**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

**SCALIC CONSTRUCTION**

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 – https://oeis.org/A278516 & https://oeis.org/A194314 )

**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?