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. | ||
= Lambda = | == Lambda == | ||
Subgroup: 3.5.7 | Subgroup: 3.5.7 | ||
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[[Val]]s: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | [[Val]]s: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | ||
== Extensions == | === Extensions === | ||
For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], [[Amity family #Bamity|bamity]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere. | For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], [[Amity family #Bamity|bamity]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere. | ||
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]]. | ||
= Sensi = | == Sensi == | ||
{{main| Sensi }} | {{main| Sensi }} | ||
{{see also| Sensipent family #Sensi }} | {{see also| Sensipent family #Sensi }} | ||
| Line 27: | Line 27: | ||
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 | ||
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[[Badness]]: 0.025622 | [[Badness]]: 0.025622 | ||
=== Sensation === | ==== Sensation ==== | ||
Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.13 | ||
| Line 69: | Line 69: | ||
Vals: {{Val list| 19, 27, 46, 111de, 157de }} | Vals: {{Val list| 19, 27, 46, 111de, 157de }} | ||
== Sensor == | === Sensor === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 82: | Line 82: | ||
Badness: 0.037942 | Badness: 0.037942 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 95: | Line 95: | ||
Badness: 0.025575 | Badness: 0.025575 | ||
== Sensis == | === Sensis === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 108: | Line 108: | ||
Badness: 0.028680 | Badness: 0.028680 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 121: | Line 121: | ||
Badness: 0.020017 | Badness: 0.020017 | ||
== Sensus == | === Sensus === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 134: | Line 134: | ||
Badness: 0.029486 | Badness: 0.029486 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 147: | Line 147: | ||
Badness: 0.020789 | Badness: 0.020789 | ||
== Sensa == | === Sensa === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 160: | Line 160: | ||
Badness: 0.036835 | Badness: 0.036835 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 173: | Line 173: | ||
Badness: 0.023258 | Badness: 0.023258 | ||
== Hemisensi == | === Hemisensi === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 186: | Line 186: | ||
Badness: 0.048714 | Badness: 0.048714 | ||
= Bohpier = | == Bohpier == | ||
Bohpier is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | Bohpier is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | ||
| Line 201: | Line 201: | ||
[[Badness]]: 0.860534 | [[Badness]]: 0.860534 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 216: | Line 216: | ||
[[Badness]]: 0.068237 | [[Badness]]: 0.068237 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 229: | Line 229: | ||
Badness: 0.033949 | Badness: 0.033949 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.024864 | Badness: 0.024864 | ||
== Music == | === Music === | ||
by [[Chris Vaisvil]]: | by [[Chris Vaisvil]]: | ||
* [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3] | * [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3] | ||
* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | * [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | ||
= Escaped = | == Escaped == | ||
{{see also| Escapade family #Escaped }} | {{see also| Escapade family #Escaped }} | ||
| Line 266: | Line 266: | ||
[[Badness]]: 0.088746 | [[Badness]]: 0.088746 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 279: | Line 279: | ||
Badness: 0.035844 | Badness: 0.035844 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 292: | Line 292: | ||
Badness: 0.031366 | Badness: 0.031366 | ||
= Salsa = | == Salsa == | ||
{{see also| Schismatic family }} | {{see also| Schismatic family }} | ||
| Line 309: | Line 309: | ||
[[Badness]]: 0.080152 | [[Badness]]: 0.080152 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 322: | Line 322: | ||
Badness: 0.039444 | Badness: 0.039444 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 335: | Line 335: | ||
Badness: 0.030793 | Badness: 0.030793 | ||
= Pycnic = | == Pycnic == | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | ||
| Line 352: | Line 352: | ||
[[Badness]]: 0.073735 | [[Badness]]: 0.073735 | ||
= Cohemiripple = | == Cohemiripple == | ||
{{see also| Ripple family }} | {{see also| Ripple family }} | ||
| Line 369: | Line 369: | ||
[[Badness]]: 0.190208 | [[Badness]]: 0.190208 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 382: | Line 382: | ||
Badness: 0.082716 | Badness: 0.082716 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 395: | Line 395: | ||
Badness: 0.049933 | Badness: 0.049933 | ||
= Superthird = | == Superthird == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 410: | Line 410: | ||
[[Badness]]: 0.139379 | [[Badness]]: 0.139379 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 423: | Line 423: | ||
Badness: 0.070917 | Badness: 0.070917 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 436: | Line 436: | ||
Badness: 0.052835 | Badness: 0.052835 | ||
= Magus = | == Magus == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 449: | Line 449: | ||
[[Badness]]: 0.360162 | [[Badness]]: 0.360162 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 464: | Line 464: | ||
[[Badness]]: 0.1084 | [[Badness]]: 0.1084 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 477: | Line 477: | ||
Badness: 0.045108 | Badness: 0.045108 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 490: | Line 490: | ||
Badness: 0.043024 | Badness: 0.043024 | ||
= Leapweek = | == Leapweek == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 503: | Line 503: | ||
[[Badness]]: 0.140577 | [[Badness]]: 0.140577 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 516: | Line 516: | ||
Badness: 0.050679 | Badness: 0.050679 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 529: | Line 529: | ||
Badness: 0.032727 | Badness: 0.032727 | ||
= Semiwolf = | == Semiwolf == | ||
[[Subgroup]]: 3/2.7/4.5/2 | [[Subgroup]]: 3/2.7/4.5/2 | ||
| Line 540: | Line 540: | ||
[[Vals]]: {{val list|8edf, 11edf, 13edf}} | [[Vals]]: {{val list|8edf, 11edf, 13edf}} | ||
== Semilupine == | === Semilupine === | ||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | [[Subgroup]]: 3/2.7/4.5/2.11/4 | ||
| Line 551: | Line 551: | ||
[[Vals]]: {{val list|8edf, 13edf}} | [[Vals]]: {{val list|8edf, 13edf}} | ||
== Hemilycan == | === Hemilycan === | ||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | [[Subgroup]]: 3/2.7/4.5/2.11/4 | ||