[CAUT] Shulze tuning research

[rwest1 at unl.edu]

Hi, Linda,

I would tend to agree with you.  The question is this:  Does tuning  
pure 12ths over-stretch the thirds especially as they are expressed  
in 10ths and 17ths.  We may all be talking about the same result, but  
we don't have any way to verify it.  I would like to see a convention  
class/demonstration with 2 or three pianos (same model) tuned with  
the various tuning stretches, one with pure 4:2 octave, one with the  
pure 12ths, one that perhaps splits the difference, i.e, slightly  
wide 4ths/slightly narrow 5ths which is sort of a traditional ideal.   
My hypothesis is that the class participants would divide up fairly  
equally among the various choices.  Or perhaps a more radical result  
would be that a large percent would favor only one of the choices.   
It would be interesting to have the various choices and see how  
others judged which was "best."  Perhaps this has already been done  
and the verdict is already in.

And to Ric B:  You restated my point perfectly when you said that I  
was "calling for a standardized vocabulary for making clear the vague  
descriptions of tuning issues we hear routinely. And I agree. Simply  
using phrases like <<narrow octaves>> is not all that specific. I run  
into folks all the time who when pressed to describe their idea of  
phrases like <<narrow octave>> end up revealing quite different  
perceptions of what that actually is."

Richard West



On Oct 23, 2008, at 3:12 PM, Linda Stråhle wrote:

> Hi all Caut members,
>
> I will make a short input on this pure 12th, 3:1 discussion.  
> Although the stretch that is produced by such settings and ideal, I  
> think it is not beautiful considering thirds and sixths if you  
> prioritize a pure 12th. It is good and give a very good direction  
> of stretch, I most certainly agree, but it's not the one only  
> intervall that will make all the rest less important such as  
> octaves, thirds and sixths.
>
> This is of course my very personal opinion:-)
>
> Mvh,
>
> Linda
>
> Skickat från min iPhone
>
> 23 okt 2008 kl. 17.44 skrev Fred Sturm <fssturm at unm.edu>:
>
>>    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
>>
>>
>>