n4n) C mi6 b3 5 6 1 EbG A C 5(442 1nn) C 9 9 3 1 5 D E C G 5(31n 14n) C 9 9 5 1 3 D G C E 7(123 3nn) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) C 7 1 5b7 3 C G BbE 3(3n2 13n) D 11 1 4 5 3 D G A F# 6(231 n2n) 78 3. C 11 4 1 3 5 F C E G 6(*14 43*) #79 4135 Q11 C 11 4 1 3 5 F C E G 8(3n2 21n) D 7 5b7 1 3 A C D F# 7(n43 11n) F M7 1 5h7 3 F C E A 9(2n1 12n) F M76 1 6h7 3 F D E A 9(2n3 12n) F 11 4 5 1 3 BbC F A 9(n31 22n) F 96 1 6 9 3 F D G A 10(1n2 31n) F 9M7 1 3h7 9 F A E G 8(33n 21n) F 7 1 5b7 3 F C EbA 8(3n2 13n) G mi9 b3 5 9 1 BbD A G 14(22n 1n3) G 96 9 3 6 1 A B E G 12(312 1nn) G 7 b7 3 5 1 F B D G 10(132 3nn) Bb M7 1 3 5h7 BbD F A 10(n22 11n) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb M7 5 1 3h7 F BbD A 10(122 n1n) Bb 6 1 3 5 6 BbD F G 8(n44 31n) Bb 6 3 1 5 6 D BbF G 4(4n4 n31) Bb 6 5 1 3 6 F BbD G 6(n12 23n) Bb 11 5 1 4 3 F BbEbD 10(123 nn2) Bb 9 3 9 5 1 D C F Bb 3(n1n 345) Bb 9 5 9 3 1 F C D Bb 7(4n3 1n1) Bb 7 5 1 3b7 F BbD Ab 5(n23 3n1) C 11 4 1 3 5 F C E G 6(n14 43n) 79 4. F 11 4 1 5 3 BbF C A 3(14* 3*4) #80 4153 Q11 G 96 3 6 1 9 B E G A 2(343 1nn) G 7 5b7 3 1 D F B G 6(213 n3n) Bb 6 1 5 3 6 BbF D G 2(2n1 n23) Bb mi6 1 5b3 6 BbF DbG 2(2n1 n13) Bb 9 1 5 9 3 BbF C D 3(14n 31n) Bb 96 1 3 9 6 BbD C G 3(11n 3n2) Bb 96 1 6 9 3 BbG C D 3(1n2 31n) Bb 94 1 4 9 3 BbEbC D 3(12n 31n) C 11 4 3 5 1 F E G C 6(n1n 434) C 9 9 3 1 5 D E C G 5(31n 14n) C mi9 b3 5 1 9 EbG C D 3(n22 31n) Bb M7 1 3h7 5 BbD A F 3(114 n4n) Eb M7 1 3h7 5 EbG D Bb 8(114 n4n) Eb 6 1 3 6 5 EbG C Bb 8(112 n4n) Eb mi6 5b3 6 1 BbGbC Eb 3(1n1 32n) Bb 9 9 3 1 5 C D BbF 3(31n 14n) Eb 9 9 3 1 5 F G EbBb 4(n31 n14) Eb 9 5 9 1 3 BbF EbG 2(2n1 n33) Eb 9M7 1 9h7 3 EbF D G 2(n31 n23) Eb 7 5 1b7 3 BbEbDbG 2(23n n13) F 11 4 1 5 3 BbF C A 3(14n 3n4) 80 5. Eb 11 4 5 1 3 AbBbEbG 7(*31 22*) #81 4513 Q11 F 9 5 3 1 9 C A F G 4(2n3 n31) F mi9 b3 5 1 9 AbC F G 8(n22 31n) F 96 1 3 6 9 F A D G 6(n11 23n) F 96 3 1 6 9 A F D G 2(1n1 n23) F 9M7 1 3h7 9 F A E G 8(33n 21n) F 7 5 3b7 1 C A EbF 2(4nn 131) Ab 11 4 3 5 1 DbC EbAb 6(1n4 34n) Ab 6 1 3 5 6 AbC EbF 6(n44 31n) Ab mi6 1b3 5 6 AbB EbF 6(n43 31n) Ab 9 1 9 5 3 AbBbEbC 7(n31 2n3) Ab 7 1 3 5b7 AbC EbGb 7(n33 21n) Bb 11 4 1 3 5 EbBbD F 4(n14 43n) Bb 11 4 5 1 3 EbF BbD 2(n31 22n) Bb 9 9 1 3 5 C BbD F 5(1n3 32n) Bb mi9 b3 1 5 9 DbBbF C 6(1n2 n14) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) Db M7 1h7 3 5 DbC F Ab 5(2nn 121) Db 6 3 6 1 5 F BbDbAb 9(232 n1n) Db 6 5 6 1 3 AbBbDbF 6(n42 11n) Db mi6 5 6b3 1 AbBbE Db 7(n31 3n4) Db 9 9 1 3 5 EbDbF Ab 4(n1n 332) Db 9 3 1 9 5 F DbEbAb 4(n3n 312) Db 9 5 1 3 9 AbDbF Eb 9(n12 2n4) Db 96 1 6 9 3 DbBbEbF 6(1n2 31n) Db 7 5b7 1 3 AbB DbF 6(n43 11n) Eb 11 4 5 1 3 AbBbEbG 7(n31 22n) 81 6. F 11 4 3 5 1 BbA C F 3(1*4 34*) #82 4351 Q11 G M7 5 1 3h7 D G B F# 3(n12 2n1) G M7 3 1 5h7 B G D F# 3(2n2 n11) G 9 3 9 5 1 B A D G 4(1n3 45n) G 7 5 1 3b7 D G B F 2(n23 3n1) Bb mi6 1 6b3 5 BbG DbF 2(2n3 n11) Bb 11 4 1 3 5 EbBbD F 6(3n2 21n) Bb 11 1 4 3 5 BbEbD F 2(23n n21) Bb 96 1 6 9 3 BbG C D 3(1n2 31n) Bb 7 1b7 3 5 BbAbD F (3nn 132) C 9 9 5 1 3 D G C E 7(123 3nn) C 96 9 6 1 3 D A C E 5(3n2 11n) C 7 b7 5 1 3 BbG C E 3(1n2 33n) Eb 6 1 5 6 3 EbBbC G 5(4n3 14n) Eb 6 5 3 6 1 BbG C Eb 3(1n2 32n) Eb 11 5 4 1 3 BbAbEbG 3(1n3 n22) Eb 9 5 3 1 9 BbG EbF 2(2n3 n31) Eb 9 9 5 1 3 F BbEbG 6(n12 33n) Eb 96 1 3 6 9 EbG C F 4(n11 23n) Eb 9M7 1 3h7 9 EbG D F 6(33n 21n) Eb 7 5 3b7 1 BbG DbEb (3nn 020) F 11 4 3 5 1 BbA C F 3(1n4 34n) 82 7. G 11 5 1 4 3 D G C B 7(123 **2) #83 5143 Q11 A 11 4 1 3 5 D A C#E 5(3n2 21n) A 9 3 1 5 9 C#A E B 6(1n1 4n3) A mi9 5 1b3 9 E A C B 5(n12 1n4) A 96 3 6 1 9 C#F#A B 4(343 1nn) A 7 3b7 5 1 C#G E A 4(3n1 n23) C M7 3 5 1h7 E G C B 8(212 nn1) C 6 3 5 1 6 E G C A 8(212 n3n) C mi6 b3 5 1 6 EbG C A 8(112 n3n) C 9 9 5 1 3 D G C E 7(123 3nn) C 96 9 6 1 3 D A C E 5(3n2 11n) C 94 9 4 1 3 D F C E 5(32n 11n) C 7 3 5 1b7 E G C Bb 7(323 nn1) D M7 1 3h7 5 D F#C#A 7(114 n4n) D 11 1 4 3 5 D G F#A 6(23n n21) D 9 1 3 9 5 D F#E A 7(11n 34n) D mi9 1b3 9 5 D F E A 6(21n 4n1) D 96 1 3 9 6 D F#E B 7(11n 3n2) D 9M7 1 3h7 9 D F#C#E 5(33n 21n) D 7 1 3b7 5 D F#C A 5(33n 1n2) F 6 3 6 1 5 A D F C 9(n23 2n1) F 6 6 1 3 5 D F A C 5(322 1nn) F 6 6 1 5 3 D F C A 6(214 nn1) F mi6 6b3 5 1 D AbC F 3(n13 34n) F 9 1 3 9 5 F A G C 6(n11 n34) F 9 1 9 5 3 F G C A 4(n31 2n3) F 96 6 9 1 3 D G F A 6(23n n11) G 11 5 1 4 3 D G C B 7(123 nn2) 83 8. Eb 11 5 4 1 3 BbAbEbG 3(1*3 *22) #84 5413 Q11 F 11 4 3 5 1 BbA C F 3(1n4 34n) F mi9 5b3 1 9 C AbF G 4(2n2 n31) F 96 3 1 6 9 A F D G 2(1n1 n23) Ab M7 3 1 5h7 C AbEbG 4(2n2 n11) Ab 6 3 1 5 6 C AbEbF 2(4n4 n31) Ab 96 9 1 3 6 BbAbC F 3(1n3 34n) Ab 9M7 9 1 3h7 BbAbC G 3(1n3 3n2) Ab 7 3 1 5b7 C AbEbGb 3(3n3 n21) Bb M7 1h7 3 5 BbA D F 2(2nn 121) Bb 11 1 4 3 5 BbEbD F 2(23n n21) Bb mi9 1b3 5 9 BbDbF C (322 n1n) Bb mi9 1b3 5 9 BbDbF C 2(211 4nn) Bb 7 1b7 3 5 BbAbD F (3nn 132) Db 6 6 1 3 5 BbDbF Ab 9(n32 21n) Db 6 6 3 1 5 BbF DbAb 2(2n1 n14) Db 6 6 5 1 3 BbAbDbF 3(1n3 44n) Db 9 1 3 9 5 DbF EbAb 2(n11 n34) Db 9 1 5 9 3 DbAbEbF 2(n14 n31) Db 