Glossary
Double Diminished (Octatonic)
Glossary
The double diminished (octatonic) scale refers to the set class (unordered collection) of eight notes consisting of alternating semitone and whole-tone intervals. This scale is a mode of limited transposition and can be thought of as two interlocking fully-diminished seventh chords.
The diminished scale is the maximally even scale of cardinality eight, a symmetric set class which only has two modes, one starting with a semitone then a whole-tone, and one starting with a whole-tone followed by a semitone. There are only three transpositions of the scale, and they are closer in voice leading distance to transpositions of the acoustic scale (two semitones away from four of the transpositions of the acoustic scale) than to one another (four semitones away from the nearest transposition of the diminished scale).
See Beyond Diatonic for more on the set class for this scale.
The double diminished (octatonic) scale refers to the set class (unordered collection) of eight notes consisting of alternating semitone and whole-tone intervals. This scale is a mode of limited transposition and can be thought of as two interlocking fully-diminished seventh chords.
The diminished scale is the maximally even scale of cardinality eight, a symmetric set class which only has two modes, one starting with a semitone then a whole-tone, and one starting with a whole-tone followed by a semitone. There are only three transpositions of the scale, and they are closer in voice leading distance to transpositions of the acoustic scale (two semitones away from four of the transpositions of the acoustic scale) than to one another (four semitones away from the nearest transposition of the diminished scale).
See Beyond Diatonic for more on the set class for this scale.