MMA and the Circle of Fifths
How the 12 MMA transpositions map onto the circle of fifths — revealing a symmetry in the distribution of modes that the chord-by-chord framework could not have predicted.
The circle of fifths is the oldest and most fundamental organizational diagram in Western music theory. It arranges the 12 pitch classes around a circle so that adjacent pitches are a perfect fifth apart, and it has been used for centuries to visualize key relationships, modulations, and harmonic progressions. It is so fundamental that it appears in virtually every music theory textbook ever written.
The 12 transpositions of the MMA scale map onto the circle of fifths in a specific pattern — and that pattern reveals a symmetry in the distribution of MMA modes that was not visible from within the chord-by-chord framework. Looking at MMA through the circle of fifths lens adds another layer of mathematical organization to the SuperScales system.
The 12 Transpositions on the Circle
Each of the 12 pitch classes is the root of one MMA transposition. When these 12 transpositions are arranged on the circle of fifths, the mode that each transposition applies in the key of C forms a pattern:
The Pattern — Fifths Drive the Altered Mode
Looking at the circle of fifths arrangement, a clear pattern emerges: the MMA transpositions that produce the Altered mode tend to appear at specific interval positions from the key center. Moving clockwise around the circle (by fifths) from the key center C, the secondary dominant positions — A (major 6th above C), B (major 7th), E (major 3rd), D# (minor 3rd) — all produce the Altered mode. These are the positions where dominant function chords appear in the key of C’s secondary dominant system.
This is not coincidental — it is a consequence of MMA’s interval structure. The positions that produce the Altered mode are those that place MMA’s most dissonant intervals (the b2 and b4 of the scale, which become the b9 and b5 of the chord) in maximum tension against the key center. The circle of fifths organizes pitch classes by their degree of fifth-relationship to the tonic; MMA’s Altered mode appears at precisely those positions that are furthest in fifth-distance from stable diatonic function.
A New View of a Familiar Diagram
The circle of fifths has been used for centuries to organize keys by their fifth relationships and to understand modulation. The MMA transposition map gives the circle of fifths a new meaning: it is also a map of which scale modes apply at which positions relative to a key center, when MMA is the scale family being used. The same diagram that organizes key signatures now also organizes the SuperScales system’s mode distribution.
This is an example of a familiar structure revealing new information when examined through a different lens — the same pattern that runs through this entire article series. The circle of fifths was always a pitch class relationship diagram. The key center lens, applied to MMA’s transpositions, reveals that it is also a mode distribution map for the SuperScales system.
For the improviser, the circle of fifths MMA map has a practical application: when navigating a chord progression that moves through the cycle (a standard jazz II-V-I or a sequence of secondary dominants), the appropriate MMA transposition at each chord can be read directly off the circle. The math is organized; the navigation becomes systematic.
Old diagrams, new information
The circle of fifths
The circle of fifths organizes the 12 pitch classes by fifth relationships — one of the most fundamental mathematical structures in music. Mapping MMA’s mode distribution onto it reveals that the same diagram that organizes keys also organizes the SuperScales mode system.
Pattern emergence
The Altered mode’s tendency to appear at secondary dominant positions — visible only when all 12 transpositions are mapped simultaneously — is a pattern that emerges from the mathematics. It was always there; the systematic mapping made it visible.
Practical navigation
A mathematical diagram becomes musically useful when it tells the improviser something actionable: which MMA transposition to use at each position in a progression. The circle of fifths MMA map does exactly this — a theoretical structure with direct practical application.
Familiar structures, new content
The history of mathematics is full of familiar structures that turn out to contain more information than originally recognized. The circle of fifths as an MMA mode map is a musical instance: a centuries-old diagram revealing new structure when a new question is asked of it.
The mathematics section of this series is now complete. The next section turns to physics: the overtone series and MMA, acoustic properties of the Altered scale, and how instrument timbre interacts with mode selection in the SuperScales system.
The circle of fifths is documented in virtually every music theory textbook. For its mathematical properties see Balzano, “The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems,” Computer Music Journal (1980). SuperScales documentation at muse-eek.com.