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Porcupine family: Difference between revisions

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m Cleanup (1/3)
m Cleanup (2/3)
Line 11: Line 11:
[[Comma list]]: 250/243
[[Comma list]]: 250/243


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


[[POTE generator]]: ~27/25 = 163.950
[[POTE generator]]: ~27/25 = 163.950
Line 38: Line 38:
[[Comma list]]: 64/63, 250/243
[[Comma list]]: 64/63, 250/243


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


{{Multival|legend=1| 3 5 -6 1 -18 -28 }}
{{Multival|legend=1| 3 5 -6 1 -18 -28 }}
Line 59: Line 59:
Comma list: 55/54, 64/63, 100/99
Comma list: 55/54, 64/63, 100/99


Mapping: [<1 2 3 2 4|, <0 -3 -5 6 -4|]
Mapping: [{{val| 1 2 3 2 4 }}, {{val| 0 -3 -5 6 -4 }}]


POTE generator: ~11/10 = 162.747
POTE generator: ~11/10 = 162.747
Line 78: Line 78:
Comma list: 40/39, 55/54, 64/63, 66/65
Comma list: 40/39, 55/54, 64/63, 66/65


Mapping: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]
Mapping: [{{val| 1 2 3 2 4 4 }}, {{val| 0 -3 -5 6 -4 -2 }}]


POTE generator: ~10/9 = 162.708
POTE generator: ~10/9 = 162.708
Line 99: Line 99:
Comma list: 55/54, 64/63, 91/90, 100/99
Comma list: 55/54, 64/63, 91/90, 100/99


Mapping: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]
Mapping: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]


POTE generator: ~10/9 = 162.277
POTE generator: ~10/9 = 162.277
Line 118: Line 118:
Comma list: 55/54, 64/63, 100/99, 196/195
Comma list: 55/54, 64/63, 100/99, 196/195


Mapping: [<1 2 3 2 4 1|, <0 -3 -5 6 -4 20|]
Mapping: [{{val| 1 2 3 2 4 1 }}, {{val| 0 -3 -5 6 -4 20 }}]


POTE generator: ~10/9 = 162.482
POTE generator: ~10/9 = 162.482
Line 132: Line 132:
Comma list: 55/54, 64/63, 65/63, 100/99
Comma list: 55/54, 64/63, 65/63, 100/99


Mapping: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]
Mapping: [{{val| 1 2 3 2 4 3 }}, {{val| 0 -3 -5 6 -4 5 }}]


POTE generator: ~10/9 = 163.688
POTE generator: ~10/9 = 163.688
Line 144: Line 144:


= Hystrix =
= Hystrix =
Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
Hystrix provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.


[[Comma list]]: 36/35, 160/147
[[Comma list]]: 36/35, 160/147


[[Mapping]]: [<1 2 3 3|, <0 -3 -5 -1|]
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -1 }}]
 
{{Multival|legend=1| 3 5 1 1 -7 -12 }}


[[POTE generator]]: ~8/7 = 158.868
[[POTE generator]]: ~8/7 = 158.868
Line 162: Line 164:
Comma list: 22/21, 36/35, 80/77
Comma list: 22/21, 36/35, 80/77


Mapping: [<1 2 3 3 4|, <0 -3 -5 -1 -4|]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]


POTE generator: ~8/7 = 158.750
POTE generator: ~8/7 = 158.750
Line 173: Line 175:
[[Comma list]]: 225/224, 250/243
[[Comma list]]: 225/224, 250/243


[[Mapping]]: [<1 2 3 5|, <0 -3 -5 -16|]
[[Mapping]]: [{{val| 1 2 3 5 }}, {{val| 0 -3 -5 -16 }}]


Wedgie: <<3 5 16 1 17 23||
{{Multival|legend=1| 3 5 16 1 17 23 }}


[[POTE generator]]: ~10/9 = 164.412
[[POTE generator]]: ~10/9 = 164.412
Line 189: Line 191:
Comma list: 55/54, 100/99, 225/224
Comma list: 55/54, 100/99, 225/224