7 b7 5 1 3 B AbDbF 4(1n2 33n) Eb 11 5 4 1 3 BbAbEbG 3(1n3 n22) 84 Calling Chords of the Ninth 1. C 9 1 3 5 9 C E G D 3(332 *1*) #85 1359 Q9 F 6 5 1 3 6 C F A D (n12 23n) F mi6 5 1b3 6 C F AbD (n12 13n) Bb M7 1 5h7 3 BbF A D 2(2n1 12n) Bb 6 1 5 6 3 BbF G D (3n2 03n) Bb 11 1 4 5 3 BbEbF D 2(231 n2n) Bb 94 9 4 1 3 C EbBbD 3(32n 11n) C 9 1 3 5 9 C E G D 11(n33 2n1) 85 2. D 9 1 3 9 5 D F#E A 7(11* 34*) #86 1395 Q9 E 11 5 1 4 3 B E A G# 4(123 nn2) E 9 1 3 9 5 E G#F#B 5(n11 n34) E 7 b7 5 1 3 D B E G# 7(1n2 33n) G 11 5 1 4 3 D G C B 7(123 nn2) G 94 4 1 3 9 C G B A 4(2n1 1n3) G 7 5b7 1 3 D F G B 4(431 1nn) A 7 3b7 5 1 C#G E A 4(3n1 n23) C M7 1 5 3h7 C G E B 5(14n n14) C 6 1 5 3 6 C G E A 4(2n1 n23) C mi6 1 5b3 6 C G EbA 4(2n1 n13) C 11 1 4 3 5 C F E G 4(23n n21) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) D 9 1 3 9 5 D F#E A 3(n11 n34) 86 3. Eb 9 1 5 9 3 EbBbF G 4(*14 *31) #87 1593 Q9 Eb 9 1 5 9 3 EbBbF G 8(14* 31*) F 11 5 4 1 3 C BbF A 5(1n3 n22) F mi9 b3 5 1 9 AbC F G 8(n22 31n) Ab M7 5 1 3h7 EbAbC G 8(122 n1n) Ab 6 5 3 6 1 EbC F Ab 8(1n2 32n) Ab mi6 5b3 6 1 EbB F Ab 8(1n1 32n) Ab 7 5 3b7 1 EbC GbAb 5(4nn 131) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 11 4 1 5 3 EbBbF D 8(14n 3n4) Bb 9M7 3 1 9h7 D BbC A 5(3n3 1n2) Bb 7 3 1 5b7 D BbF Ab 5(3n3 n21) Db M7 1h7 3 5 DbC F Ab 5(2nn 121) Db mi6 1 6b3 5 DbBbE Ab 5(2n3 n11) Db 11 1 4 3 5 DbGbF Ab 5(23n n21) Db 7 1b7 3 5 DbB F Ab 4(3nn 132) Eb 9 1 5 9 3 EbBbF G 4(n14 n31) 87 4. C 9 1 9 5 3 C D G E 11(*31 2*3) #88 1953 Q9 D 11 5 1 4 3 A D G F# 2(123 nn2) F M7 5 1 3h7 C F A E 5(122 n1n) F 6 5 6 3 1 C D A F 3(314 n4n) F mi6 5 6b3 1 C D AbF 3(313 n4n) F 9M7 3 1 9h7 A F G E (2n2 0n1) F 7 5b7 3 1 C EbA F 4(213 n3n) G M7 3 5 1h7 B D G F# 3(212 nn1) G 11 4 5 1 3 C D G B 3(312 2nn) G mi9 b3 5 1 9 BbD G A 2(223 1nn) G 7 3 5 1b7 B D G F 2(323 nn1) Bb M7 1 3h7 5 BbD A F 3(114 n4n) Bb 6 1 3 6 5 BbD G F 3(112 n4n) Bb 7 1 3b7 5 BbD AbF (33n 1n2) C 9 1 9 5 3 C D G E 3(312 n3n) 88 5. A 9 3 1 5 9 C#A E B 6(1*1 4*3) #89 3159 Q9 B 7 5b7 3 1 F#A D#B 6(n21 3n3) D 6 1 5 3 6 D A F#B 6(2n1 n23) D mi6 1 5b3 6 D A F B 6(2n1 n13) D 94 1 4 9 3 D G E F# 7(12n 31n) G M7 5 1h7 3 D G F#B 7(12n n12) G 11 5 1 4 3 D G C B 7(123 nn2) G 9M7 1 9h7 3 G A F#B 6(n31 n23) G 7 5 1b7 3 D G F B 6(23n n13) A 9 3 1 5 9 C#A E B 6(1n1 4n3) 89 6. G 9 3 1 9 5 B G A D 2(3*3 12*) #90 3195 Q9 A 11 4 5 1 3 D E A C# (n31 22n) A 7 5b7 1 3 E G A C# 2(n43 11n) C 6 1 5 6 3 C G A E 2(4n3 14n) C 7 b7 5 1 3 BbG C E 3(1n2 33n) F M7 5 1 3h7 C F A E 5(122 n1n) F 6 5 1 3 6 C F A D (n12 23n) F mi6 5 1b3 6 C F AbD (n12 13n) F 7 5 1 3b7 C F A Eb (n12 2n0) G 9 3 1 9 5 B G A D 10(n3n 312) G 9 3 1 9 5 B G A D 2(3n3 12n) 90 7. Bb 9 3 5 9 1 D F C Bb 5(32* 1*3) #91 3591 Q9 Eb 6 1 3 6 5 EbG C Bb 8(112 n4n) Ab 6 5 6 3 1 EbF C Ab 6(314 n4n) Ab mi6 5 6b3 1 EbF B Ab 6(313 n4n) Ab 94 4 1 3 9 DbAbC Bb 5(2n1 1n3) Ab 7 5b7 3 1 EbGbC Ab 7(213 n3n) Ab 7 5 1 3b7 EbAbC Gb 3(n23 3n1) Bb 9 3 5 9 1 D F C Bb 5(32n 1n3) 91 8. A 9 3 9 5 1 C#B E A 6(1*3 45*) #92 3951 Q9 B M7 5 1 3h7 F#B D#A# 7(n12 2n1) B 11 1 4 3 5 B E D#F# 3(23n n21) B 11 4 1 3 5 E B D#F# 5(n14 43n) B 9M7 9 1 3h7 C#B D#A# 6(1n3 3n2) B 7 5 1 3b7 F#B D#A 6(n23 3n1) D mi6 1 6b3 5 D B F A 6(2n3 n11) D 11 1 4 3 5 D G F#A 6(23n n21) E 94 9 4 1 3 F#A E G# 9(32n 11n) E 7 b7 5 1 3 D B E G# 7(1n2 33n) G 6 5 3 6 1 D B E G 7(1n2 32n) G mi6 5b3 6 1 D BbE G 7(1n1 32n) G 11 4 3 5 1 C B D G 5(1n4 34n) G 9M7 1 3h7 9 G B F#A 6(n33 n21) G 7 5 3b7 1 D B F G 4(4nn 131) A 9 3 9 5 1 C#B E A 6(1n3 45n) 92 9. G 9 5 1 3 9 D G B A 3(*12 2*4) #93 5139 Q9 A 11 4 5 1 3 D E A Db 5(312 2nn) C M7 1 3 5h7 C E G B 4(221 1nn) C M7 1 5h7 3 C G B E 4(2n1 12n) C 6 3 5 1 6 E G C A 4(n21 2n3) C mi6 b3 5 1 6 EbG C A 4(n11 2n3) C 94 9 4 1 3 D F C E 5(32n 11n) D M7 1 3h7 5 D F#C#A 7(114 n4n) D mi9 1b3 9 5 D F E A 6(21n 4n1) D 11 1 4 3 5 D G F#A 6(23n n21) D 9M7 1 3h7 9 D F#C#E 5(33n 21n) F 6 6 1 5 3 D F C A 6(214 nn1) G 9 5 1 3 9 D G B A 3(n12 2n4) 93 10. Eb 9 5 3 1 9 BbG EbF 2(2*3 *31) #94 5319 Q9 F 11 4 3 5 1 BbA C F 3(1n4 34n) Ab 6 3 1 5 6 C AbEbF 2(4n4 n31) Ab 7 3b7 5 1 C GbEbAb 3(3n1 n23) Bb M7 1h7 3 5 BbA D F 2(2nn 121) Bb 7 1b7 3 5 BbAbD F (3nn 132) Db 6 6 5 1 3 BbAbDbF 3(1n3 44n) Db mi6 6 5 1b3 BbAbDbE 3(1n3 43n) Db 11 4 5 1 3 GbAbDbF 5(n31 22n) Db 94 1 4 9 3 DbGbEbF 2(n12 n31) Db 7 b7 5 1 3 B AbDbF 4(1n2 33n) Eb 9 5 3 1 9 BbG EbF 2(2n3 n31) 94 11. F 9 5 9 1 3 C G F A 4(2*1 *33) #95 5913 Q9 G 11 4 1 5 3 C G D B 5(14n 3n4) G mi9 5 1b3 9 D G BbA 7(121 n4n) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 6 3 6 5 1 D G F Bb 6(23n n12) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) Bb 7 3b7 5 1 D AbF Bb 5(3n1 n23) C M7 1 5 3h7 C G E B 5(14n n14) Eb 6 6 3 1 5 C G EbBb 4(2n1 n14) Eb 7 b7 3 1 5 DbG EbBb 6(13n 3n2) F 9 5 9 1 3 C G F A 4(2n1 n33) 95 12. A 9 5 9 3 1 E B C#A 6(4*3 1*1) #96 5931 Q9 B M7 3 1 5h7 D#B F#A# 7(2n2 n11) B 11 4 1 3 5 E B D#F# 5(n14 43n) B mi9 b3 1 9 5 D B C#F# 6(2n3 12n) B 9M7 3 1 9h7 D#B C#A# 6(3n3 1n2) B 7 3 1 5b7 D#B F#A 6(3n3 n21) D M7 1 3h7 5 