A 3/1 duodecime i mention the 3rd partial of one note with the fundamental of the 12th above. This includes inharmonicity between those two partials but does not mean that that duodecime is aurally pure, as the same is true for a 2/1 octave mentions the second partial of one note to fundamental of the octave above includes inharmonicity between that partials, but that octave is also not an aural pure octave, because of the higher partials. The duodecime used in my tunings is aurally pure (that means slightly expanded beyound the 3/1 definition), as aural tuners who do not distinct between octave types describe purity with a "sweet spot" octave. Bernhard Stopper Am 08.03.2009 um 21:19 schrieb Richard Brekne: > An interesting distinction... which I think needs to be clarified. > 3:1 in these discussions refers to tuning the 3rd partial of one > note with the fundamental of the 12th above. Doing so in a real > piano automatically includes the instruments inherent inharmonicity. > A theoretical 3:1 on paper is an entirely different matter. > > Cheers > RicB > > > > 1. Stopper has stated that his tuning is NOT a P-12ths > tuning. > > > > > I have stated that my tuning is not a 3/1 P12 tuning (in the > piano), because inharmonicity has to be added both to octaves > AND duodecimes (P12s) when implementing for the piano. > > Bernhard Stopper > > >
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