Breedsmic temperaments: Difference between revisions

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== Decoid ==

Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used its generator. It may be described as the 130&270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[~~Qintosec family|qintosec temperament~~]].

Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used its generator. It may be described as the 130 & 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[quintosec]] temperament.

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 2401/2400, 67108864/66976875

~~[[Mapping]]: [~~{{~~val~~| 10 0 47 36 ~~}}, {{val~~| 0 2 -3 -1 }}]

~~Mapping~~ generators: ~15/14, ~8192/4725

: mapping generators: ~15/14, ~8192/4725

[[POTE ~~generator~~]]: ~16/15 = 111.099

[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)

{{Optimal ET sequence|legend=1| 10, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}

{{Optimal ET sequence|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}

[[Badness]]: 0.033902

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Comma list: 2401/2400, 5632/5625, 9801/9800

Mapping: [{{~~val~~| 10 0 47 36 98 ~~}}, {{val~~| 0 2 -3 -1 -8 }}]

Mapping: {{mapping| 10 0 47 36 98 | 0 2 -3 -1 -8 }}

POTE ~~generator~~: ~16/15 = 111.070

Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)

{{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}

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Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

Mapping: [{{~~val~~| 10 0 47 36 98 37 ~~}}, {{val~~| 0 2 -3 -1 -8 0 }}]

Mapping: {{mapping| 10 0 47 36 98 37 | 0 2 -3 -1 -8 0 }}

POTE ~~generator~~: ~16/15 = 111.083

Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)

{{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}

@@ Line 443: / Line 443: @@
 == Decoid ==
-{{see also| Qintosec family #Decoid }}
+{{See also| Quintosec family #Decoid }}
-Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used its generator. It may be described as the 130&amp;270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[Qintosec family|qintosec temperament]].
+Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[15/14 equal-step tuning|linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used its generator. It may be described as the 130 &amp; 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[quintosec]] temperament.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 2401/2400, 67108864/66976875
-[[Mapping]]: [{{val| 10 0 47 36 }}, {{val| 0 2 -3 -1 }}]
+{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}
-Mapping generators: ~15/14, ~8192/4725
+: mapping generators: ~15/14, ~8192/4725
 {{Multival|legend=1| 20 -30 -10 -94 -72 61 }}
-[[POTE generator]]: ~16/15 = 111.099
+[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)
-{{Optimal ET sequence|legend=1| 10, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
+{{Optimal ET sequence|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
 [[Badness]]: 0.033902
@@ Line 468: / Line 468: @@
 Comma list: 2401/2400, 5632/5625, 9801/9800
-Mapping: [{{val| 10 0 47 36 98 }}, {{val| 0 2 -3 -1 -8 }}]
+Mapping: {{mapping| 10 0 47 36 98 | 0 2 -3 -1 -8 }}
-POTE generator: ~16/15 = 111.070
+Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)
 {{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}
@@ Line 481: / Line 481: @@
 Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
-Mapping: [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0 }}]
+Mapping: {{mapping| 10 0 47 36 98 37 | 0 2 -3 -1 -8 0 }}
-POTE generator: ~16/15 = 111.083
+Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)
 {{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}