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Brook Tyler
5 years ago
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2 Technical Secifications The -itch tuning of the three ianos (the same in every octave) is as follos, given first in the number of cents above E-flat, and then as ratios to the E-flat 1/1: Piano 1 2 D 10 1/ / /6 Db 969 7/ 9 / /16 C 7 10/6 77 2/16 0 1/ B 7 9/2 7 99/ /12 Bb 702 /2 90 / /6 A 1 / 1 / 1 169/12 Ab 71 21/ /12 0 1/6 G 6 / 20 77/6 2 9/2 Gb 20 9/ 27 7/6 27 7/6 F 1 / / /12 E 92 1/12 /2 27 6/6 Eb 0 1/ /6 7 6/2 Note that no string needs to be raised higher than its natural tuning excet for the B-flat on iano 1, hich is 2 shar (or if one refers, 2 could be subtracted from all quantities). For electronic realization of the iece, it can rove helful to reconfigure the tuning as a reference itch in cycles er second for each iano, and ratios derived from that standard: Tuning itch:.91 cs cs.2 cs D 1/ 22/121 1/7 Db 7/ 20/ 12/7 C 10/6 200/121 10/6 B 9/2 1/ 6/2 Bb /2 10/121 1/9 A / 16/ 169/126 Ab 21/16 1/ 9/7 G / 1/ 26/21 F# 9/ 10/121 2/21 F /2 1/ 1/126 E 1/12 12/ 6/6 Eb 1/1 1/1 1/1

3 In the configuration of certain tuning softares, the folloing sequences might facilitate getting the required tuning: Piano 1:.91 = Eb0 1/1, 1/12, /2, 9/, /, 21/16, /, /2, 9/2, 10/6, 7/, 1/ Piano 2: = Eb0 1/1, 12/, 1/, 10/121, 1/, 1/, 16/, 10/121, 1/, 200/121, 20/, 22/121 Piano :.2 = Eb0 1/1, 6/6, 1/126, 2/21, 26/21, 9/7, 169/126, 1/9, 6/2, 10/6, 12/7, 1/7 For uroses of analysis, the entire scale (hich I refer to as my x scale) is given belo, grouing its itches into eight harmonic series on the 1 st, rd, th, 7 th, 9 th, th, 1 th, and 1 th harmonics of E-flat, and naming each itch in a tyograhical equivalent of Ben Johnston s ust-intonation notation:

4 Pitch name atio Cents 1/1 /2 / 7/ 9/ / 1/ 1/ Db^^- 121/6 0 D 1/ Db1 7/ C#+ 22/ Db7 7/ C^ /2 9 C+ 27/ C7+ 10/ Cb1 1/ B 2/16 77 Bb^ 99/6 7 9 Cb77+ 9/2 7 7 Bb1 19/ Bb / Bbb71 91/ A+ / Ab^ / 1 1 Abb 169/ Ab7+ 21/ G^ 16/ G+ 1/6 0 9 G / 6 1 Gb1 9/2 2 1 Gb7^ 77/ F#+ 7/ F+ 9/ Fb1^ 1/ F7+ /2 1 7 E+ 1/ Eb^ /2 Eb1 6/ Eb 1/1 0 1 Eb7+ 6/ In Johnston's notation, + raises a itch by 1/0, # raises it by 2/2, b loers it by 2/2, 7 loers it by /6, ^ raises it by /2, 1 raises it by 6/6, and F-A-C, C-E-G, and G- B-D are all erfectly tuned ::6 maor triads.

