[CAUT] temperament for Schubert (Fred Sturm)

[Fred Sturm]

On Jan 12, 2009, at 3:45 PM, A440A at aol.com wrote:

> It is hard to
> imagine that the vast majority of tuning done before 1900 was  
> anything but
> irregular in the traditional manner, i.e., dissonance in the tonic  
> thirds increasing
> with the number of accidentals in the key signature.  This is the  
> common form
> of virtually every non-ET temperament documented.

	Let me offer a counter-argument, based on a "what is likely"  
scenario: the reverse WT argument. Most practical historical tuning  
systems (practical instructions for how to "lay the bearings," set the  
temperament) from 1800 on(actually this can be said of earlier systems  
as well, but I am talking about those "obviously intending ET") start  
at C and go through the circle of 5ths. Most commonly one tunes the CF  
5th, then moves upward through GDA etc. And one ends up with the FF  
octave as "proof." There is a very common tendency to make the 5ths  
too pure, so that FF ends up too wide. One then moves backward, making  
the 5ths a little narrower. Human nature will say that one will go as  
short a distance backward as one can.
	Result? The 5ths on the natural keys are the ones that are closest to  
pure, those on the sharps are the most tempered. Hence, the M3s on the  
sharps are narrowest, those on the naturals are widest: the reverse of  
WT.
	I think it is very plausible that many, many tuners produced tunings  
this way. It is in keeping with my own experience learning to tune: I  
was taught that 4ths and 5ths were more important than 3rds and 6ths,  
and so it would make sense to "hide" the worst 5ths in the sharp keys.
	It seems to me that this "unintentional tuning system" was likely  
quite prevalent for the past two centuries.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu