Tuning pitch: cps cps cps

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Jerome Jones
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2 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 D /8 9 22/ /64 Db 969 /4 938 / /16 C 8 10/64 3 2/ /8 B 38 49/32 99/64 29 /128 Bb 02 3/2 90 4/ /64 A 1 /8 1 / /128 Ab 41 / / /64 G 386 /4 320 / /32 Gb 204 9/8 2 /64 2 /64 F 1 3/ / /128 E 92 / /32 2 6/64 Eb 0 1/1 03 1/ /32 Note that no string needs to be raised higher than its natural tuning except for the B-flat on piano 1, hich is 2 sharp (or if one prefers, 2 could be subtracted from all quantities). For electronic realization of the piece, it can prove helpful to reconfigure the tuning as a reference pitch in cycles per second for each piano, and ratios derived from that standard: Tuning pitch: cps cps cps D 1/8 22/1 / Db /4 20/ 12/ C 10/64 200/1 104/63 B 49/32 18/ 6/42 Bb 3/2 180/1 /9 A /8 16/ 169/126 Ab /16 1/ 9/ G /4 14/ 26/ F# 9/8 10/1 2/ F 3/32 / 143/126 E /128 12/ 6/63 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: = Eb0 1/1, /128, 3/32, 9/8, /4, /16, /8, 3/2, 49/32, 10/64, /4, 1/8 Piano 2: = Eb0 1/1, 12/, /, 10/1, 14/, 1/, 16/, 180/1, 18/, 200/1, 20/, 22/1 Piano 3: = Eb0 1/1, 6/63, 143/126, 2/, 26/, 9/, 169/126, /9, 6/42, 104/63, 12/, / For purposes of analysis, the entire scale (hich I refer to as my 8x8 scale) is given belo, grouping its pitches into eight harmonic series on the 1 st, 3 rd, th, th, 9 th, th, th, and 1 th harmonics of E-flat, and naming each pitch in a typographical equivalent of Ben ohnston s ust-intonation notation:

4 Pitch name Ratio Cents 1/1 3/2 /4 /4 9/8 /8 /8 1/8 Db^^- 1/64 03 D 1/ Db / C#+ 22/ Db / C^ / C+ 2/ C+ 10/ Cb / B 2/16 3 Bb^ 99/64 9 Cb+ 49/32 38 Bb / Bb 3/ Bbb 91/ A+ 4/ Ab^ /8 1 1 Abb 169/ Ab+ / G^ 16/ G+ 81/ G / Gb 39/ Gb^ / F#+ / F+ 9/ Fb^ 143/128 2 F+ 3/32 1 E+ / Eb^ 33/ Eb 6/64 2 Eb 1/1 0 1 Eb+ 63/ In ohnston's notation, + raises a pitch by 81/80, # raises it by 2/24, b loers it by 24/2, loers it by 3/36, ^ raises it by 33/32, raises it by 6/64, and F-A-C, C-E-G, and G- B-D are all perfectly tuned 4::6 maor triads.

5 A couple of notes on listening to Hyperchromatica: Some people think the piano sounds seem funny or unreal. It is essential to the timbre of a normal piano that the intervals are slightly out of tune, and surrounded by the fuzziness of the resulting beats. Remove that out-of-tuneness and the piano can sound different than you re used to. It has alays been common for me to play La Monte Young s The Well-Tuned Piano for people and have them respond, Isn t that electronic It sounds more like bells than a piano. Often one s unfamiliarity ith pure tuning is misperceived as a deficiency in the piano sound. Relatedly, hen I issued a disc of Disklavier music in 200, people sometimes commented, Too bad you couldn t use a real piano, because the electronic sounds are off-putting. In fact, the Disklavier as a real, acoustic piano, ith pluckable strings. It as tuned to 18 th -century ell temperament, the notes ent by very fast, and so the divergences from normalcy made people s brains convince them that it as an electronic piano, hich as a false perception. Give yourself some time to listen to the pieces over and over, and you ll probably get used to them. I can guarantee, after hundreds of listenings myself, that the harmonies make their on purely-tuned sense, and that their logic sinks in once you can anticipate hat s going to haen. One of the purposes of these pieces is to expand your musical perception. The Disklavier (computer-driven piano, the digital manifestation of the player piano) is a different medium than the human-played piano. One can, and must, rite for it differently. With a couple of deliberate exceptions, these pieces are not playable by humans. The composer forbids performance by humans (hich can t haen anyay), and ill not cooperate ith any such attempt. The computer-driven version is the final manifestation, and the only one contemplated or permitted. These pieces ere ritten, after years of profound thought and experimentation, specifically for the Disklavier medium, ithout any compromise in hat the music as intended to achieve. If it bothers you that the music you are listening to isn t being played by humans, there are millions of piano 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 produced mechanically, for a mechanical quality of rhythm that I savor. I make this music public on the chance that there might be a handful of other people on the planet for hom the possibilities opened up here in terms of rhythmic and harmonic language might more than compensate for the loss of a fe habitual comforts. If you are not one of those rare people, you can do the composer a favor by moving on ithout comment. I guarantee you ill not alter his mind on the matter. - Kyle Gann

