Jim, If I understand your temperament correctly, you are setting something very close to a 1/5 ditonic comma meantone, with the comma divided regularly between four fifths and the octave. Your language does not necessarily imply regularly tempered divisions, but if your thirds are of equal size then these divisions of the ditonic comma would need to be equal as well. This is something different from anything I have tried, but I have come to respect your interests. Actually, it would not be so far removed from the Marpurg I temperament, which is a 1/6 comma ditonic division, all of them being fifths. In your temperament, the telling triads would be D Maj, B Maj, E Maj, and Eb Maj, but there can be no argument that all other keys are improved over both the standard ET and the traditional Pythagorean triads for two reasons. First, the fifths are pure which implies the triads to be proportionally beating (actually, 6:4 fifths are strictly proportional but that is not worth picking over) and second, the thirds within these triads would beat identical to, or very similar to, beat speeds of standard ET thirds. It then becomes an aesthetic question as to whether one prefers this color, or something else. I eventually tired of the Marpurg I temperament because I felt that the color of a 1/6 ditonic fifth matched with an ET third did not appeal to me. That is why I must wonder about these keys mentioned because a 1/5 ditonic fifth would beat slightly faster than a 1/6 fifth. This is not to say that a fifth beating 1.5 bs is too fast. To the contrary. 1/4 syntonic fifths beat even faster, and they can be glorious. The aesthetic issue, IMO, is one of balancing beat speeds in a complimentary way between fifths and thirds. Generally, the more noticeable a fifth is beating, the slower I like the thirds to be, with the clever exception of an occasional proportionally beating triad that can hide a faster beating fifth. In my experience, when a noticeably beating fifth beats in no rhythmic relationship to the thirds, and the thirds are beating as fast as standard ET, you get a color much less satisfying than a traditional Pythagorean triad with much faster thirds and a pure fifth. Hope I did not ramble too long, but thanks for sharing this preview of your article. Dennis Johnson St. Olaf College
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