In the 1860s Henry Ward Poole1 invented a clever keyboard for just-intonation.2
It looked like this:
(sorry, no picture yet)
This keyboard was an ingenious system of the type Partch would call "Poly-pythagorean". This means that it follows cycles of powers of 3, along five different odd-number axes:
3
5
7
25 [=52]
35 [=5*7]
Here is a lattice diagram depicting the ratios specified by Poole:
(sorry, no lattice diagram yet)
Altogether, there were 100 different keys (meaning keyboard levers) and pitches per "octave" in sound. If built, it would give perfectly-tuned 4:5:6:7 tetrads on 20 different "roots". The layout on the keyboard was cyclical, so that the patterns of finger movement were completely identical in every key.
Here is a graph of the pitches as they fall within one octave:
Notice that there are many schismatic equivalents. These are notes that are very close together in pitch, which I would call "xenharmonic bridges". Therefore, if Poole was willing to accept the "imperceptibility" of these equivalents, he could have reduced the size of the keyboard a great deal. His retention of these tiny intervallic differences does show it, however, to be a truly perfectly in-tune 7-limit just-intonation keyboard.
NOTES
1
Poole (1826-1890) was born in Salem, Massachusetts,
and lived the later part of his life in Mexico City,
where he was Professor of Public Instruction in the
Government Institute.
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2
REFERENCES
Silliman's American Journal of Science and Arts,
vol 44, July 1867. Poole had published his theories
on "perfect musical intonation" in the issues of
January and March, 1850.
Helmoltz, On the Sensations of Tone,
trans Alexander J Ellis, appendix 20 [by Ellis],
p 474-479.
Tipple, Esther Watson & Frye, Royal Merrill,
A Graphic Introduction to the Harmon,
1942, p 9-15.
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Last Updated on 3/13/99
By Joe Monzo
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