5 A coule of notes on listening to Hyerchromatica: Some eole think the iano sounds seem funny or unreal. It is essential to the timbre of a normal iano that the intervals are slightly out of tune, and surrounded by the fuzziness of the resulting beats. emove that out-of-tuneness and the iano can sound different than you re used to. It has alays been common for me to lay La Monte Young s The Well-Tuned Piano for eole and have them resond, Isn t that electronic It sounds more like bells than a iano. Often one s unfamiliarity ith ure tuning is miserceived as a deficiency in the iano sound. elatedly, hen I issued a disc of Disklavier music in 200, eole sometimes commented, Too bad you couldn t use a real iano, because the electronic sounds are off-utting. In fact, the Disklavier as a real, acoustic iano, ith luckable strings. It as tuned to 1 th -century ell temerament, the notes ent by very fast, and so the divergences from normalcy made eole s brains convince them that it as an electronic iano, hich as a false ercetion. Give yourself some time to listen to the ieces over and over, and you ll robably get used to them. I can guarantee, after hundreds of listenings myself, that the harmonies make their on urely-tuned sense, and that their logic sinks in once you can anticiate hat s going to haen. One of the uroses of these ieces is to exand your musical ercetion. The Disklavier (comuter-driven iano, the digital manifestation of the layer iano) is a different medium than the human-layed iano. One can, and must, rite for it differently. With a coule of deliberate excetions, these ieces are not layable by humans. The comoser forbids erformance by humans (hich can t haen anyay), and ill not cooerate ith any such attemt. The comuter-driven version is the final manifestation, and the only one contemlated or ermitted. These ieces ere ritten secifically for the Disklavier medium, ithout any comromise in hat the music as intended to achieve. If it bothers you that the music you are listening to isn t being layed by humans, there are millions of iano recordings made by humans; go listen to them. There is too much music in the orld for anyone to aste time listening to any music ishing it ere something other than hat it is. This music is roduced mechanically, for mechanical rhythmic caabilities that I savor. I make this music ublic on the chance that there might be a handful of other eole on the lanet for hom the ossibilities oened u here in terms of rhythmic and harmonic language might more than comensate for the loss of a fe habitual comforts. If you are not one of those rare eole, you can do the comoser a favor by moving on ithout comment. Finally, a ord about the notation. I rite this music in Sibelius softare, and the notation s urose is to create the MIDI file for erformance. Sibelius s relation to dynamics is quirky and inconsistent, and so the dynamic markings I need to generate the file can look redundant or inconsistent. Phrase markings don t ork hen the melody is bouncing among different ianos. Since this is music for machines, it ould be a aste of time to srinkle the score ith the conventions e use for humans ( con affezione ). I notate my music for humans very differently than this, and the divergences here do not stem from ignorance. - Kyle Gann

6 Piano 1 Piano 2 q = 0 1 r Ù K r 1 # Ù Ô 1 Ó. 1 r # Ù # b b n # b b r Kyle Gann Ù Piano q = 0 1 b # 1 1 # Ó # r r Ù Kr Coyright 2017 by Smith Grabholz Music

7 2 1 Ô Ù b Ô Ô b Ô n 1 b 1 J # 1 b b.. n n J 1 Ô # Ô # Ô 1 m r # Ù Pno 1 Ô b Ô Ô m 1 # 1 1 # J #

8 6 # 6 6 <#> # 6 6. # r 6 # Ù Pno # <#> <#> # r # 6. 6 J # 6 6 n.

9 # Ô b b # J :7 :7 b #. # # # Ô Ô Ô 6 6 :7 # r # Ù Pno 1 1 # 1 1 # J :7 # Ô Ô Ô 6 6 :7 # Ó # r Ó Ó

10 10 <#> # 6 6: Ù b Ô Ô <#> Ô r # Ù Pno = Pno <#> # n # Ô Ô Ù # r n :12.

11 6 12 Pno = 1 Pno # 6 6 7: 7:. b 1 Ó # # J #.. #.- # n Ó 1 Ó : b Ó # n# b # n# n# 1 1 7: # nb # # # #

12 1 nn Ó Ù Ô Ù Ù Kr Ô Ù Ô K r #. Ó # Ô # # # # Ù Kr # Ù Ô Ô Ù 7

13 16 Ó Ù Ù Ó # Ó Ó b Ô J b.. b. b # # Ó Ó # # :2 :2 b b b J 7: # n <#> # Pno # Ó Kr # Ó # J nn n J J :2 7:

14 1 # Ó :2 <#> # b b b b. b# J b 9 # # Ù # # # :2 7: n Pno Ó Ó J :2 7: J

15 10 20 n b b b K r bb 6: b r b Ô b b 6: b n b 6: 6: 6: :7 :7. b b b Ô n Ô Ô n b r 6: Ô Ô :7 Ô Ô 6: Ô Pno b Ô Ô Ó 6: b :7