D F#C#A 7(114 n4n) D 6 3 6 1 5 F#B D A 6(n23 2n1) D mi6 b3 6 1 5 F B D A 6(n13 2n1) D 7 3b7 1 5 F#C D A 7(n13 14n) E M7 1 5h7 3 E B D#G# 8(2n1 12n) E 9M7 1 9h7 3 E F#D#G# 7(31n 23n) E 94 1 4 9 3 E A F#G# 9(12n 31n) E 7 1 5b7 3 E B D G# 7(3n2 13n) G 11 4 3 5 1 C B D G 5(1n4 34n) G mi6 6b3 5 1 E BbD G 5(n13 34n) G 7 b7 3 5 1 F B D G 6(n13 23n) A 9 5 9 3 1 E B C#A 6(4n3 1n1) 96 13. Bb 9 9 1 3 5 C BbD F 5(1*3 32*) #97 9135 Q9 C 11 4 5 1 3 F G C E 4(n31 22n) Eb M7 1 5h7 3 EbBbD G 3(n2n 112) Eb 6 6 5 1 3 C BbEbG 5(1n3 44n) Eb mi6 6 5 1b3 C BbEbGb 5(1n3 43n) Eb 11 4 5 1 3 AbBbEbG 3(nn3 122) Eb 9M7 1 3h7 9 EbG D F 6(33n 21n) Eb 7 b7 5 1 3 DbBbEbG 6(1n2 33n) F M7 1 3 5h7 F A C E 5(n22 11n) F 7 5 3b7 1 C A EbF 2(4nn 131) F 7 1 5b7 3 F C EbA 4(n3n 213) Ab M7 3 1 5h7 C AbEbG 4(2n2 n11) Ab 6 3 1 5 6 C AbEbF 2(4n4 n31) Ab 7 3 1 5b7 C AbEbGb 3(3n3 n21) Bb 9 9 1 3 5 C BbD F (n1n 332) 97 14. D 9 9 3 1 5 E F#D A 3(*31 *14) #98 9315 Q9 D 9 9 3 1 5 E F#D A 7(31* 14*) E M7 1 5h7 3 E B D#G# 8(2n1 12n) E 11 1 4 5 3 E A B G# 8(231 n2n) E 11 4 1 5 3 A E B G# 2(14n 3n4) E 9M7 1 9h7 3 E F#D#G# 7(31n 23n) E 7 1 5b7 3 E B D G# 7(3n2 13n) G 6 6 1 5 3 E G D B 8(214 nn1) G 11 4 1 5 3 C G D B 5(14n 3n4) A 7 5b7 3 1 E G C#A 8(213 n3n) C M7 3 5 1h7 E G C B 8(212 nn1) C 6 3 5 1 6 E G C A 8(212 n3n) C mi6 b3 5 1 6 EbG C A 8(112 n3n) C 9M7 3 1 9h7 E C D B 7(3n3 1n2) C 7 3 5 1b7 E G C Bb 7(323 nn1) D 9 9 3 1 5 E F#D A 7(31n 14n) D 9 9 3 1 5 E F#D A 3(n31 n14) 98 15. F 9 9 5 1 3 G C F A 8(*12 33*) #99 9513 Q9 F 9 9 5 1 3 G C F A (012 2nn) G M7 1 3 5h7 G B D F# 7(n22 11n) G M7 1 3h7 5 G B F#D 8(n11 4n4) G 11 1 4 5 3 G C D B 7(n23 1n2) G 11 4 3 5 1 C B D G 5(1n4 34n) G mi9 1b3 5 9 G BbD A 6(n32 2n1) G 9M7 1 3h7 9 G B F#A 6(n33 n21) G 7 1 3b7 5 G B F D 10(33n 1n2) Bb M7 1 3 5h7 BbD F A 10(n22 11n) Bb M7 1 3 5h7 BbD F A 2(221 1nn) Bb M7 1 3 5h7 BbD F A 6(nn2 211) Bb 11 4 3 5 1 EbD F Bb 8(1n4 34n) Bb mi6 6b3 5 1 G DbF Bb 8(n13 34n) C M7 5 1 3h7 G C E B 8(n12 2n1) C mi9 5 1b3 9 G C EbD 8(n12 1n4) C 11 5 1 4 3 G C F E (012 nn1) C 11 5 1 4 3 G C F E 12(123 nn2) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) C 94 4 1 3 9 F C E D 9(2n1 1n3) Eb 6 3 6 1 5 G C EbBb 7(n23 2n1) Eb mi6 b3 6 1 5 GbC EbBb 7(n13 2n1) Eb 7 3b7 1 5 G DbEbBb 8(n13 14n) F 9 9 5 1 3 G C F A 8(n12 33n) 99 16. Bb 9 9 5 3 1 C F D Bb 5(12* 3*3) #100 9531 Q9 C M7 1 3 5h7 C E G B 4(221 1nn) C 11 1 4 3 5 C F E G 4(23n n21) C mi9 1b3 9 5 C EbD G 4(21n 4n1) C 7 1 3 5b7 C E G Bb 3(332 1nn) Eb M7 1 3h7 5 EbG D Bb 4(n11 4n4) Eb 6 6 3 1 5 C G EbBb 4(2n1 n14) Eb 7 b7 3 1 5 DbG EbBb 6(13n 3n2) F M7 5 1h7 3 C F E A 5(12n n12) F 7 5 1b7 3 C F EbA 4(23n n13) Ab 6 3 6 5 1 C F EbAb 4(23n n12) Ab 7 3b7 5 1 C GbEbAb 3(3n1 n23) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) 100 Calling Chords of the Minor Ninth 1. D mi9 1b3 5 9 D F A E 5(322 *1*) #101 1N59 Qmi9 G 11 5 4 1 3 D C G B 7(1n3 n22) G 6 5 1 3 6 D G B E 7(122 3nn) G mi6 5 1b3 6 D G A#E 7(121 3nn) G 7 5b7 3 1 D F B G 6(213 n3n) C M7 1 5h7 3 C G B E 4(2n1 12n) C 6 1 5 6 3 C G A E 2(4n3 14n) C 11 1 4 5 3 C F G E 4(231 n2n) C 9 9 5 1 3 D G C E 7(123 3nn) C 94 9 4 1 3 D F C E 5(32n 11n) C 7 1 5b7 3 C G BbE 3(3n2 13n) D mi9 1b3 5 9 D F A E 5(322 n1n) 2. C mi9 1b3 9 5 C EbD G 4(21* 4*1) #102 1N95 Qmi9 D 96 6 9 1 3 B E D F# 3(23n n11) F 11 5 1 4 3 C F BbA 5(123 nn2) F 9 5 1 3 9 C F A G 5(122 n4n) F 96 3 1 6 9 A F D G 2(1n1 n23) F 94 4 1 3 9 BbF A G 2(2n1 1n3) F 7 5b7 1 3 C EbF A 10(n43 11n) Bb M7 1 5 3h7 BbF D A 3(14n n14) Bb 6 1 5 3 6 BbF D G 2(2n1 n23) Bb mi6 1 5b3 6 BbF DbG 2(2n1 n13) Bb 11 1 4 3 5 BbEbD F 2(23n n21) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) C mi9 1b3 9 5 C EbD G 4(21n 4n1) 3. A mi9 b3 1 9 5 C A B E 4(2*3 12*) #103 N195 Qmi9 G M7 5 1 3h7 D G B F# 3(n12 2n1) G 6 5 1 3 6 D G B E 3(n12 23n) G mi6 5 1b3 6 D G BbE 3(n12 13n) G 11 4 1 3 5 C G B D 3(3n2 21n) G 9 5 9 3 1 D A B G 4(4n3 1n1) G 7 5 1 3b7 D G B F 2(n23 3n1) D 6 1 5 6 3 D A B F# 4(4n3 14n) D 96 1 3 6 9 D F#B E 3(n11 23n) A mi9 b3 1 9 5 C A B E 4(2n3 12n) 4. Eb mi9 b3 5 1 9 GbBbEbF 6(*22 31*) #104 N519 Qmi9 Ab 6 1 3 5 6 AbC EbF 6(n44 31n) Ab mi6 1b3 5 6 AbB EbF 6(n43 31n) Ab 11 4 1 5 3 DbAbEbC 6(14n 3n4) Ab 9 1 9 5 3 AbBbEbC 7(n31 2n3) Ab 7 b7 3 5 1 GbC EbAb 7(n13 23n) Db 6 5 6 1 3 AbBbDbF 6(n42 11n) Db 11 4 5 1 3 GbAbDbF 5(n31 22n) Db 9 1 5 9 3 DbAbEbF 6(14n 31n) Db 96 1 6 9 3 DbBbEbF 6(1n2 31n) Db 7 5b7 1 3 AbB DbF 6(n43 11n) Eb mi9 b3 5 1 9 GbBbEbF 6(n22 31n) 5. Bb mi9 b3 5 9 1 DbF C Bb 5(22* 1*3) #105 N591 Qmi9 Eb 6 1 3 6 5 EbG C Bb 8(112 n4n) Eb 11 4 1 3 5 AbEbG Bb 7(n3n 221) Eb 7 b7 3 1 5 DbG EbBb 6(13n 3n2) Ab 6 5 6 3 1 EbF C Ab 6(314 n4n) Ab mi6 5 6b3 1 EbF B Ab 6(313 n4n) Ab 9 5 1 3 9 EbAbC Bb 8(122 n4n) Ab 94 4 1 3 9 DbAbC Bb 5(2n1 1n3) Ab 7 5b7 3 1 EbGbC Ab 7(213 n3n) Bb mi9 b3 5 9 1 DbF C Bb 5(22n 1n3) 6. F mi9 5 1b3 9 C F AbG 5(121 *4*) #106 51N9 Qmi9 Bb M7 1 5h7 3 BbF A D 2(2n1 12n) Bb 6 3 5 1 6 D F BbG 6(212 n3n) Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) Bb 9 9 5 1 3 C F BbD 5(123 3nn) Bb 94 