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The generator for [[amity]] temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It tempers out the 5-limit amity comma, 1600000/1594323. 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, 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 generator for [[amity]] temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It tempers out the 5-limit amity comma, 1600000/1594323. 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, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.


Temperaments not discussed here include [[Breedsmic temperaments|amicable]] and [[Hemimage temperaments|chromat]].
Temperaments not discussed here include:
* ''[[amicable]]'', {2401/2400, 1600000/1594323} → [[Breedsmic temperaments #Amicable]]
* ''[[chromat]]'', {10976/10935, 235298/234375} → [[Hemimage temperaments #Chromat]]


= Amity =
= Amity =
{{main|Amity}}
{{main| Amity }}
{{see also|Ragismic microtemperaments #Amity}}
{{see also| Ragismic microtemperaments #Amity }}


[[Comma]]: 1600000/1594323
Subgroup: 2.3.5


[[Mapping]]: [<1 3 6|, <0 -5 -13|]
[[Comma list]]: 1600000/1594323


[[POTE tuning|POTE generator]]: ~243/200 = 339.519
[[Mapping]]: [{{val| 1 3 6 }}, {{val| 0 -5 -13 }}


[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}
[[POTE generator]]: ~243/200 = 339.519
 
{{Val list|legend=1| 7, 39, 46, 53, 152, 205, 463, 668, 873 }}


[[Badness]]: 0.021960
[[Badness]]: 0.021960


== 7-limit ==
= Septimal amity =
Subgroup: 2.3.5.7
 
[[Comma list]]: 4375/4374, 5120/5103
[[Comma list]]: 4375/4374, 5120/5103


[[Mapping]]: [<1 3 6 -2|, <0 -5 -13 17|]
[[Mapping]]: [{{val| 1 3 6 -2 }}, {{val| 0 -5 -13 17 }}


[[Wedgie]]: <<5 13 -17 9 -41 -76||
{{Multival|legend=1| 5 13 -17 9 -41 -76 }}


[[POTE tuning|POTE generator]]: ~128/105 = 339.432
[[POTE generator]]: ~128/105 = 339.432


[[EDO|Vals]]: {{Val list| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
{{Val list|legend=1| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}


[[Badness]]: 0.023649
[[Badness]]: 0.023649


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4375/4374, 5120/5103
Comma list: 540/539, 4375/4374, 5120/5103


Mapping: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]
Mapping: [{{val| 1 3 6 -2 21 }}, {{val| 0 -5 -13 17 -62 }}


POTE generator: ~128/105 = 339.464
POTE generator: ~128/105 = 339.464
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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 847/845
Comma list: 352/351, 540/539, 625/624, 847/845


Mapping: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]
Mapping: [{{val| 1 3 6 -2 21 17 }}, {{val| 0 -5 -13 17 -62 -47 }}


POTE generator: ~128/105 = 339.481
POTE generator: ~128/105 = 339.481
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== Hitchcock ==
== Hitchcock ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2200/2187
Comma list: 121/120, 176/175, 2200/2187


Mapping: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
Mapping: [{{val| 1 3 6 -2 6 }}, {{val| 0 -5 -13 17 -9 }}


POTE generator: ~11/9 = 339.390
POTE generator: ~11/9 = 339.390
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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 325/324
Comma list: 121/120, 169/168, 176/175, 325/324


Mapping: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]
Mapping: [{{val| 1 3 6 -2 6 2 }}, {{val| 0 -5 -13 17 -9 6 }}


POTE generator: ~11/9 = 339.419
POTE generator: ~11/9 = 339.419
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== Hemiamity ==
== Hemiamity ==
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5120/5103
Comma list: 3025/3024, 4375/4374, 5120/5103


Mapping: [<2 1 -1 13 13|, <0 5 13 -17 -14|]
Mapping: [{{val| 2 1 -1 13 13 }}, {{val| 0 5 13 -17 -14 }}


POTE generator: ~64/55 = 339.439
POTE generator: ~64/55 = 339.439
Line 86: Line 102:


= Accord =
= Accord =
Subgroup: 2.3.5.7
[[Comma list]]: 126/125, 100352/98415
[[Comma list]]: 126/125, 100352/98415


[[Mapping]]: [<1 3 6 11|, <0 -5 -13 -29|]
[[Mapping]]: [{{val| 1 3 6 11 }}, {{val| 0 -5 -13 -29 }}


[[Wedgie]]: <<5 13 29 9 32 31||
{{Multival|legend=1| 5 13 29 9 32 31 }}


[[POTE tuning|POTE generator]]: ~243/200 = 338.993
[[POTE generator]]: ~243/200 = 338.993


