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 = | == No-elevens subgroup == | ||
== Sensi (aka Sensation) == | === Sensi (aka Sensation) === | ||
<small>''For full 13-limit extensions, see [[Sensipent family]] or [[Sensi extensions]].''</small> | <small>''For full 13-limit extensions, see [[Sensipent family]] or [[Sensi extensions]].''</small> | ||
| Line 24: | Line 24: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.321 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.321 cents | ||
==[[Tertiaseptal]]== | === [[Tertiaseptal]] === | ||
<small>''For full 13- and 17-limit extensions, see [[Breedsmic temperaments #Tertiaseptal]].''</small> | <small>''For full 13- and 17-limit extensions, see [[Breedsmic temperaments #Tertiaseptal]].''</small> | ||
| Line 43: | Line 43: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents | ||
=== 2.3.5.7.13.17 === | ==== 2.3.5.7.13.17 ==== | ||
Subgroup: 2.3.5.7.13.17 | Subgroup: 2.3.5.7.13.17 | ||
| Line 60: | Line 60: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents | ||
= No-sevens subgroup = | == No-sevens subgroup == | ||
== Porkypine == | === Porkypine === | ||
Related temperament: [[Porcupine]] | Related temperament: [[Porcupine]] | ||
| Line 81: | Line 81: | ||
[[Tp tuning #T2 tuning|RMS error]]: 2.287 cents | [[Tp tuning #T2 tuning|RMS error]]: 2.287 cents | ||
== Mohaha == | === Mohaha === | ||
Related temperament: [[mohajira]], [[Meantone family #Migration|migration]] | Related temperament: [[mohajira]], [[Meantone family #Migration|migration]] | ||
| Line 100: | 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]] | ||
== Larry == | === Larry === | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 122: | Line 122: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | ||
== Tetracot == | === Tetracot === | ||
<small>''For full 11- and 13-limit extensions, see [[Tetracot family]].''</small> | <small>''For full 11- and 13-limit extensions, see [[Tetracot family]].''</small> | ||
| Line 141: | Line 141: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.182 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.182 cents | ||
=== 2.3.5.11.13 === | ==== 2.3.5.11.13 ==== | ||
Subgroup: 2.3.5.11.13 | Subgroup: 2.3.5.11.13 | ||
| Line 158: | Line 158: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.140 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.140 cents | ||
== Emka == | === Emka === | ||
<small>''For full 11- and 13-limit extensions, see [[Hemimean clan #Emka]] or [[Horwell temperaments #Emkay]].''</small> | <small>''For full 11- and 13-limit extensions, see [[Hemimean clan #Emka]] or [[Horwell temperaments #Emkay]].''</small> | ||
| Line 177: | Line 177: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1188 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1188 cents | ||
=== 2.3.5.11.13 === | ==== 2.3.5.11.13 ==== | ||
Subgroup: 2.3.5.11.13 | Subgroup: 2.3.5.11.13 | ||
| Line 194: | Line 194: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1250 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1250 cents | ||
= No-fives subgroup = | == No-fives subgroup == | ||
==[[Semaphore and Godzilla|Semaphore]]== | === [[Semaphore and Godzilla|Semaphore]] === | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 213: | Line 213: | ||
[[Tp tuning# T2 tuning|RMS error]]: 2.523 cents | [[Tp tuning# T2 tuning|RMS error]]: 2.523 cents | ||
== Archy == | === Archy === | ||
Archy (properly pronounced "arky", after the Greek theorist Archytas) can be thought of as "no-fives [[dominant]]" or "no-fives [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma. | Archy (properly pronounced "arky", after the Greek theorist Archytas) can be thought of as "no-fives [[dominant]]" or "no-fives [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma. | ||
| Line 232: | Line 232: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.856 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.856 cents | ||
=== Supra === | ==== Supra ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 249: | Line 249: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.977 cents | ||
==== Supraphon ==== | ===== Supraphon ===== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 266: | Line 266: | ||
[[Tp tuning #T2 tuning|RMS error]]: 2.095 cents | [[Tp tuning #T2 tuning|RMS error]]: 2.095 cents | ||
=== Suhajira === | ==== Suhajira ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 283: | Line 283: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.968 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.968 cents | ||
==== 2.3.7.11.13 ==== | ===== 2.3.7.11.13 ===== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 300: | Line 300: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.953 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.953 cents | ||
==[[Slendric]]== | === [[Slendric]] === | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 317: | Line 317: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents | ||
==[[Gamelismic clan #Baladic|Baladic]]== | === [[Gamelismic clan #Baladic|Baladic]] === | ||
Subgroup: 2.3.7.13 | Subgroup: 2.3.7.13 | ||
| Line 332: | Line 332: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.5452 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5452 cents | ||
=== 2.3.7.13.17 === | ==== 2.3.7.13.17 ==== | ||
Subgroup: 2.3.7.13.17 | Subgroup: 2.3.7.13.17 | ||
| Line 347: | Line 347: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents | ||
== Lee == | === Lee === | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 364: | Line 364: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents | ||
== Skwares == | === Skwares === | ||
