Amity family: Difference between revisions

Revision as of 13:41, 8 January 2022

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

Main article: Amity

See also: Ragismic microtemperaments § Amity

Subgroup: 2.3.5

Comma list: 1600000/1594323

Mapping: [⟨1 3 6], ⟨0 -5 -13]]

Mapping generators: ~2, ~243/200

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, 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
witch, {420175/419904, 1600000/1594323} → Wizmic microtemperaments #Witch

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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list *

* optimal patent val: 205

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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.022448

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 169/168, 176/175, 273/272

Mapping: [⟨1 3 6 -2 6 2 -1], ⟨0 -5 -13 17 -9 6 18]]

POTE generator: ~11/9 = 339.366

Optimal GPV sequence: Template:Val list

Badness: 0.019395

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]]

Mapping generators: ~99/70, ~64/55

POTE generator: ~64/55 = 260.561

Optimal GPV sequence: Template:Val list

Badness: 0.031307

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

Optimal GPV sequence: Template:Val list

Badness: 0.042468

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

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Template:Val list

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.017420

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]]

Mapping generators: ~343/240, ~7/6

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]]

Mapping generators: ~99/70, ~7/6

POTE generator: ~7/6 = 260.393

Optimal GPV sequence: 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]]

Mapping generators: ~55/39, ~7/6

POTE generator: ~7/6 = 260.618

Optimal GPV sequence: 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 -2 -7 -4], ⟨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 -2 -7 -4 -3], ⟨0 10 26 19 18]]

POTE generator: ~9/7 = 430.192

Optimal GPV sequence: 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 -2 -7 -4 -3 -11], ⟨0 10 26 19 18 41]]

