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

[Bernhard Stopper]

Am 21.10.2008 um 15:48 schrieb Richard Brekne:

> Hi Folks
>
> Ok... as promised I hunted down the article that I have said all  
> along contains the information that prompted me to create the  
> P-12ths tuning on Tunelab in 2000 along with all subsequent  
> discussion on both lists prior to Bernhard Stoppers appearance on  
> these lists some years later. As it turns out, this article PTG  
> Journal May 1982 by Gary Shulze RTT, six years before Stoppers  
> publication,  contains the entire basis for the P12th tuning along  
> with the mathematical definition for the a Perfect 12ths stretch.
>
> I quote along the accompanying footnote from the article by Shulze  
> and a comparison quote from Stoppers own publication defining the  
> comma he claims as his.
>
>   "The basis of equal temperament theory is the attempt to make all
>   fifths as beatless as possible, while preserving the purity of the
>   octave. With the modern piano in equal temperament, the beat rate of
>   the fifth does not double with each octave as theory would dictate,
>   but remains reasonably pure. In fact, the twetfth and nineteenth are
>   no more tempered then are the octave and fifteenth. The "stretch"
>   necessitated by inharmonicity seems quite consistent with the
>   stretch inherent to the tuning of these intervals pure ---  
> footnote # 2"
>
> That footnote states the following
>
>   "This stretch, disregarding inharmonicity, is exactly equal (in
>   cents) to: Log (3/(2^(19/12)) * 1200 / Log 2 for  the perfect 12th
>   and Log (6/(2^31/12))*1200/ Log 2 for the perfect ninteenth.
>
> Stoppers quote defining the comma he claims as his from his  
> publication in 1988,  six years after the Shulze article
>
>       "now rewriting the pythagorean comma as 3^12/2^19 yields for the
>   Stopper comma (sc) (3^12/2^19)^(1/19) or  3^(12/19)/2"
>
> The likenesses in thinking are obvious.

The formulas Ric states describing the "birth" of 19th root of three  
temperament, and the "likeness" with my formulas is just a  
mathematical misinterpretation of him.

The formula of Schulze does simply express the offset of a pure  
twelfth 3/1 ratio from standard equal temperament in cent.
The occurence of the number 19 (what  obviously seems to be an  
indicator for Ric for the presence 19th root) describes just the 19th  
step in standard 12th root of two ET in Schulzes formula.

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


>
>
> The Shulze article goes on to describe what is the essence of  the  
> P-12ths tuning without directly giving it that title. He describes  
> the appropriate usage of the 6:1 and 3:1 partials and why they work  
> as they do, along with a good deal of other relevant thinking.
>
> There is another article in one of the earlier journals where this  
> subject matter is taken up again. It is much shorter column as I  
> recall and specifically mentions the 19th root of three in plain  
> text.  I will find it as well.
>
> I encourage all of you who are interested in the P-12ths tuning to  
> read the article "Influences of Inharmonicity on Aural Tests in  
> Equal Temperament", Gary Shulze, RTT Lansing, MI Chapter, PTG  
> Journal May 1982.  Its good reading and gives some very good answers  
> to many of the questions the recent related threads have posed. And  
> I sincerely hope the issues surrounding who did what, where, when,  
> and under what influences is once and for all put to an honorable  
> rest.
>
> Sincerely
> Richard Brekne, RPT
>
>
>
>