Magic family: Difference between revisions

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225/224 is the [[Marvel_temperaments|marvel]] comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament.

243~~/242~~ leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This ~~"octarod comma"~~ is shared with [[Sensi|sensi]], [[Semaphore_and_Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot_family|octacot]], [[Gamelismic_clan|rodan]], [[Shrutar|shrutar]], [[Porcupine_family|hedgehog]], [[Clyde_node|clyde]], and [[Sensamagic_clan|bohpier]]. See [http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243 temperament finder].)

245/243, the sensamagic comma, leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This is shared with [[Sensi|sensi]], [[Semaphore_and_Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot_family|octacot]], [[Gamelismic_clan|rodan]], [[Shrutar|shrutar]], [[Porcupine_family|hedgehog]], [[Clyde_node|clyde]], and [[Sensamagic_clan|bohpier]]. See [http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243 temperament finder].)

By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, <<5 1 12 -8 ... ||. For this, [[104edo|104edo]] provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning.

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 /224 is the [[Marvel_temperaments|marvel]] comma. Because the augmented triad is the simplest triad in magic temperaments, it is especially significant in magic temperament.
-/242 leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This "octarod comma" is shared with [[Sensi|sensi]], [[Semaphore_and_Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot_family|octacot]], [[Gamelismic_clan|rodan]], [[Shrutar|shrutar]], [[Porcupine_family|hedgehog]], [[Clyde_node|clyde]], and [[Sensamagic_clan|bohpier]]. See [http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243 temperament finder].)
+/243, the sensamagic comma, leads to another essentially tempered 9-limit triad with two thirds approximating 9/7 and the other 6/5. It also divides the approximate 3/2 into two steps of 7/6 and one of 10/9. (This is shared with [[Sensi|sensi]], [[Semaphore_and_Godzilla|godzilla]], [[Superpyth|superpyth]], [[Tetracot_family|octacot]], [[Gamelismic_clan|rodan]], [[Shrutar|shrutar]], [[Porcupine_family|hedgehog]], [[Clyde_node|clyde]], and [[Sensamagic_clan|bohpier]]. See [http://x31eq.com/cgi-bin/uv.cgi?uvs=245:243 temperament finder].)
 By adding 100/99 to the list of commas, magic can be extended to an 11-limit version, &lt;&lt;5 1 12 -8 ... ||. For this, [[104edo|104edo]] provides an excellent tuning, as it does also for the rank three temperaments tempering out 100/99 with 225/224, 245/243 or 875/864. Septimage (see below) is also an excellent 11-limit magic tuning.