POTE generator: ~9/7 = 430.216

Optimal GPV sequence: 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

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

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

Optimal GPV sequence: Template:Val list

Badness: 0.051740

@@ Line 51: / Line 51: @@
 POTE generator: ~128/105 = 339.464
-Vals: {{Val list| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}
+Optimal GPV sequence: {{Val list| 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee }}
 Badness: 0.031506
@@ Line 64: / Line 64: @@
 POTE generator: ~128/105 = 339.481
-Vals: {{Val list| 46ef, 53, 99ef, 152f }} <nowiki>*</nowiki>
+Optimal GPV sequence: {{Val list| 46ef, 53, 99ef, 152f }} <nowiki>*</nowiki>
 <nowiki>*</nowiki> optimal patent val: [[205edo|205]]
@@ Line 79: / Line 79: @@
 POTE generator: ~11/9 = 339.390
-Vals: {{Val list| 7, 39, 46, 53, 99 }}
+Optimal GPV sequence: {{Val list| 7, 39, 46, 53, 99 }}
 Badness: 0.035187
@@ Line 92: / Line 92: @@
 POTE generator: ~11/9 = 339.419
-Vals: {{Val list| 7, 39, 46, 53, 99 }}
+Optimal GPV sequence: {{Val list| 7, 39, 46, 53, 99 }}
 Badness: 0.022448
@@ Line 105: / Line 105: @@
 POTE generator: ~11/9 = 339.366
-Vals: {{Val list| 7, 39, 46, 53, 99 }}
+Optimal GPV sequence: {{Val list| 7, 39, 46, 53, 99 }}
 Badness: 0.019395
@@ Line 120: / Line 120: @@
 POTE generator: ~64/55 = 260.561
-Vals: {{Val list| 14cde, 46, 106, 152, 350, 502d }}
+Optimal GPV sequence: {{Val list| 14cde, 46, 106, 152, 350, 502d }}
 Badness: 0.031307
@@ Line 148: / Line 148: @@
 POTE generator: ~11/9 = 339.047
-Vals: {{Val list| 7d, 39d, 46, 177c, 223bc, 269bce }}
+Optimal GPV sequence: {{Val list| 7d, 39d, 46, 177c, 223bc, 269bce }}
 Badness: 0.042468
@@ Line 178: / Line 178: @@
 POTE generator: ~243/200 = 339.763
-Vals: {{Val list| 53, 113, 166 }}
+Optimal GPV sequence: {{Val list| 53, 113, 166 }}
 Badness: 0.067891
@@ Line 191: / Line 191: @@
 POTE generator: ~39/32 = 339.764
-Vals: {{Val list| 53, 113, 166 }}
+Optimal GPV sequence: {{Val list| 53, 113, 166 }}
 Badness: 0.032996
@@ Line 204: / Line 204: @@
 POTE generator: ~11/9 = 339.814
-Vals: {{Val list| 7d, 46d, 53, 60e, 113e }}
+Optimal GPV sequence: {{Val list| 7d, 46d, 53, 60e, 113e }}
 Badness: 0.045232
@@ Line 217: / Line 217: @@
 POTE generator: ~11/9 = 339.784
-Vals: {{Val list| 7d, 46d, 53, 60e, 113e }}
+Optimal GPV sequence: {{Val list| 7d, 46d, 53, 60e, 113e }}
 Badness: 0.031331
@@ Line 245: / Line 245: @@
 POTE generator: ~243/200 = 339.554
-Vals: {{Val list| 53, 205de, 258, 311, 675, 986 }}
+Optimal GPV sequence: {{Val list| 53, 205de, 258, 311, 675, 986 }}
 Badness: 0.064853
@@ Line 258: / Line 258: @@
 POTE generator: ~243/200 = 339.554
-Vals: {{Val list| 53, 205de, 258, 311, 675, 986, 1661cf }}
+Optimal GPV sequence: {{Val list| 53, 205de, 258, 311, 675, 986, 1661cf }}
 Badness: 0.030347
@@ Line 271: / Line 271: @@
 POTE generator: ~243/200 = 339.555
-Vals: {{Val list| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
+Optimal GPV sequence: {{Val list| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
 Badness: 0.024118
@@ Line 284: / Line 284: @@
 POTE generator: ~208/171 = 339.555
-Vals: {{Val list| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
+Optimal GPV sequence: {{Val list| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
 Badness: 0.017420
@@ Line 318: / Line 318: @@
 POTE generator: ~7/6 = 260.393
-Vals: {{Val list| 14c, 32c, 46, 60e, 106de }}
+Optimal GPV sequence: {{Val list| 14c, 32c, 46, 60e, 106de }}
 Badness: 0.035504
@@ Line 333: / Line 333: @@
 POTE generator: ~7/6 = 260.618
-Vals: {{Val list| 14cf, 32cf, 46, 106def, 152def }}
+Optimal GPV sequence: {{Val list| 14cf, 32cf, 46, 106def, 152def }}
 Badness: 0.030885
@@ Line 363: / Line 363: @@
 POTE generator: ~9/7 = 430.192
-Vals: {{Val list| 14c, 39d, 53 }}
+Optimal GPV sequence: {{Val list| 14c, 39d, 53 }}
 Badness: 0.042947
@@ Line 376: / Line 376: @@
 POTE generator: ~9/7 = 430.216
-Vals: {{Val list| 14cf, 39df, 53 }}
+Optimal GPV sequence: {{Val list| 14cf, 39df, 53 }}
 Badness: 0.029753
@@ Line 406: / Line 406: @@
 POTE generator: ~33/28 = 286.797
-Vals: {{Val list| 46, 113, 159 }}
+Optimal GPV sequence: {{Val list| 46, 113, 159 }}
 Badness: 0.051111
@@ Line 419: / Line 419: @@
 POTE generator: ~13/11 = 286.789
-Vals: {{Val list| 46, 113, 159 }}
+Optimal GPV sequence: {{Val list| 46, 113, 159 }}
 Badness: 0.030297
@@ Line 432: / Line 432: @@
 POTE generator: ~13/11 = 286.795
-Vals: {{Val list| 46, 113, 159 }}
+Optimal GPV sequence: {{Val list| 46, 113, 159 }}
 Badness: 0.022036
@@ Line 462: / Line 462: @@
 POTE generator: ~3200/2673 = 307.906
-Vals: {{Val list| 39d, 74cd, 113, 152, 417, 569de, 721de }}
+Optimal GPV sequence: {{Val list| 39d, 74cd, 113, 152, 417, 569de, 721de }}
 Badness: 0.051740

Amity family: Difference between revisions

Revision as of 13:41, 8 January 2022

Contents

Amity

Extensions

Septimal amity

11-limit

13-limit

Hitchcock

13-limit

17-limit

Hemiamity

Accord

11-limit

Houborizic

11-limit

13-limit

Houbor

13-limit

Paramity

11-limit

13-limit

17-limit

19-limit

Bamity

11-limit

13-limit

Hamity

11-limit

13-limit

Gamity

11-limit

13-limit

17-limit

Familia

11-limit

Navigation menu

Amity family: Difference between revisions

Revision as of 13:41, 8 January 2022

Amity

Extensions

Septimal amity

11-limit

13-limit

Hitchcock

13-limit

17-limit

Hemiamity

Accord

11-limit

Houborizic

11-limit

13-limit

Houbor

13-limit

Paramity

11-limit

13-limit

17-limit

19-limit

Bamity

11-limit

13-limit

Hamity

11-limit

13-limit

Gamity

11-limit

13-limit

17-limit

Familia

11-limit

Navigation menu

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