The Well-Tuned Piano
By Kyle Gann
La Monte Young began work on his magnum opus, The Well-Tuned
Piano, in 1964. For 27 years he kept the tuning a secret - only a few close
friends knew it. In 1991, I told La Monte
that I had figured out the tuning and wanted to publish an analysis of the work.
He thought it over and agreed that it was time to release the tuning into public
discourse.
The tuning, in all octaves, is as follows, given first in frequency ratios to
the tonic E-flat, then in cents (1/1200ths of an octave) above E-flat:
| Notes: | Eb | E | F | F# | G | G# | A | Bb | B | C | C# | D |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratios: | 1/1 | 567/512 | 9/8 | 147/128 | 21/16 | 1323/1024 | 189/128 | 3/2 | 49/32 | 7/4 | 441/256 | 63/32 |
| Cents: | 0 | 177 | 204 | 240 | 471 | 444 | 675 | 702 | 738 | 969 | 942 | 1173 |
(If you don't have enough experience with just intonation to make sense of this chart, try reading the step-by-step Just Intonation Explained section.)
Note that the scale does not uniformly ascend: G# is lower than G, and C# is lower than C. This is so that all perfect fifths (3/2 ratios) will be spelled as perfect fifths on the keyboard.
The premise of this tuning is actually very simple, and analogous to the tuning from which European classical tuning evolved. Young's tuning can be arranged in a grid in which the perfect fifths (3/2 ratios) run in one direction (here: upwards), and the pure minor sevenths (7/4 ratios) in another (left to right):
| 49/32 | 147/128 | 441/256 | 1323/1024 | |
| 7/4 | 21/16 | 63/32 | 189/128 | 567/512 |
| 1/1 | 3/2 | 9/8 |
For more information on The Well-Tuned Piano, see my article "La Monte Young's The Well-Tuned Piano" in Perspectives of New Music Vol. 31 No. 1 (Winter 1993), pp. 134-162.
Copyright 1997 by Kyle Gann
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