[CAUT] Schulze article is no proof of prior art of Stopper temperament. Was: The Origins of P12ths tuning.

[Fred Sturm]

On Oct 22, 2008, at 9:30 AM, Bernhard Stopper wrote:

> For those who are in doubt about about the maths, Schulzes intention  
> becomes exactly clear in an other statement he makes in the same  
> article (which Ric does not post here), where he wants the "the  
> octaves as pure as possible", together with the twelfths and the  
> ninteenths. That is in fact the complete opposite of my intention of  
> adding stretch to pure octaves (in case of present inharmonicity we  
> can speak of "sweet spotted" pure octaves) additionally stretched by  
> adding the nineteenth of the pythagorean comma (the Stopper comma).
>
> So the goal of Schulze is just to align as much as possible  
> coincidents ( including the 3/1 third partial matched to the first  
> partial twelfth) together, including the octave and the nineteenth.  
> That may work only for a small range of the scale with an present  
> amount of appropriate inharmonicity, but has nothing to do with  
> defining a new temperament.
>
> The intention of Stopper temperament is to split the pythagorean  
> comma completely on the octaves side, to keep the duodecimes pure.  
> In case of present inharmonicity, this can simply be kept by taking  
> sweet spotted octaves and sweet spotted duodecimes.
>
> Conclusion is: No prior art of Stopper temperament intention was  
> presented in this article.
>
> Best regards,
>
> Bernhard Stopper

	I confess I am somewhat confused by your terms "sweet spotted octaves  
and sweet spotted duodecimes." In the aural execution of your  
temperament, it is necessary to tune a large number of octaves. Are  
you using the term "sweet spotted octaves" for the octaves tuned while  
producing the temperament? Or are they intended to be wide of "sweet  
spotted" by a Stopper comma? In which case, how do you determine that  
they are precisely that wide?
	I believe that your interpretation of Shulze's article is not  
entirely correct. He does not talk about "octaves as pure as  
possible," but rather octaves, double octaves, 12ths and 19ths that  
all "give the impression" of being beatless. And of course he means  
this in the context of inharmonicity. He believes that the best result  
is one that takes into consideration the naturally occurring  
inharmonicity, and that, in fact, the best solution for maximizing  
"pure sounding octaves" as well as "pure sounding fifths" is a tuning  
that is based on "pure" 12ths and/or 19ths (pure meaning beatless in  
this context). And, in fact, the P19 (double octave fifth) temperament  
is the one he preferred - which will obviously produce octaves wider  
than the Stopper temperament system based on the duodecime (P12).
	It is quite clear that his approach and yours are distinct, that he  
is not primarily "defining a new temperament." On the other hand, he  
is definitely describing a temperament, or rather two temperaments,  
one based on equal division of the P12, the other on the equal  
division of the P19. There can be absolutely no question of this.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu