Subgroup temperaments: Difference between revisions
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Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. | Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. | ||
= No-elevens subgroup = | |||
== Sensi (aka Sensation) == | |||
<small>''For full 13-limit extensions, see [[Sensipent family]] or [[Sensi extensions]].''</small> | |||
Subgroup: 2.3.5.7.13 | |||
[[Comma list]]: 91/90, 126/125, 169/168 | |||
[[Gencom]]: [2 9/7; 91/90 126/125 169/168] | |||
[[Gencom|Gencom mapping]]: [{{val|1 6 8 11 0 10}}, {{val|0 -7 -9 -13 0 -10}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 6 8 11 10}}, {{val|0 -7 -9 -13 -10}}] | |||
[[Tp tuning|POL2 generator]]: ~9/7 = 443.322 | |||
{{Val list|legend=1| 19, 27, 46, 111de, 157de }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 1.321 cents | |||
==[[Tertiaseptal]]== | |||
<small>''For full 13- and 17-limit extensions, see [[Breedsmic temperaments #Tertiaseptal]].''</small> | |||
Subgroup: 2.3.5.7.13 | |||
[[Comma list]]: 625/624, 2401/2400, 4096/4095 | |||
[[Gencom]]: [2 117/112; 625/624 2401/2400 4096/4095] | |||
[[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1}}, {{val|0 -22 5 -3 0 42}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 3 2 3 1}}, {{val|0 -22 5 -3 42}}] | |||
[[Tp tuning|POL2 generator]]: ~117/112 = 77.173 | |||
{{Val list|legend=1| 31, 109, 140, 171, 311 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents | |||
=== 2.3.5.7.13.17 === | |||
Subgroup: 2.3.5.7.13.17 | |||
[[Comma list]]: 625/624, 833/832, 1225/1224, 4096/4095 | |||
[[Gencom]]: [2 68/65; 625/624 833/832 1225/1224 4096/4095] | |||
[[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1 1}}, {{val|0 -22 5 -3 0 42 48}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 3 2 3 1 1}}, {{val|0 -22 5 -3 42 48}}] | |||
[[Tp tuning|POL2 generator]]: ~68/65 = 77.177 | |||
{{Val list|legend=1| 31, 109f, 140, 171, 311 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents | |||
= No-sevens subgroup = | = No-sevens subgroup = | ||
== Porkypine == | == Porkypine == | ||
Related temperament: [[Porcupine]] | |||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 23: | Line 82: | ||
== Mohaha == | == Mohaha == | ||
Related temperament: [[mohajira]], [[Meantone family #Migration|migration]] | |||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 39: | Line 100: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.392 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.392 cents | ||
===Music=== | === Music === | ||
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy Stiltner]] | [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy Stiltner]] | ||
| Line 60: | Line 121: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | ||
== Tetracot == | |||
<small>''For full 11- and 13-limit extensions, see [[Tetracot family]].''</small> | |||
Subgroup: 2.3.5.11 | |||
[[Comma list]]: 100/99, 243/242 | |||
[[Gencom]]: [2 10/9; 100/99 243/242] | |||
[[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2}}, {{val|0 4 9 0 10}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 1 1 2}}, {{val|0 4 9 10}}] | |||
[[Tp tuning|POL2 generator]]: ~10/9 = 175.985 | |||
{{Val list|legend=1| 7, 27d, 34, 41, 75d }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 1.182 cents | |||
=== 2.3.5.11.13 === | |||
Subgroup: 2.3.5.11.13 | |||
[[Comma list]]: 100/99, 144/143, 243/242 | |||
[[Gencom]]: [2 10/9; 100/99 243/242] | |||
[[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2 4}}, {{val|0 4 9 0 10 -2}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 1 1 2 4}}, {{val|0 4 9 10 -2}}] | |||
[[Tp tuning|POL2 generator]]: ~10/9 = 176.196 | |||
{{Val list|legend=1| 7, 27d, 34, 41, 75d }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 1.140 cents | |||
= No-fives subgroup = | = No-fives subgroup = | ||
| Line 202: | Line 299: | ||
== Skwares == | == Skwares == | ||
Related temperament: [[Meantone family #Squares|squares]] | |||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 534: | Line 633: | ||
== Didacus == | == Didacus == | ||
Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]] | |||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
[[Comma]]: 3136/3125 | [[Comma]]: 3136/3125 | ||
[[Gencom]]: [2 28/25; 3136/3125] | [[Gencom]]: [2 28/25; 3136/3125] | ||
| Line 729: | Line 828: | ||
== Hypnosis == | == Hypnosis == | ||
Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]] | |||
Subgroup: 2.3.7.11/5.13 | Subgroup: 2.3.7.11/5.13 | ||
[[Comma list]]: 169/168, 540/539, 729/728 | [[Comma list]]: 169/168, 540/539, 729/728 | ||
[[Mapping|Sval mapping]]: [{{val|1 0 -3 8 0}}, {{val|0 3 11 -13 7}}] | [[Mapping|Sval mapping]]: [{{val|1 0 -3 8 0}}, {{val|0 3 11 -13 7}}] | ||