Meantone family: Difference between revisions

Cleanup for recent additions
m Fix a link (and remove the excessive)
Line 1,238: Line 1,238:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 50/49, 81/80, 864/847
Comma list: 50/49, 81/80, 864/847


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


Mapping generators: ~7/5, ~16/11
Mapping generators: ~7/5, ~16/11


[[POTE generator]]: ~11/8 = 552.5303
POTE generator: ~11/8 = 552.5303


{{Val list|legend=1| 24d, 26, 50d }}
Vals: {{Val list| 24d, 26, 50d }}


[[Badness]]: 0.0707
Badness: 0.0707


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 50/49, 78/77, 81/80, 144/143
Comma list: 50/49, 78/77, 81/80, 144/143


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


[[POTE generator]]: ~11/8 = 552.5324
POTE generator: ~11/8 = 552.5324


{{Val list|legend=1| 24d, 26, 50d }}
Vals: {{Val list| 24d, 26, 50d }}


[[Badness]]: 0.0400
Badness: 0.0400


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


[[Comma list]]: 50/49, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 78/77, 81/80, 85/84, 144/143


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


[[POTE generator]]: ~11/8 = 552.6558
POTE generator: ~11/8 = 552.6558


{{Val list|legend=1| 24d, 26 }}
Vals: {{Val list| 24d, 26 }}


[[Badness]]: 0.0295
Badness: 0.0295


==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


[[Comma list]]: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143
Comma list: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143


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


[[POTE generator]]: ~11/8 = 552.6382
POTE generator: ~11/8 = 552.6382


{{Val list|legend=1| 24d, 26 }}
Vals: {{Val list| 24d, 26 }}


[[Badness]]: 0.0231
Badness: 0.0231


== Pombe ==
== Pombe ==
Pombe (named after the African millet beer) is a variant of [[#teff]] by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall.
Pombe (named after the African millet beer) is a variant of [[#Teff]] by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13