Passion family: Difference between revisions
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== Passion == | == Passion == | ||
Passion is generated by a ~16/15 semitone, five of which reach a ~4/3 perfect fourth; its [[ploidacot]] is omega-pentacot. It follows that both 3 and 5 should be tuned sharp. [[73edo]] does this and may be recommended as a tuning. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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== Septimal passion == | == Septimal passion == | ||
Septimal passion tempers out 64/63, the archytas comma, connecting itself to the [[archytas clan]]. It may be described as the 12 & 49 temperament. The interval class of 7 is found by exactly 10 generator steps, which calls for a flatter tuning of the fourth, and [[49edo]] may be recommended as a tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Passionate == | == Passionate == | ||
Passionate tempers out 126/125 and may be described as {{nowrap| 12 & 73 }}. The optimum of this temperament is closer to its 5-limit counterpart's, but prime 7 is much more complex, at +22 generator steps away. 73edo and [[85edo]] in the 85c val are among the possible tunings. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Passive == | == Passive == | ||
This low-complexity extension tempers out 225/224 as well as [[256/245]]. Two generator steps represent ~[[8/7]]. As one might expect, 12edo is about as accurate as it can be tuned. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Freivald == | == Freivald == | ||
Freivald splits the [[octave complement]] of the semitone generator of passion in two, each of which is used for ~11/8. It may be described as {{nowrap| 24 & 37 }}; its ploidacot is delta-decacot. [[61edo]] may be recommended as a tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||