File:The Quadruple-Diminished Scale.png

This is my interpretation of a hexadecatonic quadruple diminished scale (Quadruple Augmented "mode" in the image below - with the A7 Harmony below that, it becomes dually-functioning), playable in 24edo. One can think of this as two Wyschnegradsky's octatonic scales spaced a quarter-step apart, or as a Wyschnegradsky's octatonic with tonics to produce four different dominant 7th (or four minor 6th) chords, two of which are tuned in quarter-tone. The purpose of this is to facilitate the modulation between keys in 12edo and 24edo, sans the disintegration of A=440hz. For example, a movement from V7 to Ihf7 to I7 in A=440hz, that I care to deem "the superperfect cadence".