Mapping: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]
Mapping: [{{val| 1 2 3 5 4 }}, {{val| 0 -3 -5 -16 -4 }}]


POTE generator: ~10/9 = 164.552
POTE generator: ~10/9 = 164.552
Line 203: Line 205:
Comma list: 55/54, 65/64, 91/90, 100/99
Comma list: 55/54, 65/64, 91/90, 100/99


Mapping: [<1 2 3 5 4 3|, <0 -3 -5 -16 -4 5|]
Mapping: [{{val| 1 2 3 5 4 3 }}, {{val| 0 -3 -5 -16 -4 5 }}]


POTE generator: ~10/9 = 164.953
POTE generator: ~10/9 = 164.953
Line 214: Line 216:
[[Comma list]]: 250/243, 525/512
[[Comma list]]: 250/243, 525/512


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


Wedgie: <<3 5 -13 1 -29 -44||
{{Multival|legend=1| 3 5 -13 1 -29 -44 }}


[[POTE generator]]: ~10/9 = 166.041
[[POTE generator]]: ~10/9 = 166.041
Line 230: Line 232:
Comma list: 55/54, 100/99, 525/512
Comma list: 55/54, 100/99, 525/512


Mapping: [<1 2 3 1 4|, <0 -3 -5 13 -4|]
Mapping: [{{val| 1 2 3 1 4 }}, {{val| 0 -3 -5 13 -4 }}]


POTE generator: ~10/9 = 165.981
POTE generator: ~10/9 = 165.981
Line 244: Line 246:
Comma list: 55/54, 65/64, 100/99, 105/104
Comma list: 55/54, 65/64, 100/99, 105/104


Mapping: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|]
Mapping: [{{val| 1 2 3 1 4 3 }}, {{val| 0 -3 -5 13 -4 5 }}]


POTE generator: ~10/9 = 165.974
POTE generator: ~10/9 = 165.974
Line 256: Line 258:


= Hedgehog =
= Hedgehog =
Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.
Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out [[245/243]], the sensamagic comma. 22edo provides the obvious tuning, but if you are looking for an alternative, you could try the {{val| 146 232 338 411 }} val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.


[[Comma list]]: 50/49, 245/243
[[Comma list]]: 50/49, 245/243


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


Wedgie: <<6 10 10 2 -1 -5||
{{Multival|legend=1| 6 10 10 2 -1 -5 }}


[[POTE generator]]: ~9/7 = 435.648
[[POTE generator]]: ~9/7 = 435.648
Line 273: Line 275:
Comma list: 50/49, 55/54, 99/98
Comma list: 50/49, 55/54, 99/98


Mapping: [<2 1 1 2 4|, <0 3 5 5 4|]
Mapping: [{{val| 2 1 1 2 4 }}, {{val| 0 3 5 5 4 }}]


POTE generator: ~9/7 = 435.386
POTE generator: ~9/7 = 435.386
Line 284: Line 286:
Comma list: 50/49, 55/54, 65/63, 99/98
Comma list: 50/49, 55/54, 65/63, 99/98


Mapping: [<2 1 1 2 4 3|, <0 3 5 5 4 6|]
Mapping: [{{val| 2 1 1 2 4 3 }}, {{val| 0 3 5 5 4 6 }}]


POTE generator: ~9/7 = 435.861
POTE generator: ~9/7 = 435.861
Line 295: Line 297:
Comma list: 40/39, 50/49, 55/54, 66/65
Comma list: 40/39, 50/49, 55/54, 66/65


Mapping: [<2 1 1 2 4 6|, <0 3 5 5 4 2|]
Mapping: [{{val| 2 1 1 2 4 6 }}, {{val| 0 3 5 5 4 2 }}]


POTE generator: ~9/7 = 437.078
POTE generator: ~9/7 = 437.078
Line 306: Line 308:
Comma list: 50/49, 245/243, 385/384
Comma list: 50/49, 245/243, 385/384


Mapping: [<2 1 1 2 12|, <0 3 5 5 -7|]
Mapping: [{{val| 2 1 1 2 12 }}, {{val| 0 3 5 5 -7 }}]


