i.e. for completion: the six three note combinations in one pure twelfth that has those 1/1, 2/1, 3/1 and 3/2 fractal beat ratios between octave and fifth beats consist of : the lower octave and the upper octave-outer fifth, the upper octave and the lower octave-outer fifth, the lower octave and his lower inner-octave fifth (implies a fourth also), the lower octave an his upper inner-octave fifth (implies a fourth also), the upper octave and his lower inner-octave fifth (implies a fourth also), the upper octave an his upper inner-octave fifth (implies a fourth also). regards, Bernhard Stopper > > > Beside the mathematical mysteries, this fact is responsible for the > phenomene, that in every three-note interval combination consisting of an > octave and a fifth, the beats are phased out to a pure state in the > stopper-tuning (there are six such three-note combinations in a perfect > twelfth who have all a pure state in the Stopper Tuning). > > > > The new method works with the phenomen of the symmetric outphasing by > finding the tones through efficient temperament step combinations of pure > three-note combinations of octaves and fifths. > >
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