After Nancarrow No.21

A mensural palindromic composition for player (virtual) piano

Duration: 03′ 15″

#21 is one of Conlan Nancarrow’s most famous player piano studies, which is here explained by Carlos Sandoval (Nancarrow’s assistent of 27 years). “This canon is a good example how our perception of music works, related to our perception’s physical limitations and wonderful capacity of synthesis.” For reference, here’s Conlon Nancarrow, Study for Player Piano No. 21 on YouTube. This composition is rhythmically inspired by Nancarrow, but it is not a pastiche, this particular piece combines both palindromic rhythms & scales.

About this piece – After Nancarrow #21

The tempo is increased (and decreased) over 96 measures, from 110 to 382 bpm (increasing by 6bpm per measure). Piano 1 fades from left to right throughout, Piano 2 from right to left.

Piano 1 accelerates from 100bpm (bar 1) to 382 bpm (bar 48), then reverses this, decelerating from 382 (bar 49) to 100 bpm at bar 96.

Piano 2 decelerates from 382bpm (bar 1) to 100 bpm (bar 48), then reverses this, accelerating from 100 (bar 49) to 382 bpm at bar 96.

Piano 1 score here, Piano 2 score here


This piece uses the Outagraphic (complimentary or anti) extended scales derived from Pitch C-1 (16 Hz) , which is said to be the lower threshold at which pitch & rhythm coincide, the pitch/pulse threshold. 16 Hz = 8x demisemiquavers at 120 bpm = Pitch C-1. Frequencies below 16 hz are perceived as being part of a rhythmic event, 16 hz + is generally perceived as pitch. NB; Sensorimotor rhythm (SMR), regarded as a “resting” brain wave, has a frequency within the range of 13 to 15 Hz.

The primary ascending LIE pitches from C-1 are: C-1 (+1) C#-1 (+2) Eb-1 (+3) F#-1 (+4) Bb-1 (+5) Eb0 (+6) A0 (+7) E1 (+8) C2 (+9) A2 (+10) G3 (+11) F#4 (+12) F#5 (+13) G6 (+14) A7 (+15) C9

The primary descending LIE pitches from C9 are: C-1 (+15) Eb0 (+14) F1 (+13) F#2 (+12) F#3 (+11) F4 (+10) Eb5 (+9) C6 (+8) G#6 (+7) Eb7 (+6) A7 (+5) D8 (+4) F#8 (+3) A8 (+2) B8 (+1) C9

C-1 to C9 = 10 x 8ve’s = 120 chromatic pitch range. As all scales that start from any of the primary pitches will always contain C-1, a palindromic Piano keyboard LIE scale ascending from A0 to Eb7 is here used; A0(+1)Bb0(+2)C1(+3)Eb1(+4)G1(+5)C2(+6)F#2(+7)C#3(+8)A3(+9)F#4(+10)E5(+11)Eb6(+12)Eb7 and descending from Eb7 to A0 = A0(+12) A1(+11) G#2(+10) F#3(+9) Eb4(+8) B4(+7) F#5(+6) C6(+5) F6(+4) A6(+3) C7(+2) D7(+1) Eb7.

The combined A0/Eb7 Scale = A0(+1) Bb0(+2) C1(+3) Eb1(+4) G1(+2) A1(+3) C2(+6) F#2(+2) G#2(+5) C#3(+5) F#3(+3) A3(+6) Eb4(+3) F#4(+5) B4(+5) E5(+2) F#5(+6) C6(+3) Eb6(+2) F6(+4) A6(+3) C7(+2) D7(+1)Eb7.

The mid point of the combined A0/Eb7 scale is C4, the palindromic C4 Lie scale is; C1, G#1, Eb2, A2, D3, F#3, A3, B3, C4, C#4, Eb4, F#4, Bb4, Eb5, A5, E6, C7, A7, this plus the prime A0/Eb7 scale is, Palindromic Prime Scale 1:

A0(+1)Bb0(+2)C1(+3)Eb1(+4)G1(+1)G#1(+1)A1(+3)C2(+3)Eb2(+3)F#2(+2)G#2(+1)A2(+4)C#3(+1)D3(+4)F#3(+3)A3(+2)B3(+1)C4(+1)C#4(+2)Eb4(+3)F#4(+4)Bb4(+1)B4(+4)Eb5(+1)E5(+2)F#5(+3)A5(+3)C6(+3)Eb6(+1)E6(+1)F6(+4)A6(+3)C7(+2)D7(+1)Eb7 (intervallic distances = 12341133321414321-12341412333114321).

There are 44 Outagraphic pitches (22 + 22 = 44) associated with this particular scale:

B0, C#1 D1, E1 F1 F#1, Bb1 B1, C#2 D2, E2 F2, G2, Bb2 B2 C3, Eb3 E3 F3, G3 G#3, Bb3, D4, E4 F4, G4 G#4 A4, C5 C#5 D5, F5, G5 G#5, Bb5 B5, C#6 D6, F#6 G6 G#6, Bb6 B6, C#7

(1,2,3,2,2,2,1,3,3 |2,1 | 1,2 | 3,3,1,2,2,2,3,2,1 – & )

Score Usage

The left hand rotates the lowest 11 pitches (+ an additional F#1) in an ostinati sequence lasting 12 bars, which is repeated 8 times at diverse tempi .

The right hand (piano 2) plays a repeated 72 note phrase that uses the remaining 33 pitches of the scale and is repeated every 4 bars (18 notes per bar) at diverse tempi. Rather than Ligeti’s “frozen” time continuum, as with Nancarrow’s original piece, we are here left with a sense of suspension or vertigo. Nancarrow was always keen to stress his interest in the listeners emotional responses to his music. Is levitation an emotive response?