POTE generator: ~9/7 = 435.425
POTE generator: ~9/7 = 435.425
Line 320: Line 322:
[[Comma list]]: 49/48, 250/243
[[Comma list]]: 49/48, 250/243


[[Mapping]]: [<1 2 3 3|, <0 -6 -10 -3|]
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -6 -10 -3 }}]


Wedgie: <<6 10 3 2 -12 -21||
{{Multival|legend=1| 6 10 3 2 -12 -21 }}


[[POTE generator]]: ~21/20 = 82.505
[[POTE generator]]: ~21/20 = 82.505
Line 331: Line 333:
Comma list: 49/48, 55/54, 245/242
Comma list: 49/48, 55/54, 245/242


Mapping: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -6 -10 -3 -8 }}]


POTE generator: ~21/20 = 82.504
POTE generator: ~21/20 = 82.504
Line 340: Line 342:
Comma list: 49/48, 55/54, 91/90, 100/99
Comma list: 49/48, 55/54, 91/90, 100/99


Mapping: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]
Mapping: [{{val| 1 2 3 3 4 5 }}, {{val| 0 -6 -10 -3 -8 -19 }}]


POTE generator: ~21/20 = 62.530
POTE generator: ~21/20 = 62.530
Line 351: Line 353:
Comma list: 40/39, 49/48, 55/54, 66/65
Comma list: 40/39, 49/48, 55/54, 66/65


Mapping: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -6 -10 -3 -8 -4 }}]


POTE generator: ~21/20 = ~14/13 = 81.759
POTE generator: ~21/20 = ~14/13 = 81.759
Line 365: Line 367:
Comma list: 250/243, 686/675
Comma list: 250/243, 686/675


Mapping: [<1 5 8 10|, <0 -9 -15 -19|]
Mapping: [{{val| 1 5 8 10 }}, {{val| 0 -9 -15 -19 }}]


Wedgie: <<9 15 19 3 5 2||
{{Multival|legend=1| 9 15 19 3 5 2 }}


POTE generator: ~9/7 = 454.448
POTE generator: ~9/7 = 454.448
Line 378: Line 380:
Comma list: 55/54, 100/99, 686/675
Comma list: 55/54, 100/99, 686/675


Mapping: [<1 5 8 10 8|, <0 -9 -15 -19 -12|]
Mapping: [{{val| 1 5 8 10 8 }}, {{val| 0 -9 -15 -19 -12 }}]


POTE generator: ~9/7 = 454.512
POTE generator: ~9/7 = 454.512
Line 389: Line 391:
Comma list: 55/54, 91/90, 100/99, 169/168
Comma list: 55/54, 91/90, 100/99, 169/168


Mapping: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|]
Mapping: [{{val| 1 5 8 10 8 9 }}, {{val| 0 -9 -15 -19 -12 -14 }}]


POTE generator: ~13/10 = 454.429
POTE generator: ~13/10 = 454.429
Line 400: Line 402:
[[Comma list]]: 250/243, 1728/1715
[[Comma list]]: 250/243, 1728/1715


[[Mapping]]: [<1 2 3 3|, <0 -9 -15 -4|]
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -9 -15 -4 }}]


Wedgie: <<9 15 4 3 -19 -33||
{{Multival|legend=1| 9 15 4 3 -19 -33 }}


[[POTE generator]]: ~36/35 = 54.384
[[POTE generator]]: ~36/35 = 54.384
Line 413: Line 415:
Comma list: 55/54, 100/99, 5324/5145
Comma list: 55/54, 100/99, 5324/5145


Mapping: [<1 2 3 3 4|, <0 -9 -15 -4 -12|]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -9 -15 -4 -12 }}]


POTE generator: ~36/35 = 54.376
POTE generator: ~36/35 = 54.376
Line 424: Line 426:
Comma list: 55/54, 65/63, 100/99, 352/343
Comma list: 55/54, 65/63, 100/99, 352/343


Mapping: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -9 -15 -4 -12 -7 }}]


POTE generator: ~36/35 = 54.665
POTE generator: ~36/35 = 54.665
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