Music & Mathematics MMA as a Generating System How one scale family — through 12 transpositions, 7 modes, and a complete subset structure — generates more usable harmonic material than any other 7-note scale. Bruce ArnoldMusic & Mathematics A generating system is a small set of rules or elements that produces a large, organized output.[…]

Music & Mathematics Subsets of MMA The 10 hexatonics, 12 pentatonics, and 16 arpeggios hidden inside the MMA scale — and why the power set of a 7-note scale is a complete harmonic toolkit. Bruce ArnoldMusic & Mathematics The Melodic Minor Ascending scale contains 7 pitch classes. Its power set — the collection of all[…]

Music & Mathematics 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. Bruce ArnoldMusic & Mathematics The SuperScales book documents 84 chord-scale relationships derived from the Melodic Minor Ascending scale family. This number is not[…]

Music & Mathematics Set Class 7-34 The mathematics behind MMA’s uniqueness — why its interval vector makes it different from all other 7-note scales, and what the numbers reveal about its harmonic structure. Bruce ArnoldMusic & Mathematics In pitch class set theory, every scale or chord is classified by its set class — a label[…]

Music & Science 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. Bruce ArnoldMusic & Science The previous articles in this series documented how the 12 MMA transpositions cover all dominant-function chords[…]

Music & Science The Seven Modes of MMA A detailed portrait of each mode of the Melodic Minor Ascending scale — its interval structure, characteristic sound, chord function, and place in the key center coverage system. Bruce ArnoldMusic & Science The Melodic Minor Ascending scale, like the major scale, generates seven modes — one starting[…]

Music & Science Secondary Dominants and the MMA How all 12 transpositions of the Melodic Minor Ascending scale distribute across every dominant-function chord in a key center — and what this means for improvisation. Bruce ArnoldMusic & Science A secondary dominant is a dominant seventh chord borrowed to temporarily function as the V7 of a[…]

Music & Science The Key Center Lens How changing the reference frame from chord-by-chord to key center is a paradigm shift — and what relationships become visible once you make it. Bruce ArnoldMusic & Science In 1962, Thomas Kuhn published The Structure of Scientific Revolutions, introducing the concept of the paradigm shift: a change not[…]

Music & Science What Makes a Scale Universal Why the Melodic Minor Ascending scale is the only 7-note scale in Western music where all 12 transpositions function over real chords in a single key center — and how SuperCollider proved it. Bruce ArnoldMusic & Science A strong claim was made in the first article of[…]

Music & Science The Scale That Was Always There The Melodic Minor Ascending scale has been in every jazz theory book for generations. Its deepest property — a relationship to all 12 dominant chords in a single key center — was hiding in plain sight until someone asked a different question. Bruce ArnoldMusic & Science[…]