[[EDO|Vals]]: {{Val list| 7d, 46, 131c, 177c }}
{{Val list|legend=1| 7d, 46, 131c, 177c }}


[[Badness]]: 0.095612
[[Badness]]: 0.095612


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 896/891
Comma list: 121/120, 126/125, 896/891


Mapping: [<1 3 6 11 6|, <0 -5 -13 -29 -9|]
Mapping: [{{val| 1 3 6 11 6 }}, {{val| 0 -5 -13 -29 -9 }}


POTE generator: ~11/9 = 339.047
POTE generator: ~11/9 = 339.047
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= 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".
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 64827/64000
[[Comma list]]: 245/243, 64827/64000


[[Mapping]]: [<2 1 -1 3|, <0 5 13 6|]
[[Mapping]]: [{{val| 2 1 -1 3 }}, {{val| 0 5 13 6 }}


[[Wedgie]]: <<10 26 12 18 -9 -45||
{{Multival|legend=1| 10 26 12 18 -9 -45 }}


[[POTE tuning|POTE generator]]: ~7/6 = 260.402
[[POTE generator]]: ~7/6 = 260.402


[[EDO|Vals]]: {{Val list| 46, 60, 106d }}
{{Val list|legend=1| 46, 60, 106d }}


[[Badness]]: 0.083601
[[Badness]]: 0.083601


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 441/440
Comma list: 121/120, 245/243, 441/440


Mapping: [<2 1 -1 3 3|, <0 5 13 6 9|]
Mapping: [{{val| 2 1 -1 3 3 }}, {{val| 0 5 13 6 9 }}


POTE generator: ~7/6 = 260.393
POTE generator: ~7/6 = 260.393
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 245/243, 441/440
Comma list: 91/90, 121/120, 245/243, 441/440


Mapping: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|]
Mapping: [{{val| 2 1 -1 3 3 0 }}, {{val| 0 5 13 6 9 17 }}


POTE generator: ~7/6 = 260.618
POTE generator: ~7/6 = 260.618
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= 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".
Subgroup: 2.3.5.7


[[Comma list]]: 2430/2401, 4000/3969  
[[Comma list]]: 2430/2401, 4000/3969  


[[Mapping]]: [<1 8 19 15|, <0 -10 -26 -19|]
[[Mapping]]: [{{val| 1 8 19 15 }}, {{val| 0 -10 -26 -19 }}


[[Wedgie]]: <<10 26 19 18 2 -29||
{{Multival|legend=1| 10 26 19 18 2 -29 }}


[[POTE tuning|POTE generator]]: ~9/7 = 430.219
[[POTE generator]]: ~9/7 = 430.219


[[EDO|Vals]]: {{Val list| 14c, 39d, 53 }}
{{Val list|legend=1| 14c, 39d, 53 }}


[[Badness]]: 0.073956
[[Badness]]: 0.073956


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 2200/2187
Comma list: 99/98, 121/120, 2200/2187


Mapping: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]
Mapping: [{{val| 1 8 19 15 15 }}, {{val| 0 -10 -26 -19 -18 }}


POTE generator: ~9/7 = 430.192
POTE generator: ~9/7 = 430.192
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 275/273, 572/567
Comma list: 99/98, 121/120, 275/273, 572/567


Mapping: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]
Mapping: [{{val| 1 8 19 15 15 30 }}, {{val| 0 -10 -26 -19 -18 -41 }}


POTE generator: ~9/7 = 430.216
POTE generator: ~9/7 = 430.216
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= 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).
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 1250000/1240029
[[Comma list]]: 225/224, 1250000/1240029


[[Mapping]]: [<1 3 6 13|, <0 -5 -13 -36|]
[[Mapping]]: [{{val| 1 3 6 13 }}, {{val| 0 -5 -13 -36 }}


[[Wedgie]]: <<5 13 36 9 43 47||
{{Multival|legend=1| 5 13 36 9 43 47 }}


[[POTE tuning|POTE generator]]: ~243/200 = 339.763
[[POTE generator]]: ~243/200 = 339.763


[[EDO|Vals]]: {{Val list| 7d, 46d, 53, 113, 166 }}
{{Val list|legend=1| 7d, 46d, 53, 113, 166 }}


[[Badness]]: 0.066638
[[Badness]]: 0.066638


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1250000/1240029
Comma list: 225/224, 385/384, 1250000/1240029


Mapping: [<1 3 6 13 -9|, <0 -5 -13 -36 44|]
Mapping: [{{val| 1 3 6 13 -9 }}, {{val| 0 -5 -13 -36 44 }}