9 4 1 3 C EbBbD 3(32n 11n) Eb 6 6 1 5 3 C EbBbG 4(214 nn1) Eb 11 5 1 4 3 BbEbAbG 3(123 nn2) Eb 9 5 9 1 3 BbF EbG 2(2n1 n33) Eb 96 6 9 1 3 C F EbG 4(23n n11) F mi9 5 1b3 9 C F AbG 5(121 n4n) 7. G mi9 5b3 1 9 D BbG A 6(2*2 *31) #107 5N19 Qmi9 C 96 9 1 3 6 D C E A 7(1n3 34n) C 7 3b7 5 1 E BbG C 7(3n1 n23) F 6 6 5 1 3 D C F A 7(1n3 44n) F mi6 6 5 1b3 D C F Ab 7(1n3 43n) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 94 1 4 9 3 F BbG A 6(n12 n31) F 7 b7 5 1 3 EbC F A 8(1n2 33n) G mi9 5b3 1 9 D BbG A 6(2n2 n31) Calling Chords of the Nine-six 1. F 96 1 3 6 9 F A D G 6(*11 23*) #108 1369 Q96 G 11 4 3 5 1 C B D G 5(1n4 34n) Bb mi6 5 1b3 6 F BbDbG 6(n12 13n) C mi9 b3 1 9 5 EbC D G 7(2n3 12n) Eb M7 1 5h7 3 EbBbD G 7(2n1 12n) Eb 6 6 5 1 3 C BbEbG 5(1n3 44n) Eb mi6 b3 5 1 6 GbBbEbC 7(n11 2n3) Eb 11 4 5 1 3 AbBbEbG 7(n31 22n) Eb 94 9 4 1 3 F AbEbG 8(32n 11n) F 96 1 3 6 9 F A D G 6(n11 23n) 2. C 96 1 3 9 6 C E D A 5(11* 3*2) #109 1396 Q96 F 11 5 1 4 3 C F BbA 5(123 nn2) G 11 4 1 5 3 C G D B 5(14n 3n4) Bb M7 1 5 3h7 BbF D A 3(14n n14) Bb mi6 b3 5 6 1 DbF G Bb 3(442 1nn) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) C 96 1 3 9 6 C E D A 5(11n 3n2) 3. Bb 96 1 6 9 3 BbG C D 3(1*2 31*) #110 1693 Q96 C 11 4 5 1 3 F G C E 4(n31 22n) C mi9 b3 5 1 9 EbG C D 3(n22 31n) Eb mi6 5b3 6 1 BbGbC Eb 3(1n1 32n) F M7 3 1 5h7 A F C E (2n2 n11) F 11 4 1 3 5 BbF A C (3n2 21n) Ab M7 1h7 3 5 AbG C Eb (1nn 010) Ab M7 1h7 3 5 AbG C Eb 12(2nn 121) Ab 6 6 1 3 5 F AbC Eb 4(n32 21n) Bb 96 1 6 9 3 BbG C D 11(n1n 231) Bb 96 1 6 9 3 BbG C D 3(1n2 31n) 110 4. A 96 3 1 6 9 C#A F#B 6(1*1 *23) #111 3169 Q96 D mi6 1 5b3 6 D A F B 6(2n1 n13) E 11 1 4 3 5 E A G#B 8(23n n21) E mi9 1b3 9 5 E G F#B 8(21n 4n1) G M7 5 1h7 3 D G F#B 7(12n n12) G 6 5 6 1 3 D E G B 4(421 1nn) G 11 4 5 1 3 C D G B 3(312 2nn) G 11 5 4 1 3 D C G B 7(1n3 n22) A 96 3 1 6 9 C#A F#B 6(1n1 n23) 111 5. Eb 96 3 6 1 9 G C EbF 6(*34 31*) #112 3619 Q96 Ab mi6 1b3 5 6 AbB EbF 6(n43 31n) Db 11 4 1 5 3 GbDbAbF 11(14n 3n4) Db 11 5 1 4 3 AbDbGbF (123 nn2) Db 11 5 1 4 3 AbDbGbF 13(123 nn2) Eb 96 3 6 1 9 G C EbF 6(n34 31n) 112 6. F 96 6 1 3 9 D F A G 6(211 *3*) #113 6139 Q96 Bb 6 3 5 1 6 D F BbG 6(212 n3n) Bb mi6 b3 5 1 6 DbF BbG 6(112 n3n) C M7 1 3h7 5 C E B G 4(22n 1n1) B 11 1 4 3 5 B E EbGb 3(23n n21) Eb mi6 1b3 5 6 EbGbBbC 5(433 1nn) Eb 11 1 4 5 3 EbAbBbG 7(231 n2n) F 96 6 1 3 9 D F A G 6(211 n3n) 113 7. G 96 6 9 1 3 E A G B 8(23* *11) #114 6913 Q96 A M7 5 1h7 3 E A G#C# 9(12n n12) A 11 5 1 4 3 E A D C# 9(123 nn2) A mi9 5 1b3 9 E A C B 9(121 n4n) C M7 3 1 5h7 E C G B 8(2n2 n11) C 9M7 3 1 9h7 E C D B 7(3n3 1n2) D M7 1 5 3h7 D A F#C# 7(14n n14) F 6 1 3 6 5 F A D C 6(n11 2n4) F mi9 1b3 9 5 F AbG C 9(21n 4n1) G 96 6 9 1 3 E A G B 8(23n n11) 114 8. A 96 9 1 3 6 B A C#F# 4(1*3 34*) #115 9136 Q96 B M7 1h7 3 5 B A#D#F# 3(2nn 121) B 11 1 4 3 5 B E D#F# 3(23n n21) B mi9 1b3 9 5 B D C#F# 3(21n 4n1) D mi6 6 5 1b3 B A D F 4(1n3 43n) D 11 4 5 1 3 G A D F# 6(n31 22n) D 94 9 4 1 3 E G D F# 7(32n 11n) E 11 5 4 1 3 B A E G# 4(1n3 n22) E mi9 5b3 1 9 B G E F# 3(2n2 n31) E 9M7 1 3h7 9 E G#D#F# 7(33n 21n) G M7 3 1 5h7 B G D F# 3(2n2 n11) G 6 3 6 5 1 B E D G 3(23n n12) A 96 9 1 3 6 B A C#F# 4(1n3 34n) 115 9. C 96 9 6 1 3 D A C E 5(3*2 11*) #116 9613 Q96 D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 9M7 1 3h7 9 D F#C#E 5(33n 21n) F M7 1 3 5h7 F A C E 5(n22 11n) F mi6 6b3 5 1 D AbC F 7(133 4nn) F 11 4 3 5 1 BbA C F 3(1n4 34n) G M7 5 1 3h7 D G B F# 7(122 n1n) G 11 5 1 4 3 D G C B 7(123 nn2) C 96 9 6 1 3 D A C E 5(3n2 11n) 116 10. F 96 9 3 6 1 G A D F 6(*31 21*) #117 9361 Q96 G M7 1 3 5h7 G B D Gb 7(n22 11n) Bb M7 1h7 3 5 BbA D F 2(2nn 121) Bb mi6 6 1b3 5 G BbDbF 6(n32 11n) Bb 11 4 1 3 5 EbBbD F 6(3n2 21n) Eb 6 3 5 1 6 G BbEbC 7(n21 2n3) Eb mi6 b3 5 1 6 GbBbEbC 7(n11 2n3) F 96 9 3 6 1 G A D F 6(n31 21n) 117 Calling Chords of the Nine Major Seven 1. Eb 9M7 1 3h7 9 EbG D F 6(33* 21*) #118 13M9 Q9M7 F 11 4 3 5 1 BbA C F 3(1n4 34n) F 9 3 9 5 1 A G C F 10(n1n 345) F 7 b7 3 5 1 EbA C F 8(132 3nn) Ab 6 5 1 3 6 EbAbC F 4(n12 23n) Ab mi6 5 1b3 6 EbAbB F 8(121 3nn) Ab 11 5 1 4 3 EbAbDbC 8(123 nn2) Ab 9 5 1 3 9 EbAbC Bb 8(122 n4n) Ab 7 5 1 3b7 EbAbC Gb 7(233 n1n) Bb M7 1h7 3 5 BbA D F 14(2nn 121) Bb 11 4 1 3 5 EbBbD F 6(3n2 21n) Bb 9 9 1 3 5 C BbD F 5(1n3 32n) Bb 96 9 1 3 6 C BbD G 5(1n3 34n) Bb 7 1b7 3 5 BbAbD F 13(3nn 132) Db 6 6 5 1 3 BbAbDbF 3(1n3 44n) Db mi6 b3 5 1 6 E AbDbBb 9(112 n3n) Db 11 4 5 1 3 GbAbDbF 5(n31 22n) Db 9 9 5 1 3 EbAbDbF 8(123 3nn) Db 96 9 6 1 3 EbBbDbF 6(3n2 11n) Db 94 9 4 1 3 EbGbDbF 6(32n 11n) Db 7 b7 5 1 3 B AbDbF 4(1n2 33n) Eb 9M7 1 3h7 9 EbG D F 6(33n 21n) 118 2. A 9M7 9 1 3h7 B A C#G# 4(1*3 3*2) #119 913M Q9M7 B M7 1h7 3 5 B A#D#F# 3(2nn 121) B 11 1 4 3 5 B E D#F# 3(23n n21) B 9 1 3 9 5 B D#C#F# 4(11n 34n) B mi9 1b3 9 5 B D C#F# 3(21n 4n1) B 96 1 3 9 6 B D#C#G# 4(11n 3n2) B 7 1b7 3 5 B A D#F# 2(3nn 132) D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 6 6 5 1 3 B A D F# 4(1n3 44n) D mi6 6 5 1b3 B A D F 4(1n3 43n) D 9 9 5 1 3 E A D F# 5(n12 