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 | ||
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[[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 | ||
| Line 65: | Line 65: | ||
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 | ||
| Line 104: | Line 104: | ||
Badness: 0.031307 | Badness: 0.031307 | ||
== Houborizic | == Houborizic == | ||
The ''houborizic'' temperament (53&113 | The ''houborizic'' temperament (53&113) tempers out the [[marvel comma]], 225/224. It is so named because it is closely related to the '''houboriz tuning''' (generator: 339.774971 cents). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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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 | ||
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Badness: 0.045232 | Badness: 0.045232 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.031331 | Badness: 0.031331 | ||
== Paramity | == Paramity == | ||
The ''paramity'' temperament (53&311 | The ''paramity'' temperament (53&311) tempers out the horwell comma (65625/65536) and [[garischisma]] (33554432/33480783). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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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 | The ''gamity'' temperament (46&113) 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. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[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 | The ''familia'' temperament (113&152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.144551 | [[Badness]]: 0.144551 | ||
=== 11-limit | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Revision as of 04:18, 5 June 2021
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 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
Subgroup: 2.3.5
Comma list: 1600000/1594323
Mapping: [⟨1 3 6], ⟨0 -5 -13]
POTE generator: ~243/200 = 339.519
Badness: 0.021960
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.
Temperaments discussed elsewhere include:
- amicable, {2401/2400, 1600000/1594323} → Breedsmic temperaments #Amicable
- chromat, {10976/10935, 235298/234375} → Hemimage temperaments #Chromat
Septimal amity
Subgroup: 2.3.5.7
Comma list: 4375/4374, 5120/5103
Mapping: [⟨1 3 6 -2], ⟨0 -5 -13 17]
Wedgie: ⟨⟨ 5 13 -17 9 -41 -76 ]]
POTE generator: ~128/105 = 339.432
Badness: 0.023649
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4374, 5120/5103
Mapping: [⟨1 3 6 -2 21], ⟨0 -5 -13 17 -62]
POTE generator: ~128/105 = 339.464
Vals: Template:Val list
Badness: 0.031506
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 847/845
Mapping: [⟨1 3 6 -2 21 17], ⟨0 -5 -13 17 -62 -47]
POTE generator: ~128/105 = 339.481
Vals: Template:Val list
Badness: 0.028008
Hitchcock
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2200/2187
Mapping: [⟨1 3 6 -2 6], ⟨0 -5 -13 17 -9]
POTE generator: ~11/9 = 339.390
Vals: Template:Val list
Badness: 0.035187
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 325/324
Mapping: [⟨1 3 6 -2 6 2], ⟨0 -5 -13 17 -9 6]
POTE generator: ~11/9 = 339.419
Vals: Template:Val list
Badness: 0.022448
Hemiamity
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5120/5103
Mapping: [⟨2 1 -1 13 13], ⟨0 5 13 -17 -14]
POTE generator: ~64/55 = 339.439
Vals: Template:Val list
Badness: 0.031307
Houborizic
The houborizic temperament (53&113) tempers out the marvel comma, 225/224. It is so named because it is closely related to the houboriz tuning (generator: 339.774971 cents).
Subgroup: 2.3.5.7
Comma list: 225/224, 1250000/1240029
Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]
Wedgie: ⟨⟨ 5 13 36 9 43 47 ]]
POTE generator: ~243/200 = 339.763
Badness: 0.066638
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1250000/1240029
Mapping: [⟨1 3 6 13 -9], ⟨0 -5 -13 -36 44]
POTE generator: ~243/200 = 339.763
Vals: Template:Val list
Badness: 0.067891
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 2200/2197
Mapping: [⟨1 3 6 13 -9 2], ⟨0 -5 -13 -36 44 6]
POTE generator: ~39/32 = 339.764
Vals: Template:Val list
Badness: 0.032996
Houbor
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 2200/2187
Mapping: [⟨1 3 6 13 6], ⟨0 -5 -13 -36 -9]
POTE generator: ~11/9 = 339.814
Vals: Template:Val list
Badness: 0.045232
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 325/324
Mapping: [⟨1 3 6 13 6 2], ⟨0 -5 -13 -36 -9 6]
POTE generator: ~11/9 = 339.784
Vals: Template:Val list
Badness: 0.031331
Paramity
The paramity temperament (53&311) tempers out the horwell comma (65625/65536) and garischisma (33554432/33480783).