POTE generator: ~243/200 = 339.763
POTE generator: ~243/200 = 339.763
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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 2200/2197
Comma list: 225/224, 325/324, 385/384, 2200/2197


Mapping: [<1 3 6 13 -9 2|, <0 -5 -13 -36 44 6|]
Mapping: [{{val| 1 3 6 13 -9 2 }}, {{val| 0 -5 -13 -36 44 6 }}


POTE generator: ~39/32 = 339.764
POTE generator: ~39/32 = 339.764
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== Houbor ==
== Houbor ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 2200/2187
Comma list: 121/120, 225/224, 2200/2187


Mapping: [<1 3 6 13 6|, <0 -5 -13 -36 -9|]
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}


POTE generator: ~11/9 = 339.814
POTE generator: ~11/9 = 339.814
Line 232: Line 272:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 325/324
Comma list: 121/120, 225/224, 275/273, 325/324


Mapping: [<1 3 6 13 6 2|, <0 -5 -13 -36 -9 6|]
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}


POTE generator: ~11/9 = 339.784
POTE generator: ~11/9 = 339.784
Line 244: Line 286:
= 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.
Subgroup: 2.3.5.7


[[Comma list]]: 1029/1024, 1071875/1062882
[[Comma list]]: 1029/1024, 1071875/1062882


[[Mapping]]: [<1 -2 -7 4|, <0 15 39 -5|]
[[Mapping]]: [{{val| 1 -2 -7 4 }}, {{val| 0 15 39 -5 }}


[[Wedgie]]: <<15 39 -5 27 -50 -121||
{{Multival|legend=1| 15 39 -5 27 -50 -121 }}


[[POTE tuning|POTE generator]]: ~189/160 = 286.787
[[POTE generator]]: ~189/160 = 286.787


[[EDO|Vals]]: {{Val list| 46, 113, 159 }}
{{Val list|legend=1| 46, 113, 159 }}


[[Badness]]: 0.125733
[[Badness]]: 0.125733


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 1071875/1062882
Comma list: 385/384, 441/440, 1071875/1062882


Mapping: [<1 -2 -7 4 8|, <0 15 39 -5 -19|]
Mapping: [{{val| 1 -2 -7 4 8 }}, {{val| 0 15 39 -5 -19 }}


POTE generator: ~33/28 = 286.797
POTE generator: ~33/28 = 286.797
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 10985/10976
Comma list: 325/324, 364/363, 385/384, 10985/10976


Mapping: [<1 -2 -7 4 8 8|, <0 15 39 -5 -19 -18|]
Mapping: [{{val| 1 -2 -7 4 8 8 }}, {{val| 0 15 39 -5 -19 -18 }}


POTE generator: ~13/11 = 286.789
POTE generator: ~13/11 = 286.789
Line 280: Line 328:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
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|]
Mapping: [{{val| 1 -2 -7 4 8 8 6 }}, {{val| 0 15 39 -5 -19 -18 -8 }}


POTE generator: ~13/11 = 286.795
POTE generator: ~13/11 = 286.795
Line 292: Line 342:
= 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.
Subgroup: 2.3.5.7


[[Comma list]]: 16875/16807, 1600000/1594323
[[Comma list]]: 16875/16807, 1600000/1594323


[[Mapping]]: [<1 8 19 20|, <0 -25 -65 -67|]
[[Mapping]]: [{{val| 1 8 19 20 }}, {{val| 0 -25 -65 -67 }}


[[Wedgie]]: <<25 65 67 45 36 -27||
{{Multival|legend=1| 25 65 67 45 36 -27 }}


[[POTE tuning|POTE generator]]: ~11907/10000 = 307.941
[[POTE generator]]: ~11907/10000 = 307.941


[[EDO|Vals]]: {{Val list| 113, 152, 265, 417, 986d }}
{{Val list|legend=1| 113, 152, 265, 417, 986d }}


[[Badness]]: 0.144551
[[Badness]]: 0.144551


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 1600000/1594323
Comma list: 540/539, 1375/1372, 1600000/1594323


Mapping: [<1 8 19 20 5|, <0 -25 -65 -67 -6|]
Mapping: [{{val| 1 8 19 20 5 }}, {{val| 0 -25 -65 -67 -6 }}


POTE generator: ~3200/2673 = 307.906
POTE generator: ~3200/2673 = 307.906
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Badness: 0.051740
Badness: 0.051740


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity family| ]] <!-- main article -->
[[Category:Amity|#]] <!-- key article -->
[[Category:Amity|#]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Amity_family"