Diminished-Augmented Ring Structure
A small interactive music-theory tool for theorists & mathematicians.
Key
Saturate →
Circle of Fifths →
← Staff & Sets
Borromean Functor →
← Circle of Fifths
The three diatonic vii°7 chords
As pitch class sets
Three diminished 7
th
chords on the Circle of Fifths
The augmented triad — one note from each diminished chord, separated by M3
Functor and the Borromean condition
Category 𝓐 as Borromean rings
Each ring lies
over
one neighbor and
under
the other. No two are linked alone — but all three together cannot be separated.