The 2,521 Trichord Pair Études
How MMA’s 10 hexatonic subsets connect the SuperScales system to the Sound Cells trichord pair series — and how 2,521 études were generated from that connection.
The SuperScales book includes 2,521 trichord pair études — exercises that use MMA’s hexatonic subsets as the source material for trichord pair practice. This number is not arbitrary: it follows from the intersection of MMA’s 10 hexatonics with the 78-volume Sound Cells trichord pair system, filtered by the hexatonic subsets that produce musically useful trichord combinations, across all 12 keys and multiple exercise formats.
= 2,521 trichord pair études
The Connection Between SuperScales and Sound Cells
The 2,521 études are where the SuperScales system and the Sound Cells hexatonic trichord pair system explicitly connect. The Sound Cells series (78 volumes, one per trichord pair combination) provides the trichord pair framework — how to practice two trichords alternating and pivoting over a drone. The SuperScales system provides the source scale — MMA — from which the trichord pairs are drawn.
Several of MMA’s hexatonic subsets correspond directly to volumes in the Sound Cells series. When a student practices the Lydian Dominant mode’s hexatonic subset as a Sound Cells trichord pair, they are doing two things simultaneously: practicing the MMA Lydian Dominant mode, and practicing the Sound Cells hexatonic pair that that subset represents. The two systems reinforce each other.
Types of Études
Each hexatonic subset generates multiple exercise formats, and the 2,521 total reflects the full enumeration of these formats across all keys:
The Generation Pipeline for Études
Each étude was generated using the same LilyPond + SuperCollider pipeline described in earlier articles. Python specified the hexatonic subset, the trichord split, the key, and the exercise format. LilyPond generated the score. SuperCollider generated the audio against the appropriate drone. The output was organized by MMA mode, by hexatonic subset, by key, and by exercise format.
The 2,521 total reflects filtering: not every hexatonic subset produces a musically useful trichord pair combination in every format. Some subsets split into trichords that have too much pitch-class overlap to function independently as paired entities. These were filtered out, leaving 2,521 études that all meet the criterion of clear trichord differentiation within the MMA sound world.
The connection between SuperScales and Sound Cells that these études embody is pedagogically important: a student working through the SuperScales book is not learning an isolated system but entering a larger ecosystem. The trichord pair logic from Sound Cells applies directly; the scale degree awareness from the key center ear training applies directly; the drone practice from the MetroDrone applies directly. Every hour spent on any part of the system deepens every other part.
System integration and production at scale
System intersection
The 2,521 études live at the intersection of two systems — SuperScales and Sound Cells. Exercises at system intersections are particularly valuable because they develop multiple competencies simultaneously without requiring additional practice time.
Filtering for quality
Not every generated combination was included — filtering for musical coherence reduced the raw combinatorial total to 2,521 pedagogically useful études. Automated generation plus manual or algorithmic quality filtering is the production pattern for large educational content libraries.
2,521 as tractable
2,521 études sounds like a large number. But organized across 10 hexatonics × 12 keys × ~21 formats, each group is small and learnable. Structure converts an overwhelming quantity into a navigable curriculum. The organization is as important as the content.
Ecosystem over isolation
A pedagogical system that connects to other systems is more valuable than one that stands alone. Every connection between SuperScales and Sound Cells is a pathway for transfer — learning that reinforces multiple competencies rather than building a single isolated skill.
The next article examines how AI assistance — specifically Claude — accelerated the analysis and production of the SuperScales book, and what the collaboration between human musical expertise and AI text and mathematical analysis actually looked like in practice.
Trichord pair practice methodology is documented in the Sound Cells and Trichord Pairs series at muse-eek.com. LilyPond documentation at lilypond.org. The 2,521 SuperScales trichord pair études are included in the SuperScales book.