Tour of regular temperaments: Difference between revisions
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+ parakleismic family & sengic temperaments |
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; [[Ditonmic family]] (P8, c4P4/13) | ; [[Ditonmic family]] (P8, c4P4/13) | ||
: This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti. | : This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti. | ||
; [[Parakleismic family]] (P8, c3P4/13) | |||
: This tempers out the [[parakleisma]], {{monzo| 8 14 -13 }} (1224440064/1220703125). The generator is a slightly sharpened ~5/3 major sixth. Thirteen generators minus three octaves equal ~4/3, and fourteen generators minus three octaves equal ~8/5. | |||
; [[Luna family]] (P8, ccP4/15) | ; [[Luna family]] (P8, ccP4/15) | ||
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: These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti. | : These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti. | ||
; Sengic temperaments | ; [[Sengic temperaments]] | ||
: Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti. | : Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti. | ||