Fred Sturm schrieb: > 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. That is my definition too. > 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? > These results are actually beeing prepared for publication. (Early 2009) Regards, Bernhard Stopper > Regards, > Fred Sturm > University of New Mexico > fssturm at unm.edu > > > --
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