Known in Persian music as "zer ef kend", or the string of pearls, any one of these will contain two different Petroushka chords, a result first elucidated by Arthur Berger.
Cohn's theorem claims that this is the only collection of pitch-classes in equal temperament that can by partitioned into all six dyad classes. Known in Persian music as "zer ef kend", or the string of pearls, any one of these will contain two different Petroushka chords, a result first elucidated by Arthur Berger. It was classified by Olivier Messaien as the second mode of limited transposition, which indicated its three possible transpositions; its complement is the diminished seventh chord.  It is exclusively used in "Diminshed Fifths" from Bartok's Mikrokosmos, and in Kashchey the Immortal, Rimsky-Korsakov used it as a melodic element to indicate the supernatural. Known in jazz music as the diminished scale, for 10 points, identify this scale which alternates whole steps and half steps, and is so named for its eight distinct notes.
Cohn's theorem claims that this is the only collection of pitch-classes in equal temperament that can by partitioned into all six dyad classes.
{octatonic} scale (prompt on "{diminished scale}" early)