16 21 b b 6: 6: b b :7 b n n b Ù Ô b b b b m :7 Ó # # # m # # # # #. Pno b

17 12 2 = Pno <#> <#> 2 # # # m 7: 7: 7 mf # # # Ó # # # # # # # b b. # Ô Ô Ô Ô J # mf mf # b b # # Ó # b Ô Ô Ô Ô Ô Ô # # # b b b > > > b

18 26 m # # n m # # n Ù Ó.. 1 = 27 # # # # Ó #

19 1 2 b # b b b b 6 # b Ô Ó :7 b b m J Ù Ô b. b 6 b # Ô # n :7 6 # Ô Pno b # n Ô Ô 6 6 :7 b n m Ó Ó Ù Ô

20 0 Ó # n 1.. # J J J Pno.. 7

21 16 2 J J Ó m 6 7 r # # # 6 m J # J J J 7 #. #. J # # # Ó # # J Pno 7 m Ó J # Ù Ô Ù # # J

22 # n b b b b b 12: Ô b b Ô Ó b Ó 17 # # # Ô # 12: # Ó # Ó Pno b b Ù b 12: # b Ô Ô b b r Ù Kr

23 1 6 m b b b b b b Ô Ù b b Ô J b J J J bb :2 : Kr 17:10 b Ó Ô 17:10 J Ó Ó Pno b b n Ô Ù Ô Ù 7 b b J J b b Ù K r b m b J J Ó b 17:10 :2 :

24 Ù b Ù b b Ô Ó 19 Kr b Ù b # b b. b b b n b b b # Ô Ó # # J b b Ù b Ô Ó Pno b Kr b b # b ## #

25 20 0 Ó b J # # # # Kr Ù b Ô #. # Pno Ó # Ó

26 1 # # # 21 <#> # J J Ó # # # # # Ó # 1: # J Ó 1: :2 # J # J J J Ó 1: :2 Pno # # # J Ó

27 22 Ó # # Pno Ó # # b Ó # # # # b # # # J # # # ## # J Ó # = # n 1 m # #. # # #

28 6 J J Ó Ó J :6 : J 2 K r # Ó # # # m Ó # Ù Ó. # # J # # # J : :6 # Pno #

29 2 1 Ó. J Ó J # Ó 1 # # # # # # Pno Ó #

30 0 # Ô Ô 6: 6: 6: 6: 6: # Ó # :7 b Ô # Ô Ô Ô r 2 Ô # Ô Ô Ô # 6: 6: Ó :7 6: 6: # n Ù Ô # Ù Ô Pno # b b # b 6: Ô # b b Ô Ô 6: 6: 6: 6: :7 # b Ô # Ô b Ô Ù b J # Ó # Ù J b Kr

31 26 1 # n J 1 #. n # b Ù # # # # n # # 1 # # J <#> # r Pno # b Kr b J # b 1 b b J Ó b

32 27 b b b Ó b Ù b b b J r Ó # n b m b. b b # J.-.- b b J Pno ## r Kr b b b J # n

33 2 6 Pno b b b m b b # b b. b b b m b b Ó m

34 7 # n 1 1 b Ó n n b # n b b n n Kr 29 ## m # # # # b # # 1 1 # # Ó # J J Ó # J J #.- Ù Ô Ù Ô Pno # n b 1 1 # # n # n # Ó #

35 0 Ô Ô Ô 6 6 Ô Ô Ô Ó Ô Ô Ô Ô Ô Ô Ó b b# J b <#> # Ô Ô Ô Ô Ô Ô <#> <#> 6 6 # Ô Ô Ô Ô Ô J # # # J

36 60 n b b b b b Ô b Ô bbb Ô b b b 9 7:6 Ô bb b r b b J b 1 # Ô n # # Ô 9 # # Ô Ô Pno # 9 b b Ô b b 7:6

37 2 61 J J J b J b n Ù K r n b b J Ù # b Ô b b n b Ó 1:10 1:10 J Ó # # # nn # # # # Pno b J J J Ó b 1:10 Kr b b 7 19 b b

