Sensamagic clan: Difference between revisions
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The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. | The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]]. | ||
Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]]. | |||
== BPS == | == BPS == | ||
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[[Optimal GPV sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | [[Optimal GPV sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | ||
=== Overview to extensions === | |||
The full 7-limit extensions' relation to BPS is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are | |||
* [[#Sensi]] | |||
* ''[[Hedgehog]]'', {50/49, 245/243} → [[Porcupine family #Hedgehog|Porcupine family]] | |||
* ''[[Fourfives]]'', {245/243, 235298/234375} → [[Fifive family #Fourfives|Fifive family]] | |||
The others are weak extensions. See | |||
* ''[[Father]]'', {16/15, 28/27} → [[Father family #Father|Father family]] | |||
* ''[[Sidi]]'', {25/24, 245/243} → [[Dicot family #Sidi|Dicot family]] | |||
* [[Godzilla]], {49/48, 81/80} → [[Meantone family #Godzilla|Meantone family]] | |||
* [[Superpyth]], {64/63, 245/243} → [[Archytas clan #Superpyth|Archytas clan]] | |||
* ''[[Hemiaug]]'', {128/125, 245/243} → [[Augmented family #Hemiaug|Augmented family]] | |||
* [[Magic]], {225/224, 245/243} → [[Magic family #Septimal magic|Magic family]] | |||
* [[Rodan]], {245/243, 1029/1024} → [[Gamelismic clan #Rodan|Gamelismic clan]] | |||
* ''[[Shrutar]]'', {245/243, 2048/2025} → [[Diaschismic family #Shrutar|Diaschismic family]] | |||
* ''[[Octacot]]'', {245/243, 2401/2400} → [[Tetracot family #Octacot|Tetracot family]] | |||
* ''[[Clyde]]'', {245/243, 3136/3125} → [[Kleismic family #Clyde|Kleismic family]] | |||
* ''[[Pental]]'', {245/243, 16807/16384} → [[Pental family #Septimal pental|Pental family]] | |||
* ''[[Bamity]]'', {245/243, 64827/64000} → [[Amity family #Bamity|Amity family]] | |||
as well as sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below. | |||
== Sensi == | == Sensi == | ||
{{ | {{Main| Sensi }} | ||
{{ | {{See also| Sensipent family #Sensi }} | ||
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth." | Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth." | ||
=== Septimal sensi === | === Septimal sensi === | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 126/125, 245/243 | [[Comma list]]: 126/125, 245/243 | ||