Editing Octatonic scale (section)

===Bitonality===
In [[Béla Bartók]]'s piano piece, "Diminished Fifth" from ''[[Mikrokosmos (Bartók)|Mikrokosmos]]'', octatonic collections form the basis of the pitch content. In mm. 1–11, all eight pitch classes from the E{{music|b}} diminished scale appear. In mm. 1–4, the pitch classes A, B, C, and D appear in the right hand, and the pitch classes E{{music|b}}, F, G{{music|b}}, and A{{music|b}} are in the left hand. The collection in the right hand outlines the first four notes of an A minor scale, and the collection in the left hand outlines the first four notes of an E{{music|b}} minor scale. In mm. 5–11, the left and right hand switch—the A minor tetrachord appears in the left hand, and the E{{music|b}} minor tetrachord appears in the right hand.{{Original research inline|date=April 2015}}

From this, one can see that Bartók has partitioned the octatonic collection into two (symmetrical) four-note segments of the natural minor scales a tritone apart. Paul Wilson argues against viewing this as [[bitonality]] since "the larger octatonic collection embraces and supports both supposed tonalities".{{sfn|Wilson|1992|loc=27}}

Bartók also utilizes the two other octatonic collections so that all three possible octatonic collections are found throughout this piece (D{{music|b}}, D, and E{{music|b}}). In mm. 12–18, all eight pitch classes from the D{{music|b}} octatonic collection are present. The E{{music|b}} octatonic collection from mm. 1–11 is related to this D{{music|b}} octatonic collection by the transposition operations, T, T4, T7, T10. In mm. 26–29, all eight pitch classes from the D octatonic collection appear. This collection is related to the E{{music|b}} octatonic collection from mm. 1–11 by the following transposition operations: T2, T5, T8, T11.{{Original research inline|date=April 2015}}

Other relevant features of the piece include the groups of three notes taken from the whole-half diminished scale in mm. 12–18. In these measures, the right hand features D{{music|b}}, E{{music|b}}, and G{{music|b}}, the tetrachord without the 3rd (F). The left hand has the same tetrachord transposed down a tritone (G, A, C). In mm. 16, both hands transpose down three semitones to B{{music|b}}, C, E{{music|b}} and E, G{{music|b}}, A respectively. Later on, in mm. 20, the right hand moves on to A− and the left back to E{{music|b}}−. After repeating the structure of mm. 12–19 in mm. 29–34 the piece ends with the treble part returning to A− and the bass part returning to E{{music|b}}.{{Original research inline|date=April 2015}}