Canousmic temperaments: Difference between revisions

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== Superlimmal ==

The superlimmal temperament (80 & 311) uses an ever slightly sharpened [[27/25|large limma]] as the generator, nine exceed the octave by [[126/125]]. It gets all the primes up to 29 reasonably covered, but still acceptible just as a 13-limit microtemperament, judging from its [[comma basis]]. ~~The 80-tone~~ [[MOS scale]] is presumably the place to start~~, and a 151-tone MOS~~ is ~~possible~~. It can also be extended to prime 37 by tempering out ([[27/25]])/([[40/37]]) = [[1000/999]], where 40/37 is notably the mediant of [[27/25]] and [[13/12]], which could be interpreted as an explanation of the sharpened limma.

The superlimmal temperament (80 & 311) uses an ever slightly sharpened [[27/25|large limma]] as the generator, nine exceed the octave by [[126/125]]. It gets all the primes up to 29 reasonably covered, but still acceptible just as a 13-limit microtemperament, judging from its [[comma basis]]. While the [[MOS scale]] may not be the most effective approach, the 80-tone MOS is presumably the place to start if it is used. It can also be extended to prime 37 by tempering out ([[27/25]])/([[40/37]]) = [[1000/999]], where 40/37 is notably the mediant of [[27/25]] and [[13/12]], which could be interpreted as an explanation of the sharpened limma.

Subgroup: 2.3.5.7

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Subgroup: 2.3.5.7.11.13.17.19.23.29.37

Comma list: 595/594, 760/759, 784/783, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274~~, 1480/1479~~

Comma list: 595/594, 760/759, 784/783, 925/924, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274

Mapping:

Mapping: [{{val| 1 8 12 18 11 1 6 11 7 16 15 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 -99 -87 }}]

[{{val| 1 8 12 18 11 1 6 11 7 16 15 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 -99 -87 }}]

POTE generator: ~27/25 = 135.0460

Vals: {{val list| 80, 311 }}

Vals: {{val list| 80, 231, 311 }}

Badness: ?

Badness: 0.010901

[[Category:Regular temperament theory]]

@@ Line 99: / Line 99: @@
 == Superlimmal ==
-The superlimmal temperament (80 &amp; 311) uses an ever slightly sharpened [[27/25|large limma]] as the generator, nine exceed the octave by [[126/125]]. It gets all the primes up to 29 reasonably covered, but still acceptible just as a 13-limit microtemperament, judging from its [[comma basis]]. The 80-tone [[MOS scale]] is presumably the place to start, and a 151-tone MOS is possible. It can also be extended to prime 37 by tempering out ([[27/25]])/([[40/37]]) = [[1000/999]], where 40/37 is notably the mediant of [[27/25]] and [[13/12]], which could be interpreted as an explanation of the sharpened limma.
+The superlimmal temperament (80 &amp; 311) uses an ever slightly sharpened [[27/25|large limma]] as the generator, nine exceed the octave by [[126/125]]. It gets all the primes up to 29 reasonably covered, but still acceptible just as a 13-limit microtemperament, judging from its [[comma basis]]. While the [[MOS scale]] may not be the most effective approach, the 80-tone MOS is presumably the place to start if it is used. It can also be extended to prime 37 by tempering out ([[27/25]])/([[40/37]]) = [[1000/999]], where 40/37 is notably the mediant of [[27/25]] and [[13/12]], which could be interpreted as an explanation of the sharpened limma.
 Subgroup: 2.3.5.7
@@ Line 196: / Line 196: @@
 Subgroup: 2.3.5.7.11.13.17.19.23.29.37
-Comma list: 595/594, 760/759, 784/783, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274, 1480/1479
+Comma list: 595/594, 760/759, 784/783, 925/924, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274
-Mapping:
+Mapping: [{{val| 1 8 12 18 11 1 6 11 7 16 15 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 -99 -87 }}]
-[{{val| 1 8 12 18 11 1 6 11 7 16 15 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 -99 -87 }}]
 POTE generator: ~27/25 = 135.0460
-Vals: {{val list| 80, 311 }}
+Vals: {{val list| 80, 231, 311 }}
-Badness: ?
+Badness: 0.010901
 [[Category:Regular temperament theory]]