Subgroup: 2.3.5.7
Comma list: 65625/65536, 1600000/1594323
Mapping: [⟨1 3 6 -17], ⟨0 -5 -13 70]]
POTE generator: ~243/200 = 339.553
Badness: 0.113655
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 19712/19683, 41503/41472
Mapping: [⟨1 3 6 -17 36], ⟨0 -5 -13 70 -115]]
POTE generator: ~243/200 = 339.554
Vals: Template:Val list
Badness: 0.064853
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Mapping: [⟨1 3 6 -17 36 17], ⟨0 -5 -13 70 -115 -47]]
POTE generator: ~243/200 = 339.554
Vals: Template:Val list
Badness: 0.030347
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Mapping: [⟨1 3 6 -17 36 17 -31], ⟨0 -5 -13 70 -115 -47 124]]
POTE generator: ~243/200 = 339.555
Vals: Template:Val list
Badness: 0.024118
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Mapping: [⟨1 3 6 -17 36 17 -31 15], ⟨0 -5 -13 70 -115 -47 124 -38]]
POTE generator: ~208/171 = 339.555
Vals: Template:Val list
Badness: 0.017420
Accord
Subgroup: 2.3.5.7
Comma list: 126/125, 100352/98415
Mapping: [⟨1 3 6 11], ⟨0 -5 -13 -29]
Wedgie: ⟨⟨ 5 13 29 9 32 31 ]]
POTE generator: ~243/200 = 338.993
Badness: 0.095612
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 896/891
Mapping: [⟨1 3 6 11 6], ⟨0 -5 -13 -29 -9]
POTE generator: ~11/9 = 339.047
Vals: Template:Val list
Badness: 0.042468
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".
Subgroup: 2.3.5.7
Comma list: 245/243, 64827/64000
Mapping: [⟨2 1 -1 3], ⟨0 5 13 6]
Wedgie: ⟨⟨ 10 26 12 18 -9 -45 ]]
POTE generator: ~7/6 = 260.402
Badness: 0.083601
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3], ⟨0 5 13 6 9]
POTE generator: ~7/6 = 260.393
Vals: Template:Val list
Badness: 0.035504
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3 0], ⟨0 5 13 6 9 17]
POTE generator: ~7/6 = 260.618
Vals: Template:Val list
Badness: 0.030885
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".
Subgroup: 2.3.5.7
Comma list: 2430/2401, 4000/3969
Mapping: [⟨1 8 19 15], ⟨0 -10 -26 -19]
Wedgie: ⟨⟨ 10 26 19 18 2 -29 ]]
POTE generator: ~9/7 = 430.219
Badness: 0.073956
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 2200/2187
Mapping: [⟨1 8 19 15 15], ⟨0 -10 -26 -19 -18]
POTE generator: ~9/7 = 430.192
Vals: Template:Val list
Badness: 0.042947
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 275/273, 572/567
Mapping: [⟨1 8 19 15 15 30], ⟨0 -10 -26 -19 -18 -41]
POTE generator: ~9/7 = 430.216
Vals: Template:Val list
Badness: 0.029753
Gamity
The gamity temperament (46&113) tempers out the gamelisma, 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three.
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1071875/1062882
Mapping: [⟨1 -2 -7 4], ⟨0 15 39 -5]
Wedgie: ⟨⟨ 15 39 -5 27 -50 -121 ]]
POTE generator: ~189/160 = 286.787
Badness: 0.125733
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 1071875/1062882
Mapping: [⟨1 -2 -7 4 8], ⟨0 15 39 -5 -19]
POTE generator: ~33/28 = 286.797
Vals: Template:Val list
Badness: 0.051111
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 10985/10976
Mapping: [⟨1 -2 -7 4 8 8], ⟨0 15 39 -5 -19 -18]
POTE generator: ~13/11 = 286.789
Vals: Template:Val list
Badness: 0.030297
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Mapping: [⟨1 -2 -7 4 8 8 6], ⟨0 15 39 -5 -19 -18 -8]
POTE generator: ~13/11 = 286.795
Vals: Template:Val list
Badness: 0.022036
Familia
The familia temperament (113&152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1600000/1594323
Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]
Wedgie: ⟨⟨ 25 65 67 45 36 -27 ]]
POTE generator: ~11907/10000 = 307.941
Badness: 0.144551
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 1600000/1594323
Mapping: [⟨1 8 19 20 5], ⟨0 -25 -65 -67 -6]
POTE generator: ~3200/2673 = 307.906
Vals: Template:Val list
Badness: 0.051740