[CAUT] Shulze tuning research

[Fred Sturm]

	I have been in correspondence with Gary Shulze, and would like to  
share with the list some interesting information concerning the  
research he did, on the basis of which he wrote the article we have  
been discussing. In 1981, while he was working as a teaching assistant  
under Owen Jorgensen, he had been looking into the aural principles  
that are present in fine piano tuning, and had become aware of the  
fact that beatless P12 and P19 intervals tended to be a feature of  
such tuning. He said that his discussions with other tuners made clear  
that they had come to the same conclusion.
	He did calculated tunings based on the logarithmically equal division  
of the P12 and of the P19, taking into account inharmonicity. These  
were very tedious calculations based on the computer capabilities of  
the time, involving the use of formulae to calculate frequency, and  
then to convert frequency into the cents system.
	Having made these calculations, he proceeded to compare the results  
with readings made on an aurally tuned Steinway D. And he found a  
remarkable degree of correspondence. Hence, he proposed (in his  
article) the notion of the P19 temperament as a basis for aural tuning  
in which stretch and inharmonicity melded to produce "excellent  
results."
	To the best of my knowledge he took this no further, in the sense of  
coming up with a "system" for producing this tuning. It was more along  
the lines of developing guidelines for "proving" a tuning as one was  
producing it, using the P12 and P19 to show that you were using the  
appropriate stretch (and as a basis for adjusting if necessary).
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu