for three retuned, comuter-driven ianos y Kyle Gann 20
Technical Secifications The 33-itch tuning of the three ianos (the same in every octave) is as follos, given first in the numer of cents aove E-flat, and then as ratios to the E-flat 1/1: Piano 1 2 3 D 1088 15/8 225/128 1044 /64 D 6 /4 38 55/32 06 2/16 C 85 105/64 3 25/16 840 /8 B 38 4/32 55 /64 2 5/128 B 02 3/2 50 45/32 60 1/64 A 551 /8 551 /8 481 16/128 A 41 21/16 440 165/128 408 81/64 G 386 5/4 320 /64 342 3/32 G 204 /8 25 5/64 25 5/64 F 155 35/32 2 143/128 2 143/128 E 2 5/128 53 33/32 2 65/64 E 0 1/1 03 121/64 3 63/32 Note that no string needs to e raised higher than its natural tuning excet for the B-flat on iano 1, hich is 2 shar (or if one refers, 2 could e sutracted 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: 38.81 cs 36.641 cs 38.2833 cs D 15/8 225/121 / D /4 20/ 12/ C 105/64 200/121 104/63 B 4/32 18/ 65/42 B 3/2 180/121 / A /8 16/ 16/126 A 21/16 15/ / G 5/4 14/ 26/21 F /8 150/121 25/21 F 35/32 / 143/126 E 5/128 12/ 65/63 E 1/1 1/1 1/1
In the configuration of certain tuning softares, the folloing sequences might facilitate getting the required tuning: Piano 1: 38.81 = E0 1/1, 5/128, 35/32, /8, 5/4, 21/16, /8, 3/2, 4/32, 105/64, /4, 15/8 Piano 2: 36.641485 = E0 1/1, 12/, /, 150/121, 14/, 15/, 16/, 180/121, 18/, 200/121, 20/, 225/121 Piano 3: 38.283333 = E0 1/1, 65/63, 143/126, 25/21, 26/21, /, 16/126, /, 65/42, 104/63, 12/, / For uroses of analysis, the entire scale (hich I refer to as my 8x8 scale) is given elo, grouing its itches into eight harmonic series on the 1 st, 3 rd, 5 th, th, th, th, th, and 15 th harmonics of E-flat, and naming each itch in a tyograhical equivalent of Ben ohnston s ust-intonation notation:
Pitch name Ratio Cents 1/1 3/2 5/4 /4 /8 /8 /8 15/8 D^^- 121/64 03 D 15/8 1088 15 5 3 1 D /64 1044 C+ 225/128 15 D/4 6 1 C^ 55/32 38 5 C+ 2/16 06 3 C+ 105/64 85 15 C /8 840 1 B 25/16 3 5 B^ /64 55 C+ 4/32 38 B 5/128 2 15 B 3/2 02 3 1 B 1/64 60 A+ 45/32 50 15 5 3 A^ /8 551 1 A 16/128 481 A+ 21/16 41 3 G^ 165/128 440 15 G+ 81/64 408 G 5/4 386 5 1 G 3/32 342 3 G^ /64 320 F+ 5/64 25 15 5 F+ /8 204 3 1 F^ 143/128 2 F+ 35/32 155 5 E+ 5/128 2 15 E^ 33/32 53 3 E 65/64 2 5 E 1/1 0 1 E+ 63/32 3 In ohnston's notation, + raises a itch y 81/80, raises it y 25/24, loers it y 24/25, loers it y 35/36, ^ raises it y 33/32, raises it y 65/64, and F-A-C, C-E-G, and G- B-D are all erfectly tuned 4:5:6 maor triads.
A coule of notes on listening to Hyerchromatica: Some eole think the iano sounds seem funny or unreal. It is essential to the timre of a normal iano that the intervals are slightly out of tune, and surrounded y the fuzziness of the resulting eats. Remove that out-of-tuneness and the iano can sound different than you re used to. It has alays een 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 ells than a iano. Often one s unfamiliarity ith ure tuning is miserceived as a deficiency in the iano sound. Relatedly, hen I issued a disc of Disklavier music in 2005, eole sometimes commented, Too ad you couldn t use a real iano, ecause the electronic sounds are off-utting. In fact, the Disklavier as a real, acoustic iano, ith luckale strings. It as tuned to 18 th -century ell temerament, the notes ent y very fast, and so the divergences from normalcy made eole s rains 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 roaly 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 delierate excetions, these ieces are not layale y humans. The comoser forids erformance y 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 others you that the music you are listening to isn t eing layed y humans, there are millions of iano recordings made y 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 caailities that I savor. I make this music ulic on the chance that there might e a handful of other eole on the lanet for hom the ossiilities oened u here in terms of rhythmic and harmonic language might more than comensate for the loss of a fe haitual coorts. If you are not one of those rare eole, you can do the comoser a favor y moving on ithout comment. Finally, a ord aout the notation. I rite this music in Sielius softare, and the notation s urose is to create the MIDI file for erformance. Sielius 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 ouncing among different ianos. Since this is music for machines, it ould e 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
Piano 1 q = 4 nn 5 Kyle Gann 2016- Piano 2 Piano 3 = n q = 4 r n n K r 4 5 5 5
2 10 5 5 5 < < <
. r K r 5 5 5. r 3 < K r R
4 < < r K r 5 5 5 r r 3 < r r RÔ R 3
22 r R n n 5 5 5 5 r 5 3 < < r r n n
6 26 < n 3 5 5 5 5 < r 3 K r n R r n R R R R R R Ô
30 < < R n 5 5 5 5 n r R n < < < n n R
8 34 < < r 5 n n < n R r n n n K r
3 < RÔ. 3 R Ô R Ô < R Ô RÔ n R Ô
10 3 R Ô RÔ RÔ RÔ R Ô n n n R RÔ RÔ RÔ < RÔ n RÔ RÔ RÔ R n r
42 n R Ô RÔ n RÔ n R RÔ RÔ R n RÔ r
12 44 R RÔ RÔ n n R Ô R Ô. n < R n RÔ R Ô.
46 n R Ô R Ô R Ô R Ô RÔ < < n m RÔ n R Ô n r n n n RÔ
14 48 < n R Ô RÔ n RÔ RÔ r n RÔ RÔ RÔ RÔ RÔ RÔ < RÔ n n RÔ
50 n n r RÔ RÔ n 15 R Ô RÔ n RÔ R
16 52 n R Ô R Ô RÔ n R r n 3 RÔ RÔ < r RÔ R 3 R Ô n RÔ RÔ 3
54 R RÔ n n n r r n RÔ RÔ RÔ n RÔ RÔ < R R n RÔ R n RÔ n RÔ n
18 56 n RÔ r n r n n < RÔ n n RÔ
5 n n R Ô R Ô n R Ô < < < n r n r RÔ R Ô n n RÔ r r RÔ R Ô n RÔ r r n
20 61 R Ô RÔ RÔ < R Ô R Ô R Ô RÔ RÔ n R Ô RÔ RÔ
63 R Ô n R Ô R Ô RÔ < r n 21 RÔ R Ô n RÔ n 5 R n n RÔ n n 23
22 66 < 5 5 5 < R R R R R R 3 nn n 23 23 23 15 15 15
6 < < R 5 5 5 R R < < 3 R 23 23 23 23 15 R 15 15 R
24 2 < < < < R 3 5 5 5 r r 3 r R R R R R 23 23 23 15 15 15
5 f 3 n 25 < < < < r < f 5 5 5 R n n < R R R r 3 n R R 23 23 23 15 15 15 f R
26 8 r n 3 < < R R R 5 3 3 < < n 23 23 15 R 3 < < n n r 15 5 23 5 15 r R R R R R
81 r 2 < < < R < n n 23 23 23 15 15 15 r
28 84 K r < < n n 23 23 23 15 15 15
8 m < R 5 5 R m R R R 2 < < R R R < m n m 5
30 0 < 5 5 5 n 5 5 n R < < R 5 n R R R <
3 < R R n RÔ R Ô n 5 5 5 31 < R R 5 5 5 < R R R
32 6 < n 5 5 5 R 5 5 5 n < < n n < n R R R R
5 5 5 5 n R < n 5 5 < < R R R R 33
34 102 R n < 5 5 5 5 5 5 n 5 5 < R < R R R
106 < 5 n m 5 5 < < R 5 < R R 5 5 n R r R 35
36 10 r r < 5 5 5 5 5 5 <
2 r 3 < r f 5 5 5 < < r < r r f 5 5 5
38 5 f R < < < r R 5 5 5 < r 5 5 5
8 n 3 < 5 5 5 < R < < r 5 5 5
40 121 r n < 5 5 5 < r n 5 5 5 n
124 f 41 R R < R 5 5 5 r R r r
42 12 R f 5 5 5 R 5 r
0 n 5 5 5 r < < n < r < R R 43
44 3 5 5 5 < n f < R 5 5
6 R Ô 5 RÔ R Ô < < 5 45 RÔ R Ô RÔ RÔ R Ô RÔ < R r < R R < < < < < 5 R Ô RÔ n 5 5 5
46 8 R < < 5 RÔ r R < < < < < < 5 5 R Ô RÔ
< 5 < < RÔ < < < 5 < < < 5 RÔ n RÔ < R Ô RÔ R Ô n n n n 4
48 141 RÔ RÔ R < n m R
143 3 R 3 3 < 4 < R < n
50 145 < < << < < < RÔ RÔ n
146 < < 51 << < < < RÔ n n n r R r
52 148 < < << < < < < r n nn n n n n R R R R R R
151 R n R n R 53 n R R R R n R R R R R R
54 154 < R R n R R R < n n n R n R R R n R R
15 R n n R n 55 R R R R R R R R R n R R R R R
56 < 160 < R R R n n R R R R < n R R R R n R R R R n R
< 163 5 R n R R < r Ù n R R R R R R R n R n R R R n R R
58 165 n R R n n n R R R R R R R R n R R R R R
168 5 < n R R R R < R R R R R R R R n R
60 1 < R n R R n R n R R R R R R
4 < R n nn R R R R R < n 61 < n R R n R R R R n R n R R R R
62 < f f
182 < < 63 f f n n < <
64 18 < n f f m n r r r n f m f m
1 < < < 65
66 5 < n 3 n n
200 6 r n n < f
68 204 r < < r n n
< 208 R 6 r r n r <
0 212 R r n n < < n n n n n
215 Ù 1 n n n r n n n n n r r
2 220 n < < R R R n R R R n < < R R R < n R R R R R R R r R R R R R n
3 223 n R R R R n R R R R R < < < R R n n R R n R R R n R R r R R
4 226 R R R n R n R R R n R n n R R r n R R R R R n R n R r n R
5 22 < < n n = <. < r n r 233 < < n < n n n n n n n n n n n < < r r
6 23 < < n n n < < n 3 r r
241 < < < < n n n n n n n n n < r r
8 246 < < < n n n n n n n n r f f n r R
< < < 251 < n < 3 < n < < r n f f r 3 r
80 < < < < 255 f r f < n n r n r
81 25 < << n < < Kr n Aril - uly 25, 20 Germanton, NY