[CAUT] Schubert temperament redux

[Fred Sturm]

	Over the past couple months, I have done quite a lot of research on  
tuning history. Among other things I came across a reference to an  
article by a scholar named Thomas McGeary. Our library doesn't have  
the Journal of the American Musical Society, where the article  
appeared, but one of the perks of the caut job is full access to  
interlibrary loan services. I requested the article a week ago, and  
yesterday a photocopy appeared in my mailbox.
	The article is a survey of practical tuning instructions published in  
German between 1770 and 1840, and was published in 1989. McGeary says  
he focused entirely on tuning instructions rather than theoretical  
writings in order to get at what practical musicians were likely to  
have done. The article makes clear that equal temperament was by far  
the dominant method of tuning during that period in German-speaking  
Europe, the only well-known variant being Kirnberger II, a crude and  
unattractive tuning system that seems to have been discussed more than  
it was actually used. [Essentially, it has 10 just 5ths and two 5ths  
that share the comma: VERY narrow. Those two 5ths are GD and DA, hence  
very prominent in the tuning. There are three just M3s, two  
intermediate M3s, remainder are "Pythagorean" (wider than ET). Two of  
the triads containing the just M3s also have the 1/5 comma 5ths, hence  
the sound is rather bizarre - sounds horribly out of tune to me. K II  
was the first historical temperament I tried. Haven't touched it since.]
	 Of 22 total sources studied, fully 14 describe only equal  
temperament, four offer variants of Kirnberger II, and two have both  
equal and Kirnberger. The remaining two offer tuning methods that were  
obscure in their time and remain so today (one of them featured just  
fifths in the natural keys, tempered in the sharps, yielding a  
“reverse well temperament”). Of the 12 examples published after 1800,  
10 describe only equal temperament, one mentions Kirnberger II along  
with equal temperament, and one offers an obscure, idiosyncratic  
system, unrelated to any other.
McGeary, Thomas. "German-Austrian keyboard temperaments and tuning  
methods, 1770- 1840: Evidence from Contemporary Sources”. Journal of  
the American Musical Instrument Society 25 (1989), pp. 90 -116.
Regards,
Fred Sturm
University of New Mexico