38 6 Ó Kr # Ùb Ù Kr Ù Kr Ù b # Ùb Ô Ù # # Ô Ó Kr # Ù Kr # # K r Pno b Kr Ó # b. Kr # # Ô

39 6 # Ó b b b # Ó # # r J # Pno # # # Ó

40 66 # J Ù Kr Kr Ùb Ô Ù Ó Ù Kr Ù Kr Ù b # Ù b Ù # Ô # Ó # # # Ó Kr # Ù Kr Ù # Kr Ù# Ó # Ô Pno # # K r Ù # Ô

41 6 67 b n b b b b b Ó K r Ù KrÙ b b b Ù Kr Kr Ù b Ù bb ÙÔ Ù b b b.. Ó K r Ó Ù Ô Ô Pno b b Ó b Kr b b K r b K r b Ô b Ô

42 69 # # 19 b b 19 n # # n Ó # # # Ó # Ó Ó # 7 Pno 19 # Ó # Ó Ó 21 # # #

43 70 b # # 21 b 19 <#> #. # Ó # 21 # # 19 Ù J Pno 19 <#> # Ó # 21 Ó # r Ó # Ó

44 71 Pno = Pno <#> 72 # # J Ó 21 n #. # ẇ :2 1:10 19 n n. n 2:20 # n 9

45 0 7 b > # # b 2 # 19. # # # J 19 2 Kr # Ù Pno # Ó # r Ó > # 2

46 7 2 <#> # # > b b # n 19 # n b 1 # # # 2 19 Ù Pno # # J Ó 19 # #.> > J Ó 2 J # Ô # r

47 2 7 Pno n n n n 19 n 17 n n.. = Pno

48 77 Pno # # # J Ô # # # J :

49 7 b b bb 7: 7: 6 6 n # # # # > > n n # # n # # # # nn 7: 7: 9: # n # # # # # n. # # Pno 7: 7: 6 # # n # n # 6

50 79 # Ó Ô Ó Ó # Ô Ô b Ô n Ô # Ô b b 9 9 # Ô Ô n Ô # Ô b n Ô Ô # Ô Ô <#> # n 7 7 <#> # # # n # # Ô # # n # Ô.- 9 Ô # Ô # # n # Ô <#> # J # 9 # Ô # Ô Ô Pno Ó Ó Ô b Ô Ô Ô # Ô Ô 9 9 n # n Ô Ô Ô # Ô Ô

51 6 0 n Ô Ô n n n 9 Ù Kr n. # # Ô # Ô # Ô # n 9 Â # # # # # Ô Ô # Ô Ù # # # Â

52 1 Kr 9 Ó r. 7 # # # Ù # # # # 9 r r # # # # <#> # # # # # # # Ó Ó #. #

53 b b# b b b b # J J # b b b n b 1 b. b n b 1 b = 1 n b b b b Ô Ô Ô Ô b b J b J 1 b Ó b J Pno b b b. b Ó Ô Ô Ô J Ó Kr b b 1 b b J Ó b J J Ó b b

54 7 = Pno # # # # # # # # # # # 9 # # # Ó # b b #. # # # # # # # # # # # # #. #. Ó b # # 9

55 0 91 Ó # # # # # # # # # # b = 92 Ó # # # #. # b b b # b b Pno # # #

56 # 9 Ó b b # 7 b J J b #. 1 9 # # # # # # 9 # 9# # 9 # # # J Pno 9 # # #

57 2 Pno J 9 # # 9 b # b # b 9 Ó 9 # J 9# # J 9 # 9 # # # # # # J

58 b Ô 6 6 # Ô n : Ù J # n.- Ô :7 9 7 # # 9 J J Ô # n Ô Ù 6 6 # Pno August 1, January 2, 2017 Germanton, NY b Ô Ô Ù

Tuning pitch: cps cps cps

Tuning pitch: cps cps cps !!!! Technical Specifications The 33-pitch tuning of the three pianos (the same in every octave) is as follos, given first in the number of cents above E-flat, and then as ratios to the E-flat 1/1: Piano