33n) D 7 b7 5 1 3 C A D F# 5(1n2 33n) E M7 5 1h7 3 B E D#G# 4(12n n12) E 11 5 4 1 3 B A E G# 4(1n3 n22) E 9 5 9 1 3 B F#E G# 3(2n1 n33) E 7 5 1b7 3 B E D G# 3(23n n13) G 6 3 6 5 1 B E D G 3(23n n12) G 9 3 9 5 1 B A D G 4(1n3 45n) G 7 3b7 5 1 B F D G 2(3n1 n23) A 9M7 9 1 3h7 B A C#G# 4(1n3 3n2) 119 3. C 9M7 3 1 9h7 E C D B 7(3*3 1*2) #120 319M Q9M7 D 9 9 3 1 5 E GbD A 7(31n 14n) D 7 3b7 1 5 GbC D A 7(n13 14n) F 6 1 5 6 3 F C D A 7(4n3 14n) F 9 1 5 9 3 F C G A 6(n14 n31) F 7 1 5b7 3 F C EbA 8(3n2 13n) G 11 1 4 5 3 G C D B 7(n23 1n2) G 9 1 9 5 3 G A D B 6(n31 2n3) G 96 6 9 1 3 E A G B 8(23n n11) Bb 6 5 6 3 1 F G D Bb 8(314 n4n) Bb mi6 5b3 6 1 F DbG Bb 6(n1n 132) Bb 9 5 9 3 1 F C D Bb 7(4n3 1n1) Bb 7 5b7 3 1 F AbD Bb 9(213 n3n) C 9M7 3 1 9h7 E C D B 7(3n3 1n2) 4. F 9M7 1 9h7 3 F G E A 4(*31 *23) #121 19M3 Q9M7 G 11 4 1 5 3 C G D B 5(14n 3n4) G 9 3 1 5 9 B G D A 4(1n1 4n3) Bb M7 5 1 3h7 F BbD A 6(n12 2n1) Bb 6 5 6 3 1 F G D Bb 4(n31 4n4) Bb 9 5 9 3 1 F C D Bb 7(4n3 1n1) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) Bb 7 5b7 3 1 F AbD Bb 5(n21 3n3) C M7 1 5 3h7 C G E B 5(14n n14) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) Eb mi6 b3 6 1 5 GbC EbBb 7(n13 2n1) Eb 9 9 3 1 5 F G EbBb 8(31n 14n) Eb 7 b7 3 1 5 DbG EbBb 6(13n 3n2) F 9M7 1 9h7 3 F G E A 4(n31 n23) Calling Chords of the Nine-four 1. C 94 9 4 1 3 D F C E 5(32* 11*) #122 9413 Q94 D M7 1 3h7 5 D F#C#A 7(114 n4n) D 9 1 3 5 9 D F#A E 5(332 n1n) D mi9 1b3 5 9 D F A E 5(322 n1n) D 96 1 3 6 9 D F#B E 7(112 3nn) D 9M7 1 3h7 9 D F#C#E 5(33n 21n) D 7 1 3b7 5 D F#C A 5(33n 1n2) F 9 3 9 5 1 A G C F 2(1n3 45n) F 9 3 9 5 1 A G C F 10(n1n 345) F 7 3b7 5 1 A EbC F (2n0 n12) F 7 3b7 5 1 A EbC F 12(3n1 n23) G 11 5 1 4 3 D G C B 7(123 nn2) G 9 5 1 3 9 D G B A 7(122 n4n) G mi9 5 1b3 9 D G BbA 7(121 n4n) G 96 9 1 3 6 A G B E 2(1n3 34n) G 94 4 1 3 9 C G B A 4(2n1 1n3) G 7 5b7 3 1 D F B G 6(213 n3n) Bb 6 3 6 1 5 D G BbF 6(232 n1n) Bb 7 3b7 1 5 D AbBbF 3(n13 14n) C 94 9 4 1 3 D F C E 5(32n 11n) 2. D 94 1 4 9 3 D G E F# 7(12* 31*) #123 1493 Q94 E 9 5 3 1 9 B G#E F# 3(2n3 n31) E mi9 5b3 1 9 B G E F# 3(2n2 n31) E 7 b7 3 1 5 D G#E B 7(13n 3n2) G 9 5 9 3 1 D A B G 4(4n3 1n1) G 94 4 1 3 9 C G B A 4(2n1 1n3) G 7 5b7 3 1 D F B G 2(n21 3n3) A 11 4 1 5 3 D A E C# 7(14n 3n4) A 9 3 1 5 9 C#A E B 6(1n1 4n3) A 7 3b7 5 1 C#G E A 4(3n1 n23) C M7 1h7 3 5 C B E G 4(2nn 121) C 7 1b7 3 5 C BbE G 3(3nn 132) D 94 1 4 9 3 D G E F# 7(12n 31n) 3. A 94 4 1 3 9 D A C#B 6(2*1 1*3) #124 4139 Q94 B 9 3 5 9 1 D#F#C#B 6(32n 1n3) B mi9 b3 5 9 1 D F#C#B 6(22n 1n3) B 7 3b7 5 1 D#A F#B 6(3n1 n23) D 9 9 5 1 3 E A D F# 5(n12 33n) D 94 9 4 1 3 E G D F# 7(32n 11n) D 94 1 4 9 3 D G E F# 7(12n 31n) E 11 1 4 3 5 E A G#B 8(23n n21) E 9 1 3 9 5 E G#F#B 5(n11 n34) E mi9 1b3 9 5 E G F#B 8(21n 4n1) E 96 1 3 6 9 E G#C#F# 5(n11 23n) E 7 b7 3 1 5 D G#E B 7(13n 3n2) G 6 6 1 5 3 E G D B 8(214 nn1) A 94 4 1 3 9 D A C#B 6(2n1 1n3) Calling Chords of the Seventh 1. F 7 1 3 5b7 F A C Eb 4(*33 21*) #125 1357 Q7 A 7+5 1 3+5b7 A DbF G 8(n33 31n) Ab 7b5 1 3b5b7 AbC D Gb 7(n33 11n) Bb 97 1 3 9b7 BbD C Ab 3(11n 3n3) F 7 1 3 5b7 F A C Eb 4(*33 21*) Bb mi6 5 1b3 6 F BbDbG 6(n12 13n) C 11 4 5 1 3 F G C E 4(n31 22n) Eb 9 9 5 3 1 F BbG Eb 10(12n 3n3) Eb mi6 b3 5 6 1 GbBbC Eb 4(n44 21n) F 7 1 3 5b7 F A C Eb 4(n33 21n) 125 2. D 7 1 3b7 5 D F#C A 5(33* 1*2) #126 1375 Q7 Db 7b5 1 3b7b5 DbF B G 6(113 n3n) D 7+5 1 3b7+5 D F#C A# 5(33n 1n3) Db 97 1 3b7 9 DbF B Eb 6(113 3nn) D 13 1 3b7 6 D F#C B 5(33n 1n4) D 7 1 3b7 5 D F#C A 5(33* 1*2) E 9 1 9 5 3 E F#B G# 7(312 n3n) G 6 5 1 3 6 D G B E 7(122 3nn) G 11 5 1 4 3 D G C B 7(123 nn2) G 9 5 1 3 9 D G B A 7(122 n4n) C M7 3 5 1h7 E G C B 8(212 nn1) C 6 3 5 1 6 E G C A 8(212 n3n) C mi6 b3 5 1 6 EbG C A 8(112 n3n) C 9 9 5 1 3 D G C E 7(123 3nn) C 94 9 4 1 3 D F C E 5(32n 11n) D 7 1 3b7 5 D F#C A 5(33n 1n2) 126 3. Eb 7 1 5b7 3 EbBbDbG 6(3*2 13*) #127 1573 Q7 D 7b5 1b5b7 3 D G#C F# 5(3n1 13n) Db 74 1 4b7 3 DbGbB F 6(123 n1n) Db 7+5 1+5b7 3 DbA B F 4(3n3 13n) Eb 97 1 9b7 3 EbF DbG 6(31n 13n) Eb 7 1 5b7 3 EbBbDbG 6(3*2 13*) F 11 1 4 5 3 F BbC A 9(231 n2n) Ab M76 6 1 3h7 F AbC G 8(322 n1n) Ab M7 5 1 3h7 EbAbC G 8(122 n1n) Ab 6 5 6 3 1 EbF C Ab 6(314 n4n) Ab mi6 5b3 6 1 EbB F Ab 8(1n1 32n) Ab 9 5 9 3 1 EbBbC Ab 5(4n3 1n1) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 11 4 1 3 5 EbBbD F 6(3n2 21n) Bb 9M7 3 1 9h7 D BbC A 5(3n3 1n2) Db 6 3 6 1 5 F BbDbAb 9(232 n1n) Db 9 9 3 1 5 EbF DbAb 6(31n 14n) Db mi6 b3 6 1 5 E BbDbAb 9(132 n1n) Eb 7 1 5b7 3 EbBbDbG 14(n3n 213) 127 4. C 7 1b7 3 5 C BbE G 3(3** 132) #128 1735 Q7 B 7b5 1b7 3b5 B A D#F 2(3nn 131) A 7+5 1b7 3+5 A G C#F 2(1n3 n11) D 13 1b7 3 6 D C F#B 7(1n3 n12) C 7 1b7 3 5 C BbE G 3(3** 132) D 9 1 5 9 3 D A E Gb 7(14n 31n) D 94 1 4 9 3 D G E F# 7(12n 31n) F 11 5 4 1 3 C BbF A 5(1n3 n22) F 9 5 3 1 9 C A F G 4(2n3 n31) F 9M7 1 3h7 9 F A E G 4(n33 n21) G 11 4 3 5 1 C B D G 5(1n4 34n) Bb M7 3 1 5h7 D BbF A 6(2n2 n11) Bb 6 3 1 5 6 D BbF G 4(4n4 n31) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) C 7 1b7 