Re: Galpin tuning and Zarlino 2/7-comma (1558)

Hello, there, and Mark Lindley has a remark in his article "Instructions
for the clavier diversely tempered" (Early Music 5, No. 1, January 1977.
pp. 18-23 at 20: "(Meantone temperament with major thirds and sixths
slightly smaller than pure, though recommended by Zarlino in 1558 and by
A. R. McClure in a brilliant article in the first issue of the _Galpin
Society Journal_ (1949), is rather difficult to tune and will therefore be
omitted here."

Zarlino's favored temperament in his publications of 1558 and 1571 is
2/7-comma meantone, which results in major and minor thirds 1/7 comma from
just, and also in a just chromatic semitone at 25:24, ~71 cents (or two
sytonic commas narrower than the Pythagorean apotome at 2187:2048, ~114
cents).

Since I haven't seen the McClure article, I'm not sure about exactly what
flavor of meantone it describes, although Lindley associates this tuning
with Zarlino's. One might infer that the temperament is greater than
1/4-comma but less than 1/3-comma (with pure minor thirds).

An interesting exponent of Zarlino's 2/7-comma tuning is Vincenzo Galilei,
who finds it the best choice for plucked keyboards although he considers
12-tet with equal semitones (as tuned on the lute) in principal the ideal
tuning. I find it noteworthy that although he takes equal semitones as the
theoretical ideal, he prefers a keyboard temperament of a bit more than
1/4-comma -- agreeing with Zarlino, whom he often debates in his writings.

Most respectfully,

Margo Schulter
mschulter@value.net