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8 = = <#> r # <#> # # n <#> r # <#> # 1 <#> r n r # 3 # # # r # # r # # #

9 4 1 p 1 1 p # r r # = 1 r

10 20 p p b b 1 1 b b b r b b b b r b p b p b b r

11 6 22 b # R b b r # b b r b r # p 1 1 p r R b b r 1

12 24 <#> b b b <#> # r b <#> b b 1

13 8 2 b <#> # b b r b r b b r n 1 b # r #

14 9 26 b b <#> # # <#> # R r r <#> # R b # n n # n n 1 r # R 1 1

15 10 28 <#> b R n 1 1 R r <#> b n r # # # # # # # # R

16 R # r <#> r b r # # # <#> #

17 12 32 b b # 1 b r b b

18 33 1 b b # b r r b n b r n r

19 b b b # # # r b r #

20 36 = 3 1 <#> <#> 1 r b b b R RÔ b r b b R b 1

21 # r # R r

22 40 <#> 1 1 # # R r <#> r # # 1 b #

23 18 42 # 1 1 <#> r # # R # # r # R # # b b r # r #

24 44 b b n b b # n b 1 1 b b r b n b r r <#> r b b

25 r b b # b b # r b b # b b b b r # b Kr #

26 48 b # # R # # 1 1 r b b r # r b #r # # r # R # r <#> # # <#>

27 22 0 r 1 # # # # 1 1 # # # r # # # # #

28 23 2 <#> # # # # 1 1 <#> r # # # <#> # # # # r # #

29 24 4.> <#> RÔ 1 1 <#> # # <#> r # <#>.> R R # # r # n

30 6 <#> # r 1 1 r # # # # # # # # # # # 2

31 26 8 # # # # r r r b 1 1 n # b r b n # # r # R b r b b

32 2 60 n b b r n b b r b b r 1 1 <#> <#> r b b b b b r b b b b b

33 28 62 b n b 1 1 b b b # b b b r bn b r # b n # b 1 b b b

34 64 # b b <#> r # 1 1 # b b # r n 29 # # # n r

35 30 66 n R 1 r r n # # # R r

36 6 1 r r # # # R Ô R # R r # r r # # r 31

37 32 = r # # # # # <#> n 1 1 <#> n # # # r

38 0 <#> # # n 1 # n 33 r

39 34 1 r r # <#> # 1 # r 1 r 1

40 3 3 r 1 1 b R r b p

41 36 4 b 1 # b b # b b b b # # 1 1 b R # # r #

42 3 <#> b b 1 W b # R # r <#> 1 R # R 1 <#>

43 38 6 b <#> # W <#> <#> # # # # # # 1 n R <#>

44 <#> # R <#> <#> # 1 # W 1 b b b b b b # R 39 b b b R

45 40 9 1 R b R b b n 1 1 b 1 nw b b b

46 41 80 W 1 1 b W b R 1 b 1 n b

47 42 81 # b b # b b b b # n b 1 b b R 1 R 1

48 82 1 W n <#> r n n 1 n R b b R 43 # # # # # 1

49 44 83 R 1 1 # r # <#> # <#> <#> <#> <#> # R n # 1 # n # # R # # # r b #

50 84 # R <#> # # <#> <#> # <#> <#> <#> <#> # 1 <#> # R R <#> #

51 46 8 # W <#> # <#> r # # <#> <#> R 1 <#> # R

52 R <#> # <#> # # <#> # 1 1 1

53 48 8 R R R <#> # <#> # 1 1 <#> <#> <#> R 1

54 88 # b b R R b # b # b b # # b # # # 49

55 0 89 n> R > n b b b 1 1 # # b

56 90 > b > b 1 b # 1 > 1 <#> # # > r

57 2 91 b # 1 1 > > r

58 3 92 # 1 1 # r b> b> # #

59 > > <#> <#> # 1 # # # # # # # r

60 94 1 > b b> b b n # b r <#> # > n # n # n 1 # # > n

61 6 9 n> 1 n> b n # n # b r # # > 1 # > # n r b

62 96 b 1 # # > n > # > > # # n 1 # r > # > b

63 8 9 1 # 1 <#> <#> # > # b <#> # > > > 1 r b > > # # b

64 98 b > p 1 b r b 3 9

65 60 99 b R 1 n

66 R

67 R b b r b 3 3 b # # 3 3 # # # b b b b 3 3 # # b

68 63 10 b b b b b bn b b b b b b b n b 3 3 n # 3 # 3 # # # b # b # # b b 3 3 b b

69 b n # n b b # n n b # # # # n # n # n n n n

70 6 1 b# b b b b b b# b b b # # # # # # b

71 66 b 3 b b b b # b # # b b 1

72 6 6 b 1 b <#> <#> # # <#> b

73 68 8 9 9 r # # n Completed une 1-, 2016 from a summer 201 sketch Germanton, NY

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-7-71 7 07 7 -, 6 7-71 61 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