Music by the numbers

When I was younger, the John Mehegan theory books were in all the stores, and although maligned for his approach by some critical theorists, I found his "four-tone" concept,  jazz as four-note chords, a useful starting place. Years later I found a much more refined approach in The Jazz Piano Book by Mark Levine -- no matter what your instrument I recommend this wonderful volume -- and even if you read music slowly (or not at all) find a piano and figure out what the chord voicings and progressions he describes actually sound like!

Mehegan's jazz theory is based on chords with four notes, and the use of Roman numerals to describe degrees of the scale and chord qualities. For clarity, we often describe things in the key of C, but to be truly accomplished, we know we should understand all twelve keys. It may seem counter-intuitive, because learning to analyze songs in terms of numerical equivalence will take extra time at first, but knowing music "by the numbers" makes it easier to transpose and play in all keys later.

There are perhaps fifteen basic chord types one might regularly encounter, and only four basic scale types. Once the proper spelling for each key is mastered, it makes sense to analyze new songs starting with the home chord as Roman numeral I, continuing up the scale with ii, iii, IV, V, vi and vii. Our seven basic modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian) are developed from the major scale -- no surprises -- no accidentals. Then there are the secondary dominants. When we change ii to II, vi to VI, iii to III, they become dominant 7th chords in the four-tone system.

With seven tones in the major scale, and four tones given in the definition of the chord, the other three notes in the corresponding scale for each chord can be chosen easily. II7 becomes Mixolydian, the scale for VI7 becomes an inversion of ii melodic minor ascending (in the key of C) A B C# D E F G A and the scale for III7 is an inversion of vi harmonic minor E F G# A B C D E. In actual practice, II7 is likely going to appear as a Lydian dominant (D7+11, or D7+4) D E F# G# A B C D. VI7 (written A7b13, A7+5, or simply A7) may be realized as descending A G F E D C# Bb A, and III7 can show up as a fully altered dominant (III7+5+9, III7alt...), a diminished whole-tone scale E F G G#(Ab) Bb C D E. Sometimes the V7 is altered to G7b9 -- either G Ab B C D E F G or perhaps G Ab Bb B C# D E F G (G7b9+11) -- a full diminished scale. The Lydian dominant can show up anywhere when used to resolve down a half-step, but it can also "relax" from bVII7+11 to I or progress from II7+11 to iim7.

Diminished and whole tone scales are symmetrical. The diminished scale can be played two ways, either starting with a whole step, or (as in the case of the dominant b9 scale) a half step. It's either W H W H W H W H or H W H W H W H W. The diminished scale starting with a whole step often appears as a # iv chord. The diminished scale starting with the whole step can be used to great effect as the basic elements of the scale are reminiscent of the top four notes of a dominant (Mixolydian) scale, or the first four notes of minor, and extending a little further, the flatted fifth appears and sounds quite bluesy. (Blues scale in C: C Eb F F# G Bb C)

The dominant 7b9 chord can be considered as a diminished scale starting with a half step, but it sounds best when using a W H scale referenced to the third or the fifth of the chord. The other symmetrical scale in common use, the whole tone (W W W W W W) can be used against a dominant with #5 added, G A B C# D# F G, G7+5. At times a chord notated as a +5 is actually a b13, so one has to determine from usage which scale to use.

Here are the most common four-tone chords one will see:

I Maj7, iim7, iiim7, IVMaj7+4, V7, vim7, viim7b5, III7+9, VI7(b13), II7+11, V7b9, V7b9+11, V7+5, #ivdim7, ivmMaj7

Each one of the above takes a different seven note scale (eight notes when diminished or if adding a passing tone). Four (sometimes more) notes are defined, three are variable, usually pulled from the key signature or surrounding tonality. The seven notes in the major scale give rise to the seven basic modes. When one changes the third of a major I chord to minor the resulting scale is called melodic minor ascending, e.g. C D Eb F G A B C. (Melodic minor descending is the same as the Aeolian mode, in this case an Eb major scale referenced to C: C Bb Ab G F Eb D C) Eight note scales are usually derived by adding a passing tone between 5 and 6 in the scale of a major chord, between 7 and 8 in a dominant chord-scale, and between 3 and 4 of a minor scale.

If one creates seven modes from the melodic minor ascending scale, the mode based on the second degree of the scale is seldom used, but the other "modes" (also known as "chord-scales") correspond to our secondary dominants and other altered scales. Using C melodic minor ascending as a starting point one develops these scales: Eb Lydian augmented, F Lydian dominant, G dominant b13, A super-Locrian (m7b5 add 9) and B fully altered dominant (diminished whole-tone scale). It takes a while to get used to but things simplify to the point where our basic choice of scales comes down to the seven inversions of major found in the common modes, five common inversions of melodic minor ascending, the two types of fully diminished scale and the whole tone scale (C D E F# G# A# or C# D# F G A B).

Once we learn our basic fifteen chord-scales in all twelve keys and begin thinking of music "by the numbers" then we are using a more functional approach to our playing. We become more concerned with "where a chord is going" rather than obsessing about its vertical structure. When we relax on a "one" chord or riff on a pedal point, we're either "home" or "away." And what type of home and what type of away are defined by context as much as by the chord symbol notated in the sheet music.