Amity family: Difference between revisions
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The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you. | The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you. | ||
= Amity = | == Amity == | ||
{{main| Amity }} | {{main| Amity }} | ||
{{see also| Ragismic microtemperaments #Amity }} | {{see also| Ragismic microtemperaments #Amity }} | ||
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[[Badness]]: 0.021960 | [[Badness]]: 0.021960 | ||
== Extensions == | === Extensions === | ||
The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, and 16875/16807 for familia. | The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, and 16875/16807 for familia. | ||
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* ''[[chromat]]'', {10976/10935, 235298/234375} → [[Hemimage temperaments #Chromat]] | * ''[[chromat]]'', {10976/10935, 235298/234375} → [[Hemimage temperaments #Chromat]] | ||
= Septimal amity = | == Septimal amity == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 39: | Line 39: | ||
[[Badness]]: 0.023649 | [[Badness]]: 0.023649 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 52: | Line 52: | ||
Badness: 0.031506 | Badness: 0.031506 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.028008 | Badness: 0.028008 | ||
== Hitchcock == | === Hitchcock === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 78: | Line 78: | ||
Badness: 0.035187 | Badness: 0.035187 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 91: | Line 91: | ||
Badness: 0.022448 | Badness: 0.022448 | ||
== Hemiamity == | === Hemiamity === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.031307 | Badness: 0.031307 | ||
= Houborizic = | == Houborizic == | ||
The ''houborizic'' temperament (53&113, named by [[User:Xenllium|Xenllium]]) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents). | The ''houborizic'' temperament (53&113, named by [[User:Xenllium|Xenllium]]) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents). | ||
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[[Badness]]: 0.066638 | [[Badness]]: 0.066638 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 134: | Line 134: | ||
Badness: 0.067891 | Badness: 0.067891 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 147: | Line 147: | ||
Badness: 0.032996 | Badness: 0.032996 | ||
== Houbor == | === Houbor === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 160: | Line 160: | ||
Badness: 0.045232 | Badness: 0.045232 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 173: | Line 173: | ||
Badness: 0.031331 | Badness: 0.031331 | ||
= Paramity = | == Paramity == | ||
The ''paramity'' temperament (53&311, named by [[User:Xenllium|Xenllium]]) tempers out the horwell comma (65625/65536) and [[garischisma]] (33554432/33480783). | The ''paramity'' temperament (53&311, named by [[User:Xenllium|Xenllium]]) tempers out the horwell comma (65625/65536) and [[garischisma]] (33554432/33480783). | ||
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[[Badness]]: 0.113655 | [[Badness]]: 0.113655 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 201: | Line 201: | ||
Badness: 0.064853 | Badness: 0.064853 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 214: | Line 214: | ||
Badness: 0.030347 | Badness: 0.030347 | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 227: | Line 227: | ||
Badness: 0.024118 | Badness: 0.024118 | ||
== 19-limit == | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 240: | Line 240: | ||
Badness: 0.017420 | Badness: 0.017420 | ||
= Accord = | == Accord == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 255: | Line 255: | ||
[[Badness]]: 0.095612 | [[Badness]]: 0.095612 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 268: | Line 268: | ||
Badness: 0.042468 | Badness: 0.042468 | ||
= Bamity = | == Bamity == | ||
Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name "bamity" is a play on the words "bi-" and "amity". | Bamity has a period of half octave and tempers out the sensamagic comma, [[245/243]]. The name "bamity" is a play on the words "bi-" and "amity". | ||
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[[Badness]]: 0.083601 | [[Badness]]: 0.083601 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 298: | Line 298: | ||
Badness: 0.035504 | Badness: 0.035504 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 311: | Line 311: | ||
Badness: 0.030885 | Badness: 0.030885 | ||
= Hamity = | == Hamity == | ||
Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words "half" and "acute minor tenth". | Hamity has a generator of about 430 cents which represents [[9/7]]. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words "half" and "acute minor tenth". | ||
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[[Badness]]: 0.073956 | [[Badness]]: 0.073956 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 341: | Line 341: | ||
Badness: 0.042947 | Badness: 0.042947 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 354: | Line 354: | ||
Badness: 0.029753 | Badness: 0.029753 | ||
= Gamity = | == Gamity == | ||
The ''gamity'' temperament (46&113, named by [[User:Xenllium|Xenllium]]) tempers out the [[1029/1024|gamelisma]], 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three. | The ''gamity'' temperament (46&113, named by [[User:Xenllium|Xenllium]]) tempers out the [[1029/1024|gamelisma]], 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three. | ||
| Line 371: | Line 371: | ||
[[Badness]]: 0.125733 | [[Badness]]: 0.125733 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 384: | Line 384: | ||
Badness: 0.051111 | Badness: 0.051111 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 397: | Line 397: | ||
Badness: 0.030297 | Badness: 0.030297 | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 410: | Line 410: | ||
Badness: 0.022036 | Badness: 0.022036 | ||
= Familia = | == Familia == | ||
The ''familia'' temperament (113&152, named by [[User:Xenllium|Xenllium]]) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five. | The ''familia'' temperament (113&152, named by [[User:Xenllium|Xenllium]]) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five. | ||
| Line 427: | Line 427: | ||
[[Badness]]: 0.144551 | [[Badness]]: 0.144551 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||