3 5 C BbE G 3(3nn 132) 128 5. Bb 7 3 1 5b7 D BbF Ab 5(3*3 *21) #129 3157 Q7 Bb 7b5 3 1b5b7 D BbE Ab 7(1n1 33n) A 7+5 3 1+5b7 C#A F G 4(3n3 n31) Bb 97 3 1 9b7 D BbC Ab 5(3n3 1n1) Bb 7 3 1 5b7 D BbF Ab 5(3*3 *21) C M7 1h7 3 5 C B E G 4(2nn 121) C 9 9 1 3 5 D C E G 3(n1n 332) C 9 9 1 3 5 D C E G 7(1n3 32n) Eb mi6 1 5b3 6 EbBbGbC 7(2n1 n13) Eb 9 1 5 9 3 EbBbF G 8(14n 31n) F 11 5 4 1 3 C BbF A 5(1n3 n22) Ab 6 5 3 6 1 EbC F Ab 8(1n2 32n) Ab mi6 5b3 6 1 EbB F Ab 8(1n1 32n) Ab 9 5 9 3 1 EbBbC Ab 5(4n3 1n1) Bb 7 3 1 5b7 D BbF Ab 5(3n3 n21) 129 6. A 7 3 5 1b7 C#E A G 4(323 **1) #130 3517 Q7 C 7+5 3+5 1b7 E G#C A# 5(n11 1n3) D 7b5 b7 1b5 3 C D G#F# 3(313 nn1) A 7 3 5 1b7 C#E A G 4(323 **1) B M7 1 3h7 5 B D#A#F# 4(114 n4n) B 9 9 3 1 5 C#D#B F# 4(31n 14n) B 94 9 4 1 3 C#E B D# 4(32n 11n) D mi6 1b3 5 6 D F A B 8(nn4 331) D mi6 1b3 5 6 D F A B 4(433 1nn) D 9 1 9 5 3 D E A F# 5(312 n3n) E 11 5 1 4 3 B E A G# 4(123 nn2) G 6 5 6 3 1 D E B G 5(314 n4n) G mi6 5 6b3 1 D E BbG 5(313 n4n) A 7 3 5 1b7 C#E A G 4(323 nn1) 130 7. C 7 3b7 1 5 E BbC G 5(*13 14*) #131 3715 Q7 B 7+5 3b7 1+5 D#A B G 4(n13 1n1) D 7b5 3b7 1b5 F#C D G# 7(n13 13n) C 13 3b7 1 6 E BbC A 5(n13 1n2) C 7 3b7 1 5 E BbC G 5(*13 14*) C 94 9 4 1 3 D F C E 5(32n 11n) D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 9 9 5 1 3 E A D F# 9(123 3nn) F 6 1 3 5 6 F A C D 3(n44 31n) F 11 1 4 5 3 F BbC A 5(n23 1n2) G 9 5 9 3 1 D A B G 4(4n3 1n1) Bb M7 5 1 3h7 F BbD A 6(n12 2n1) Bb 6 5 1 3 6 F BbD G 6(n12 23n) Bb mi6 5 1b3 6 F BbDbG 6(n12 13n) Bb 9M7 3 1 9h7 D BbC A 5(3n3 1n2) C 7 3b7 1 5 E BbC G 5(n13 14n) 131 8. Bb 7 3b7 5 1 D AbF Bb 5(3*1 *23) #132 3751 Q7 Bb 7 3b7 5 1 D AbF Bb 7(13n 45n) Bb 7b5 3b7b5 1 D AbE Bb 7(13n 3n1) Eb 7b5 b7 3 1b5 DbG EbA 4(3n1 n13) A 7+5 3b7+5 1 C#G F A 4(3n1 n33) Ab 97 3b7 9 1 C GbBbAb 3(3n1 1n3) Bb 13 3b7 6 1 D AbG Bb 7(13n n21) Bb 7 3b7 5 1 D AbF Bb 5(3*1 *23) C 9 9 5 3 1 D G E C 7(12n 3n3) C 9M7 9 1 3h7 D C E B 7(1n3 3n2) Eb M7 1 5 3h7 EbBbG D 8(14n n14) Eb 6 1 3 6 5 EbG C Bb 8(112 n4n) Eb mi6 1 6b3 5 EbC GbBb 7(2n3 n11) Eb 11 1 4 3 5 EbAbG Bb 7(23n n21) Eb 9 1 3 9 5 EbG F Bb 8(11n 34n) F 9 5 9 1 3 C G F A 4(2n1 n33) F 9 5 3 1 9 C A F G 4(2n3 n31) Ab M76 3 1 6h7 C AbF G 4(2n2 n31) Ab M7 5 1h7 3 EbAbG C 8(12n n12) Ab 11 5 1 4 3 EbAbDbC 8(123 nn2) Ab 9 5 1 3 9 EbAbC Bb 8(122 n4n) Bb 7 3b7 5 1 D AbF Bb 5(3n1 n23) 132 9. A 7 5 1 3b7 E A C#G 4(*23 3*1) #133 5137 Q7 A 7 5 1 3b7 E A C#G 5(n12 24n) A 7+5 +5 1 3b7 F A C#G 6(n11 13n) A 7b5 b5 1 3b7 D#A C#G 2(n3n 113) B 74 4 1 3b7 E B D#A 4(n2n 113) B 97 1b7 9 3 B A C#D# 4(1n3 31n) A 7 5 1 3b7 E A C#G 5(*12 24*) B 11 4 1 3 5 E B D#F# 5(n14 43n) B 9 3 1 9 5 D#B C#F# 6(3n3 12n) B mi9 b3 1 9 5 D B C#F# 6(2n3 12n) D M7 1 5h7 3 D A C#F# 6(2n1 12n) D 6 6 5 1 3 B A D F# 4(1n3 44n) D mi6 b3 5 1 6 F A D B 10(112 n3n) E M7 1 3h7 5 E G#D#B 9(114 n4n) E 11 1 4 5 3 E A B G# 8(231 n2n) E 9M7 1 3h7 9 E G#D#F# 7(33n 21n) G mi6 6b3 5 1 E BbD G 5(n13 34n) G 11 4 3 5 1 C B D G 5(1n4 34n) G 9 3 9 5 1 B A D G 4(1n3 45n) A 7 5 1 3b7 E A C#G 5(n12 24n) A 7 5 1 3b7 E A C#G 4(n23 3n1) 133 10. F 7 5 1b7 3 C F EbA 4(23* *13) #134 5173 Q7 F 7b5 b5 1b7 3 B F EbA 4(13n n13) E 7+5 +5 1b7 3 C E D G# 3(33n n13) F 7 5 1b7 3 C F EbA 4(23* *13) G 11 4 1 5 3 C G D B 5(14n 3n4) G 9 3 1 5 9 B G D A 4(1n1 4n3) G 94 4 1 3 9 C G B A 4(2n1 1n3) Bb mi6 b3 5 6 1 DbF G Bb 7(nn4 421) Bb M7 1 5 3h7 BbF D A 3(14n n14) Bb 9 9 5 3 1 C F D Bb 5(12n 3n3) Bb 9M7 9 1 3h7 C BbD A 5(1n3 3n2) C M7 1 3 5h7 C E G B 4(221 1nn) C 11 1 4 3 5 C F E G 4(23n n21) C 94 1 4 9 3 C F D E 5(12n 31n) Eb 6 6 3 1 5 C G EbBb 4(2n1 n14) F 7 5 1b7 3 C F EbA 4(23n n13) 134 11. G 7 5 3b7 1 D B F G 4(4** 131) #135 5371 Q7 G 7b5 b5 3b7 1 DbB F G 4(3nn 131) Ab 7+5 +5 3b7 1 E C GbAb 5(n1n 131) A 74 4 3b7 1 D C#G A 6(2nn 131) D 97 9 3b7 1 E F#C D 7(313 1nn) G 7 5 3b7 1 D B F G 4(4** 131) A M7 3 1 5h7 C#A E G# 5(2n2 n11) A 11 4 3 5 1 D C#E A 7(1n4 34n) A 9 3 9 5 1 C#B E A 6(1n3 45n) C M7 1h7 3 5 C B E G 4(2nn 121) C 6 6 1 3 5 A C E G 8(n32 21n) C 9 9 1 3 5 D C E G 7(1n3 32n) D M7 1h7 3 5 D C#F#A 6(2nn 121) D 9 1 5 9 3 D A E F# 7(14n 31n) F 6 6 5 1 3 D C F A 7(1n3 44n) F 11 4 5 1 3 BbC F A (312 2nn) G 7 5 3b7 1 D B F G 4(4nn 131) 135 12. C 7 5b7 1 3 G BbC E 5(*43 11*) #136 5713 Q7 C 7+5 +5b7 1 3 AbBbC E 5(n53 11n) Bb 74 4b7 1 3 EbAbBbD 3(n23 11n) G 7b5 1 3b5b7 G B DbF 6(n33 11n) C 97 9b7 1 3 D BbC E 5(3n3 11n) C 7 5b7 1 3 G BbC E 5(*43 11*) D 11 4 5 1 3 G A D F# 6(n31 22n) D mi9 b3 5 1 9 F A D E 5(n22 31n) F M7 1 3 5h7 F A C E 5(n22 11n) G M7 1 3 5h7 G B D F# 7(n22 11n) G 9 1 3 9 5 G B A D 8(n11 n34) G mi9 1b3 9 5 G BbA D 11(21n 4n1) Bb 6 6 1 3 5 G BbD F 6(n32 21n) Bb mi6 6 1b3 5 G BbDbF 6(n32 11n) Bb 11 4 1 3 5 EbBbD F 6(3n2 21n) Bb 9 3 1 9 5 D BbC F 5(3n3 12n) C 7 5b7 1 3 G BbC E 5(n43 11n) 136 13. A 7 5b7 3 1 E G C#A 4(*21 3*3) #137 5731 Q7 A 7b5 1 3b7b5 A C#G D# 2(113 n3n) A 7+5 +5b7 3 1 F G C#A 4(n31 3n3) Ab 74 4b7 3 1 DbGbC Ab 5(23n 1n1) Ab 97 9b7 3 1 BbGbC Ab 3(1n1 3n3) A 7 5b7 3 1 E G C#A 4(*21 3*3) B M7 3 5 1h7 D#F#B A# 7(212 nn1) B 