Béla Bartók: Verminderte Quinten

Описание: Diminished Fifths. (Mikrokosmos IV, 101)
Transcription by J. O. Marques

(Notes from Wikipedia)
"In Béla Bartók's piano piece, "Diminished Fifths" from Mikrokosmos, octatonic collections form the basis of the pitch content. In mm. 1–11, all eight pitch classes from the E♭ 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♭, F, G♭, and A♭ 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♭ minor scale. In mm. 5–11, the left and right hand switch—the A minor tetrachord appears in the left hand, and the E♭ minor tetrachord appears in the right hand.

"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".[52]

Bartók also utilizes the two other octatonic collections so that all three possible octatonic collections are found throughout this piece (D♭, D, and E♭). In mm. 12–18, all eight pitch classes from the D♭ octatonic collection are present. The E♭ octatonic collection from mm. 1–11 is related to this D♭ 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♭ octatonic collection from mm. 1–11 by the following transposition operations: T2, T5, T8, T11.

"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♭, E♭, and G♭, 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♭, C, E♭ and E, G♭, A respectively. Later on, in mm. 20, the right