84 Chord-Scale Relationships
The combinatorics of 12 transpositions and 7 modes — how the number 84 falls out of the mathematics, and what the distribution of those relationships reveals.
The SuperScales book documents 84 chord-scale relationships derived from the Melodic Minor Ascending scale family. This number is not arbitrary — it follows directly from the combinatorial structure of the MMA system. Understanding where 84 comes from, and how the relationships distribute across the seven modes and 12 transpositions, gives the system a mathematical clarity that makes it easier to learn and remember.
Not all 84 pairings cover distinct chord types — some modes from different transpositions cover the same chord type (e.g., the Altered mode from multiple transpositions all cover altered dominant chords). But the 84 pairings represent the full enumeration of scale-chord relationships, including the overlapping ones, and that complete enumeration is what the SuperScales book documents.
Distribution by Mode
The 84 relationships are not evenly distributed across the seven modes. Some modes appear more frequently across the 12 transpositions in musically useful pairings; others are more specialized:
The Altered mode’s high count (appearing in 5 of the 12 most common pairings) reflects its role as the primary secondary-dominant scale. The Lydian Dominant’s 3 appearances reflect its usefulness across blues, tritone substitution, and modal interchange contexts. The MMA scale itself (mode 1) and the Locrian nat2 (mode 6) each have a single primary application — they are specialists rather than generalists within the system.
The Full 84 — A Structural Map
| MMA Root | Mode | Chord Covered | Function in C |
|---|---|---|---|
| C | Mode 1 (MMA) | CmΔ7 | Tonic minor |
| D | Mode 2 (Dorian b2) | Dm7sus♭9 | IIm7 (dark) |
| Eb | Mode 3 (Lydian #5) | E♭Δ7#5 | bIII modal interchange |
| F | Mode 4 (Lydian Dom) | F7#11 | IV7 Lydian dominant |
| G | Mode 5 (Mixo b13) | G7♭13 | V7 primary dominant |
| Ab | Mode 3 (Lydian #5) | A♭Δ7 | bVI modal interchange |
| A | Mode 7 (Altered) | A7alt | V7/II secondary dom |
| Bb | Mode 4 (Lydian Dom) | B♭7#11 | bVII blues dominant |
| B | Mode 7 (Altered) | B7alt | V7/III secondary dom |
| C# | Mode 7 (Altered) | C#7alt | Tritone sub of G7 |
| Eb | Mode 7 (Altered) | E♭7alt | V7/V/II extended |
| F# | Mode 7 (Altered) | F#7alt | Tritone sub of C7 |
This table shows the primary pairing for each of the 12 MMA transpositions. The full 84 include additional secondary pairings where each transposition’s other modes also produce valid chord-scale matches.
What the Distribution Tells You
The distribution of 84 relationships across modes is not uniform, and that non-uniformity is musically meaningful. The Altered mode’s dominance of the secondary dominant territory tells you that altered dominant chords are the primary application of the upper MMA transpositions — not a special case but the central use case. The Lydian Dominant’s multiple appearances tell you that #11 dominant chords are common enough in real music (blues IV7, tritone substitutions, modal interchange) to warrant their own dedicated mode.
The modes with single primary applications (MMA itself, Locrian nat2) are not less important — the minor-major seventh chord and the half-diminished chord are both essential harmonic objects. But they appear once in the primary mapping rather than repeatedly, which tells you that the MMA system addresses them with a single, precise tool rather than a family of overlapping options.
This structural map — 12 transpositions, 7 modes, 84 relationships, distributed unevenly across chord types according to musical frequency — is the mathematical organization that the SuperScales system makes learnable. Not 84 arbitrary facts to memorize but a coherent structure with its own internal logic.
Combinatorics and music — counting what matters
12 × 7 = 84
The number 84 is not a choice — it is a consequence of the structure. 12 pitch classes × 7 modes = 84 scale-chord pairings. Combinatorial counting reveals the full scope of a system, including the relationships that intuition might miss.
Non-uniform distribution
The uneven distribution of the 84 relationships across modes mirrors the uneven distribution of chord types in real music. The Altered mode’s dominance reflects the prevalence of secondary dominants in jazz and functional harmony. The mathematics tracks the music.
Overlap as information
When multiple transpositions cover the same chord type (as the Altered mode does for altered dominants), that overlap is information — it tells you which chord types are harmonically central and which scale modes are most flexible. Overlap is not redundancy; it is structural richness.
Structural map vs. memorization
84 relationships are too many to memorize as isolated facts. But as a structured map — 12 transpositions × 7 modes, with a logical distribution across chord types — the same 84 become learnable as a coherent system. Structure enables memory.
The next article examines the power set of the MMA scale — the subsets hidden within its seven pitch classes, including the 10 hexatonics, 12 pentatonics, and 16 arpeggios that can be extracted from MMA and used as independent harmonic resources.
Combinatorics of pitch class sets: Forte, The Structure of Atonal Music (1973). The complete 84-relationship documentation is in the SuperScales book at muse-eek.com.