Amity family: Difference between revisions

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== Extensions ==
== Extensions ==
The second comma to extend the 5-limit amity include 4375/4374 for amity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 225/224 for houborizic, 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, 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:  
Temperaments discussed elsewhere include:  
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[[POTE generator]]: ~128/105 = 339.432
[[POTE generator]]: ~128/105 = 339.432


{{Val list|legend=1| 7, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}
{{Val list|legend=1| 7, 32c, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd }}


[[Badness]]: 0.023649
[[Badness]]: 0.023649
Line 48: Line 48:
POTE generator: ~128/105 = 339.464
POTE generator: ~128/105 = 339.464


Vals: {{Val list| 53, 99e, 152, 555dee, 707ddee, 859bddee }}
Vals: {{Val list| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}


Badness: 0.031506
Badness: 0.031506
Line 61: Line 61:
POTE generator: ~128/105 = 339.481
POTE generator: ~128/105 = 339.481


Vals: {{Val list| 53, 99ef, 152f }}
Vals: {{Val list| 46ef, 53, 99ef, 152f }}


Badness: 0.028008
Badness: 0.028008
Line 184: Line 184:
[[POTE generator]]: ~243/200 = 338.993
[[POTE generator]]: ~243/200 = 338.993


{{Val list|legend=1| 7d, 46, 131c, 177c }}
{{Val list|legend=1| 7d, 39d, 46, 131c, 177c }}


[[Badness]]: 0.095612
[[Badness]]: 0.095612
Line 197: Line 197:
POTE generator: ~11/9 = 339.047
POTE generator: ~11/9 = 339.047


Vals: {{Val list| 7d, 46, 177c, 223bc, 269bce }}
Vals: {{Val list| 7d, 39d, 46, 177c, 223bc, 269bce }}


Badness: 0.042468
Badness: 0.042468
Line 214: Line 214:
[[POTE generator]]: ~7/6 = 260.402
[[POTE generator]]: ~7/6 = 260.402


{{Val list|legend=1| 46, 60, 106d }}
{{Val list|legend=1| 14c, 32c, 46, 60, 106d }}


[[Badness]]: 0.083601
[[Badness]]: 0.083601
Line 227: Line 227:
POTE generator: ~7/6 = 260.393
POTE generator: ~7/6 = 260.393


Vals: {{Val list| 14c, 46, 60e, 106de }}
Vals: {{Val list| 14c, 32c, 46, 60e, 106de }}


Badness: 0.035504
Badness: 0.035504
Line 240: Line 240:
POTE generator: ~7/6 = 260.618
POTE generator: ~7/6 = 260.618


Vals: {{Val list| 46, 106def, 152def }}
Vals: {{Val list| 14cf, 32cf, 46, 106def, 152def }}


Badness: 0.030885
Badness: 0.030885
Line 283: Line 283:
POTE generator: ~9/7 = 430.216
POTE generator: ~9/7 = 430.216


Vals: {{Val list| 14cf, 53 }}
Vals: {{Val list| 14cf, 39df, 53 }}


Badness: 0.029753
Badness: 0.029753
Line 356: Line 356:
[[POTE generator]]: ~11907/10000 = 307.941
[[POTE generator]]: ~11907/10000 = 307.941


{{Val list|legend=1| 113, 152, 265, 417, 986d }}
{{Val list|legend=1| 39d, 74cd, 113, 152, 265, 417, 986d }}


[[Badness]]: 0.144551
[[Badness]]: 0.144551
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POTE generator: ~3200/2673 = 307.906
POTE generator: ~3200/2673 = 307.906


Vals: {{Val list| 113, 152, 417, 569de, 721de }}
Vals: {{Val list| 39d, 74cd, 113, 152, 417, 569de, 721de }}


Badness: 0.051740
Badness: 0.051740

Revision as of 11:46, 29 May 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, 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

Main article: Amity
See also: Ragismic microtemperaments § Amity

Subgroup: 2.3.5

Comma list: 1600000/1594323

Mapping: [⟨1 3 6], ⟨0 -5 -13]

POTE generator: ~243/200 = 339.519

Template:Val list

Badness: 0.021960

Extensions

The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 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:

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

Template:Val list

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, named by 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

Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]

Wedgie: ⟨⟨ 5 13 36 9 43 47 ]]

POTE generator: ~243/200 = 339.763

Template:Val list

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

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

Template:Val list

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

Template:Val list

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

Template:Val list

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, named by Xenllium) 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

Template:Val list

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, named by 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

Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]

Wedgie: ⟨⟨ 25 65 67 45 36 -27 ]]

POTE generator: ~11907/10000 = 307.941

Template:Val list

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

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