Porcupine family: Difference between revisions

Line 65:

Optimal tunings:

* WE: ~2 = 1200.3290{{c}}, ~10/9 = 164.1227{{c}}

* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~10/9 = 163.9951{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}

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Tuning ranges:

* 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)

* 13-odd-limit diamond monotone: ~11/10 = [160.000, 162.162] (2\15 to 5\37)

* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)

* 15-odd-limit diamond monotone: ~11/10 = 162.162 (5\37)

* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]

* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]

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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. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid ~~omega~~-tricot.

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. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid alpha-tricot.

22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) 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. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo.

@@ Line 65: / Line 65: @@
 Optimal tunings:
-* WE: ~2 = 1200.3290{{c}}, ~10/9 = 164.1227{{c}}
+* WE: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~10/9 = 163.9951{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}
 {{Optimal ET sequence|legend=0| 7, 15, 22, 73ce, 95ce }}
@@ Line 188: / Line 188: @@
 Tuning ranges:
-* 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)
+* 13-odd-limit diamond monotone: ~11/10 = [160.000, 162.162] (2\15 to 5\37)
-* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
+* 15-odd-limit diamond monotone: ~11/10 = 162.162 (5\37)
-* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
+* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
 {{Optimal ET sequence|legend=0| 15, 22, 37 }}
@@ Line 456: / Line 456: @@
 {{See also| Sensamagic clan | Stearnsmic clan }}
-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. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid omega-tricot.
+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. It is a strong extension of [[BPS]] (as BPS has no 2 or sqrt(2)). Its ploidacot is diploid alpha-tricot.
 edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) 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. A related temperament is [[echidna]], which offers much more accuracy. They merge on 22edo.