Tetracot family: Difference between revisions
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{{Mapping|legend=1| 1 1 1 5 | 0 4 9 -15 }} | {{Mapping|legend=1| 1 1 1 5 | 0 4 9 -15 }} | ||
Optimal tunings: | Optimal tunings: | ||
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{{Mapping|legend=1| 1 1 1 -1 | 0 4 9 26 }} | {{Mapping|legend=1| 1 1 1 -1 | 0 4 9 26 }} | ||
Optimal tunings: | Optimal tunings: | ||
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{{Mapping|legend=1| 1 1 1 0 | 0 4 9 19 }} | {{Mapping|legend=1| 1 1 1 0 | 0 4 9 19 }} | ||
Optimal tunings: | Optimal tunings: | ||
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Octacot cuts the Gordian knot of deciding between the monkey and bunya mappings for 7 by cutting the generator in half and splitting the difference. It adds [[245/243]] to the normal comma list, and also tempers out [[2401/2400]]. It may also be described as 41 & 68. [[68edo]] or [[109edo]] can be used as tunings, as can (5/2)<sup>1/18</sup>, which gives just major thirds. Another tuning is [[150edo]], which has a generator, 11\150, of exactly 88 cents. This relates octacot to the [[88cET]] non-octave temperament, which like [[Carlos Alpha]] arguably makes more sense viewed as part of a rank-2 temperament with octaves rather than rank-1 without them. | Octacot cuts the Gordian knot of deciding between the monkey and bunya mappings for 7 by cutting the generator in half and splitting the difference. It adds [[245/243]] to the normal comma list, and also tempers out [[2401/2400]]. It may also be described as 41 & 68. [[68edo]] or [[109edo]] can be used as tunings, as can (5/2)<sup>1/18</sup>, which gives just major thirds. Another tuning is [[150edo]], which has a generator, 11\150, of exactly 88 cents. This relates octacot to the [[88cET]] non-octave temperament, which like [[Carlos Alpha]] arguably makes more sense viewed as part of a rank-2 temperament with octaves rather than rank-1 without them. | ||
Once again and for the same reasons, it is natural to add 100/99 and 325/324 to the list of commas | Once again and for the same reasons, it is natural to add 100/99 and 325/324 to the list of commas. Generators of 3\41, 8\109 and 11\150 (88 cents) are all good choices for the 7, 11 and 13 limits. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Mapping|legend=1| 1 1 1 2 | 0 8 18 11 }} | {{Mapping|legend=1| 1 1 1 2 | 0 8 18 11 }} | ||
Optimal tunings: | Optimal tunings: | ||
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{{Mapping|legend=1| 1 1 1 1 | 0 12 27 37 }} | {{Mapping|legend=1| 1 1 1 1 | 0 12 27 37 }} | ||
Optimal tunings: | Optimal tunings: | ||
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: Mapping generators: ~7/5, ~10/9 | : Mapping generators: ~7/5, ~10/9 | ||
Optimal tuning (CTE): ~7/5 = 1\2, ~10/9 = 175.472 | Optimal tuning (CTE): ~7/5 = 1\2, ~10/9 = 175.472 | ||