9 3 5 9 1 D#F#C#B 6(32n 1n3) B mi9 b3 5 9 1 D F#C#B 6(22n 1n3) B 9M7 3 1 9h7 D#B C#A# 6(3n3 1n2) D M7 1 3h7 5 D F#C#A 7(114 n4n) D mi6 b3 6 1 5 F B D A 10(132 n1n) D 9 9 3 1 5 E F#D A 7(31n 14n) D 94 9 4 1 3 E G D F# 7(32n 11n) E 9 1 9 5 3 E F#B G# 7(312 n3n) E mi9 1b3 5 9 E G B F# 7(322 n1n) E 9M7 1 9h7 3 E F#D#G# 3(n31 n23) G 6 6 1 5 3 E G D B 8(214 nn1) G 11 4 1 5 3 C G D B 5(14n 3n4) G 9 3 1 5 9 B G D A 4(1n1 4n3) A 7 5b7 3 1 E G C#A 4(n21 3n3) 137 14. D 7 b7 3 1 5 C F#D A 5(13* 3*2) #138 7315 Q7 Db 7b5 b7 3 1b5 B F DbG 4(13n 3n1) F 7+5 b7 1 3+5 EbF A Db 6(311 1nn) D 97 b7 3 1 9 C F#D E 5(13n 31n) D 13 b7 3 1 6 C F#D B 5(13n 3n4) D 7 b7 3 1 5 C F#D A 5(13* 3*2) E M7 5 1h7 3 B E D#G# 4(12n n12) E 9 5 9 1 3 B F#E G# 3(2n1 n33) E 9M7 1 9h7 3 E F#D#G# 7(31n 23n) G 6 3 1 5 6 B G D E 13(4n4 n31) G 94 4 1 3 9 C G B A 4(2n1 1n3) A 9 3 5 9 1 C#E B A 4(32n 1n3) A 9 9 5 3 1 B E C#A 4(12n 3n3) A mi9 b3 5 9 1 C E B A 4(22n 1n3) C M7 1 5 3h7 C G E B 5(14n n14) C 6 1 5 3 6 C G E A 4(2n1 n23) C mi6 1 5b3 6 C G EbA 4(2n1 n13) C 94 1 4 9 3 C F D E 5(12n 31n) D 7 b7 3 1 5 C F#D A 5(13n 3n2) 138 15. Eb 7 b7 3 5 1 DbG BbEb 6(132 3**) #139 7351 Q7 D 7+5 b7 3+5 1 C GbBbD 5(133 3nn) B 7b5 3b7 1b5 EbA B F 4(n13 13n) F 13 b7 3 6 1 EbA D F 6(3n1 21n) Eb 7 b7 3 5 1 DbG BbEb 6(132 3**) F M7 5 1 3h7 C F A E 5(122 n1n) F 9 5 9 3 1 C G A F 14(4n3 1n1) Ab mi6 6 1b3 5 F AbB Eb 8(321 1nn) Ab 11 4 1 3 5 DbAbC Eb 4(3n2 21n) Ab 9 3 1 9 5 C AbBbEb 11(n3n 312) Ab 9 9 5 1 3 BbEbAbC 11(n12 33n) Bb mi9 b3 5 1 9 DbF BbC 5(223 1nn) Db M7 1 5h7 3 DbAbC F 5(2n1 12n) Db 6 1 5 6 3 DbAbBbF 3(4n3 14n) Db 9M7 1 3h7 9 DbF C Eb 4(33n 21n) Eb 7 b7 3 5 1 DbG BbEb 10(nn1 323) 139 16. C 7 b7 5 1 3 BbG C E 3(1*2 33*) #140 7513 Q7 C 7b5 b7b5 1 3 BbGbC E (3n3 n11) C 7+5 b7+5 1 3 BbAbC E 3(1n3 33n) E 74 b7 4 1 3 D A E G# 5(3n2 n11) E 97 b7 9 1 3 D F#E G# 7(11n 33n) G 13 b7 6 1 3 F E G B 6(n1n 433) C 7 b7 5 1 3 BbG C E 3(1*2 33*) D 11 5 4 1 3 A G D F# 2(1n3 n22) D 9 5 3 1 9 A F#D E (2n3 n31) D mi9 5b3 1 9 A F D E (2n2 n31) D 9M7 1 3h7 9 D F#C#E 5(33n 21n) F M7 3 1 5h7 A F C E (2n2 n11) F 6 3 6 5 1 A D C F (23n n12) F mi6 6b3 5 1 D AbC F 3(n13 34n) F 11 4 3 5 1 BbA C F 3(1n4 34n) F 9 3 9 5 1 A G C F 2(1n3 45n) G M7 3 1 5h7 B G D F# 3(2n2 n11) G 9 9 1 3 5 A G B D 2(1n3 32n) G 9 3 1 9 5 B G A D 2(3n3 12n) G 9M7 9 1 3h7 A G B F# 2(1n3 3n2) Bb M7 1h7 3 5 BbA D F 2(2nn 121) Bb mi6 1 6b3 5 BbG DbF 2(2n3 n11) Bb 11 1 4 3 5 BbEbD F 2(23n n21) Bb 9 1 3 9 5 BbD C F 3(11n 34n) C 7 b7 5 1 3 BbG C E 3(1n2 33n) 140 art@ end of QMAS (page) APPENDIX NEW TUNINGS The ability of the guitar to be retuned is exploited only slightly in its classical tradition. Typically, by lowering the lowest string. The value of standard tuning for guitar, E,A,D,G,B,E, is the body of work that has been created for it. But we want new music. Modern guitarists have achieved great success with re-tuned guitars. These are called "open string" tunings when the intention is to make the best use of open strings. But this is not my topic. The tuning I will propose is for all keys. Let us ask the question: what is the best way to tune a guitar? One advantage of the guitar is the ease of playing the same tablature up and down the fretboard. On the piano, with its seven white and five black keys, to do the same requires innumerable adjustments. However, if the intervals between the strings are not the same, the guitarist must adopt a changed tablature when playing the same chord across the fretboard. This makes it harder to play, and what is achieved? If the strings are tuned unevenly, we are not making the most of the instrument's capacity for chords. Therefore, let us have a tuning with the same interval between each pair of strings. Then a tablature will be the same no matter where it is played. This is simple and easy to understand. Tablatures span four, and sometimes five frets (that's how far you can reach.) What would be the best interval by which all the strings could be tuned? I think this is a question that does have one right answer, based on the major chord. Tablatures for the major triad, using uniform intervals between the strings, are compared in the table below: mi3 M3 P4 tritone P5 ----- ---- ---- ----- ---- 1-3-5 122 or 3x11 221 431 ? ? 1-5-3 1x2xx2 2x1x2 13x2 34x1 113 3-1-5 1x3x4 2x2x1 14x1 or 3x13 134 122 3-5-1 113 or 22x1 212 331 ? ? 5-1-3 134 or 2x12 122 221 431 ? 