[CAUT] Origin of P12ths StopperStimmung/tuning

[Fred Sturm]

On Oct 18, 2008, at 8:05 AM, Bernhard Stopper wrote:

> "sweet spotted" aural pure duodecimes (not 3/1 duodecimes). Further  
> using a temperament setup within the range of such an AURAL  
> duodecime, named the resulting tuning "Stopper Stimmung" and used  
> the name as a trademark for this tuning (published 1988). Although  
> StopperStimmung/tuning is BASED on the 19th root of 3,  this factor  
> is true but for the pitch unison. In fact real world StopperStimmung/ 
> tuning is NOT a logarithmic 19th root of three tuning.

Thanks for this clarification. Let me note that when most of us (on  
this list, in PTG) use the terminology 3:1, we are referring to a  
matching of the 3rd partial of the lower note with the 1st partial of  
the upper note (not a mathematically pure 3/1 relationship). I would  
describe "sweet spotted aural 12ths (=duodecimes)" as "somewhat wide  
3:1 12ths." One is accounting aurally for the 6:2, 9:3, and (in the  
bass range) 12:4 coincidence of partials as well as the 3:1, and  
making a personal judgment as to where the "sweet spot" is.
	Many aural tuners rely on "sweet spotted" octaves. It is a workable  
way to tune, but suffers from lack of precision in communicating to  
others, and it is difficult to be consistent in application. The 12th  
is somewhat less problematic, as there are fewer coinciding partials  
involved, but I still find this a less than precise way of describing  
a tuning system.

> 3. (most important)
> Having discovered symmetry present in this tuning, eliminating beats  
> in various chord combinations by constructive interference, und thus  
> having discovered WHY this tuning sounds so good:  (2004)

Are these results available to the public?

Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu