MMA and the Diatonic System
How the Melodic Minor Ascending scale relates to every chord in the diatonic system — and why this relationship unifies what chord-by-chord theory treats as separate problems.
The previous articles in this series documented how the 12 MMA transpositions cover all dominant-function chords in a key center — the primary dominant and all secondary dominants. This article extends that picture to the complete diatonic system: the seven chords that occur naturally in a major key, plus the modal interchange chords borrowed from parallel modes. The coverage is broader than the dominant function alone — and the pattern reveals a structural principle that has practical implications for how the scale is practiced.
The Complete Diatonic Chord System in C Major
A major key contains seven diatonic chords — one built on each scale degree. In the key of C:
Imaj7 (Cmaj7), IIm7 (Dm7), IIIm7 (Em7), IVmaj7 (Fmaj7), V7 (G7), VIm7 (Am7), VIIm7b5 (Bm7b5).
Beyond these seven, standard jazz practice also uses modal interchange chords borrowed from C Dorian, C Phrygian, C Lydian, C Mixolydian, C Aeolian, and C Locrian — particularly bVIImaj7, bIIImaj7, bVImaj7, IVm7, bII7 (the Neapolitan), and others. The question is: how many of these does the MMA scale family cover?
| Key degree | Chord in C | MMA transposition | Mode used |
|---|---|---|---|
| I | CmΔ7 (tonic minor) | C MMA | MMA itself |
| II | Dm7 | D MMA | Dorian b2 |
| III | Em7 (diatonic) | E MMA | Dorian b2 (over E) |
| bIII | EbΔ7#5 (modal interchange) | Eb MMA | Lydian #5 |
| IV | F7#11 (Lydian dominant) | F MMA | Lydian Dominant |
| V | G7b13 (primary dominant) | G MMA | Mixolydian b13 |
| bVI | AbΔ7 (modal interchange) | Ab MMA | Lydian #5 |
| VI | Am7 (diatonic) | A MMA | Dorian b2 (over A) |
| bVII | Bb7 (blues dominant) | Bb MMA | Lydian Dominant |
| VII | Bm7b5 (half-diminished) | B MMA | Locrian nat2 |
| V7/II | A7alt (sec. dominant) | A MMA | Altered |
| V7/V | D7alt (sec. dominant) | D# MMA | Altered |
The coverage extends across the full diatonic system and into modal interchange territory. The MMA scale family is not a specialist tool for dominant chords — it is a generalist tool for the complete harmonic language of a key center.
The Overlap Principle — Multiple Transpositions, Same Chord
One consequence of the 84 total chord-scale relationships is that some chords are covered by more than one MMA transposition. Am7, for example, can be covered by A MMA (Dorian b2 mode) in its jazz minor function or by a different transposition depending on its harmonic context. This overlap is not a problem — it is information. It tells you that some chords are more harmonically central (covered by many transpositions) and some are more peripheral (covered by only one).
What MMA Does Not Cover
Being honest about the limits of the MMA coverage is as important as documenting its breadth. The MMA scale family does not cover all chord types without qualification. Specifically:
Pure major seventh chords (Δ7 without alteration): The Lydian Dominant mode over a pure major seventh chord introduces the #11 (raised fourth), which may not be desired. A pure Cmaj7 chord with no alterations is more naturally covered by C Lydian (major scale mode 4) than by MMA.
Suspended dominant chords without the b9: The Dorian b2 mode is ideal for 7sus4b9 chords, but for a plain 7sus4 without the b9, a Mixolydian mode may be preferred. MMA’s b2 introduces an alteration that isn’t always wanted.
Pure minor seventh chords in diatonic context: When a IIm7 or VIm7 chord needs to sound completely diatonic (part of the major scale sound), the major scale’s Dorian mode is a cleaner fit than MMA’s Dorian b2, which introduces the b2 that colors the sound away from the diatonic.
These are not failures of the MMA system — they are specifications of where it works best. The MMA scale is optimized for dominant function and chromatic harmony. For purely diatonic contexts, the major scale and its modes remain the primary tool.
The Practical Consequence — One System for Complex Harmony
The practical consequence of MMA’s diatonic and chromatic coverage is a significant reduction in the cognitive complexity of navigating harmony. A musician who has internalized the MMA system and developed key center hearing can approach a complex chord progression — one full of secondary dominants, modal interchange, and altered dominants — with a single organizing framework rather than a collection of separate rules for each chord type.
This does not make the music simpler — the harmonic richness is preserved. What simplifies is the cognitive overhead of navigating it. One scale family, heard from one key center, replacing a patchwork of chord-specific rules. The music sounds the same; the process of making it feels different.
This is the practical payoff of the discovery documented in this series: not a new sound but a new way of organizing access to existing sounds. The relationship was always there. The MMA scale was always there. The key center framework and the computational verification made the organizing principle visible.
Unification and coverage in science and music
Unifying frameworks
Physics has repeatedly found that what appeared to be separate phenomena — electricity and magnetism, space and time, matter and energy — are aspects of a single unified framework. MMA’s coverage of diverse chord types from one scale family is a musical instance of the same unification principle.
Knowing the limits
A scientific theory that claims to explain everything explains nothing — it is not falsifiable. The MMA system’s documented limits (pure diatonic contexts, plain major sevenths) make it a precise tool rather than a vague claim. Knowing what it doesn’t cover is as important as knowing what it does.
Cognitive load reduction
Unified frameworks reduce cognitive load not by simplifying the underlying reality but by organizing it more efficiently. Maxwell’s equations don’t simplify electricity — they organize its complexity into four elegant relationships. MMA’s unification does the same for chromatic harmony.
Coverage maps
The table of MMA transpositions and their chord coverage is a map of the harmonic space. Like any good map, it shows both what is present and what is absent — the covered territory and the edges where other tools are needed.
The Complete Picture
The six articles in this series’ science section have traced the MMA discovery from the initial observation (a familiar scale with an unfamiliar property) through the computational verification (the only 7-note scale with universal key-center coverage) to the full picture of what that coverage includes (dominants, secondary dominants, modal interchange, half-diminished chords — most of the chromatic harmonic language of a key center).
The series now moves into mathematics: the set theory behind MMA’s uniqueness, the combinatorics of 84 chord-scale relationships, and the power set structure of a 7-note scale. The same discovery, examined through the lens of pure mathematics.
Diatonic chord theory and modal interchange are covered in Levine, The Jazz Theory Book (1995). The complete MMA diatonic coverage table, with all 84 chord-scale relationships in all 12 keys, is in the SuperScales book at muse-eek.com.