Who invented.......

[Clark]

Hi,

Huygens described 31-tone equal temperament exactly in 1693;
unfortunately, while he includes monochord string lengths and pre-cents,
his instructions are to tune from the monochord compounding chances for
error (if the tuner were, um fortunate enough to find a 31-tone
instrument).


Jorgensen includes reference to

Farey, John. "Theorems for calculating the Temperaments of such regular
Douzeaves as are commensurable or defined by a certain number of equal
parts, into which the Octave is divided." The Philosophical Magazine
(London: Richard Taylor and Company) 38 (1811): 434-36.

Farey, John sr. "An Improved Piano-Forte-New Logarithmetic Scales." The
Philosophical Magazine and Journal (London: Richard and Arthur Taylor)
45 (1815): 386-877.

also an exerpt from Farey's critique of Herr Kollman's purported equal
temperament, or "scale of nature". I haven't seen the two articles
above, but given Farey's use of Smith's beat-rate formulas, it's
possible he provided aural tuning instructions.


Clark