5-3-1 1x4xx3 1x2x2 2x14 4x13 134 or 1xx1x3 or 4x3x1 Tuning all the strings at a major third makes the best tablatures for the major triad. Intervals of the major and minor triads range from the minor third to the major sixth. Only tuning to major thirds can play the tablatures of these intervals in a 3-fret span. Although the range between high and low strings is less than standard tuning, it is better for chords with notes close together. For example, the 1-3-5-b7 chord, which in standard tuning needs an open string or a 5-fret tablature, has the tablature 3321 with a tuning of major thirds. Augmented Tuning I will call this new tuning "augmented" because the open strings are an augmented chord. On a score, it is necessary to indicate the tuning by, for example, showing the letter names of the open strings. Also, to distinguish augmented tuning from standard tuning in tablature, we'll use a lower case 'N' instead of an 'X' for the strings that do not sound. For example: 4(n3n 2n1) is a chord in augmented tuning, and (xx0 212) is a chord in regular tuning. What specific notes to use? Since standard tuning already has a major third between its third and second strings, G and B, this will be preserved. Therefore, the first string (the highest string) is tuned down a half step, to Eb, and the sixth, fifth and fourth strings are tuned to the octave of the third, second and first. It is better to call the first string "Eb" than "D#". Guitar players are used to the sharp keys because of the E and A on the open, lowest strings. But we ought to get used to the flat keys too. Piano scores use flatted keys more often that sharp ones, and wind instruments often transpose with flatted keys. Augmented tuning tunes the strings, from lowest to highest, G,B,Eb,G,B,Eb. Middle C is at the first fret of the second string. On delicate instruments, the increased tension on the bridge might cause damage. So tune it down a step, to F,A,C#,F,A,C# and the tension will be reduced. Why should a guitarist welcome a new tuning when it means learning a whole new set of tablatures? Well I think when you've learned guitar you've learned the dexterity to play it, and memorizing new tablatures is no big deal. In fact, old-time guitarists would probably welcome the challenge. There is the drawback of learning new letters. One learns to directly associate a letter name with the instrument in the special, very fast, way that music requires. But, most guitarists don't read much music anyway -- on a five line staff. Learning to read music on a 5-line staff means making letter associations on the fretboard. I think this is very much worth doing, and I would expect many of my readers who choose to pursue augmented tuning will also be learning the 5-line staff. In augmented tuning, their are only three letters on a fret -- a repeating augmented triad. So you only have to learn the sequences: G-B-Eb, Ab-C-E, A-Db-F, Bb-D-Gb, B-Eb-G, C-E-Ab, Db-F-A, D-F#-Bb, Eb-G-B, E-Ab-C, F-A-C#, and Gb-Bb-D! Well, "musicians like new things", or so they say. Some Practical Tips With the strings tuned all to major thirds, the tablature for a minor third is one fret down on the higher string, and the tablature for a major sixth is one fret up on the next higher string. With the strings tuned all to major thirds, a major second is two frets down on the higher string, and a minor seventh is two frets up on the next higher string. A tritone is two frets up on the higher string, or two frets down on the next higher string. A perfect fourth is one fret up; a perfect fifth is one fret down. An octave is at the same fret two strings higher, and unison with a higher string is at the fourth and eighth frets. This diagram shows the major scale parts that are nearby when a bass string stops the root or fifth of the scale: . 2 . . . 6 . 4 . . 5 h7 . . 2 . 1 3 . 1 5 h7 . 5 . 4 6 . . 1 3 . . . . 2 . . 4 6 Here's another way of looking at it: @std @aug 5(111 111) = 2(123 445) 4(543 221) = 5(111 111) Three practical keys are C, Eb and G. Here are their octaves in augmented tuning: C (n1n n1n) or 3(1nn 1nn) or 9(nn1 nn1) Eb (nn0 nn0) or 4(n1n n1n) or 8(1nn 1nn) G (0nn 0nn) or 4(nn1 nn1) or 8(n1n n1n) The tablature of the major and minor triads make a simple shape in augmented tuning. Here is how they would appear on an (imaginary) instrument with twelve strings: C major: 4(2n1 n2n 2n1 n2n), or 1, 5, 3, 1, 5, 3. fig@ shape of major tabs C minor: 4(2n1 n1n 2n1 n1n), or 1, 5, b3, 1, 5, b3. fig@ shape of minor tabs The whole tone scale simply plays all the strings on either the odd or even numbered frets. Here are some other triad tablatures with memorable shapes: fig@ other triad tablature shapes The Case for Augmented Tuning Compared to regular tuning, augmented tuning allows chords with smaller intervals -- especially with inner voices. Although regular tuning has greater range, augmented tuning can be lowered. The trouble with regular tuning is that its most familiar chords, on five or six strings, have become trite. One of the things I really like about using augmented tuning is that it seems to work far better for reading piano scores. Of course, one is compressing as much as five octaves, or at least three octaves, into the two octaves of a guitar. (I realize a guitar can play three octaves, but that doesn't usually mean the highest and lowest together.) Guitar is good for the singing range. Piano scores are practically the only printed music for Jazz. Reducing a piano score for guitar will work better with augmented tuning.