Related temperament: [[Meantone family #Squares|squares]] | Related temperament: [[Meantone family #Squares|squares]] | ||
| Line 383: | Line 383: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.149 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.149 cents | ||
=== 2.3.7.11 === | ==== 2.3.7.11 ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 400: | Line 400: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.099 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.099 cents | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 417: | Line 417: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.769 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.769 cents | ||
=== Skwairs === | ==== Skwairs ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 434: | Line 434: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.290 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.290 cents | ||
== Bleu == | === Bleu === | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
| Line 451: | Line 451: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.917 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.917 cents | ||
=== 2.3.7.11 === | ==== 2.3.7.11 ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 468: | Line 468: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.829 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.829 cents | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 485: | Line 485: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.752 cents | ||
== Hemif == | === Hemif === | ||
Related temperament: [[Breedsmic temperaments #Hemififths|hemififths]], namo | Related temperament: [[Breedsmic temperaments #Hemififths|hemififths]], namo | ||
| Line 504: | Line 504: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents | ||
=== 2.3.7.11 === | ==== 2.3.7.11 ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 521: | Line 521: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 538: | Line 538: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents | ||
== Ennea == | === Ennea === | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 555: | Line 555: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.0383 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.0383 cents | ||
== Leapfrog == | === Leapfrog === | ||
{{see also|Gentle region}} | {{see also|Gentle region}} | ||
| Line 574: | Line 574: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.6202 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.6202 cents | ||
=== 2.3.7.11 === | ==== 2.3.7.11 ==== | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 591: | Line 591: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.6047 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.6047 cents | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 608: | Line 608: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.7541 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.7541 cents | ||
=== Music === | ==== Music ==== | ||
*Suite for Harpsichord in A Locrian, tuning: Eb-G# in [[46edo]] by [[User:IlL|IlL]] (in progress): | *Suite for Harpsichord in A Locrian, tuning: Eb-G# in [[46edo]] by [[User:IlL|IlL]] (in progress): | ||
**I. Prelude | **I. Prelude | ||
| Line 618: | Line 618: | ||
**[[:File:Locrian Suite Gigue.mp3|VII. Gigue]] | **[[:File:Locrian Suite Gigue.mp3|VII. Gigue]] | ||
== Parapyth (Rank 3) == | === Parapyth (Rank 3) === | ||
Subgroup: 2.3.7.11 | Subgroup: 2.3.7.11 | ||
| Line 635: | Line 635: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.4149 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.4149 cents | ||
=== 2.3.7.11.13 === | ==== 2.3.7.11.13 ==== | ||
Subgroup: 2.3.7.11.13 | Subgroup: 2.3.7.11.13 | ||
| Line 654: | Line 654: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | ||
== Neutral == | === Neutral === | ||
Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]]. | Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]]. | ||
| Line 679: | Line 679: | ||
[[neutraltet17|Seventeen note mega chromatic scale]] | [[neutraltet17|Seventeen note mega chromatic scale]] | ||
=== Namo === | ==== Namo ==== | ||
Subgroup: 2.3.11.13 | Subgroup: 2.3.11.13 | ||
| Line 696: | Line 696: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents | ||
= No-threes subgroup = | == No-threes subgroup == | ||
== Didacus == | === Didacus === | ||
Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]] | Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]] | ||
| Line 717: | Line 717: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2138 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2138 cents | ||
== Llywelyn == | === Llywelyn === | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
| Line 734: | Line 734: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.5391 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5391 cents | ||
== Rainy == | === Rainy === | ||
Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]]. | Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]]. | ||
| Line 753: | Line 753: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.058596 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.058596 cents | ||
= 2.9.7.11 subgroup = | == 2.9.7.11 subgroup == | ||
== Machine == | === Machine === | ||
Subgroup: 2.9.7.11 | Subgroup: 2.9.7.11 | ||
| Line 772: | Line 772: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.977 cents | ||
== Apparatus == | === Apparatus === | ||
Subgroup: 2.9.7.11 | Subgroup: 2.9.7.11 | ||
| Line 789: | Line 789: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents | ||
== Mechanism == | === Mechanism === | ||
Subgroup: 2.9.7.11 | Subgroup: 2.9.7.11 | ||
| Line 806: | Line 806: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents | ||
= 2.9.15.7 subgroup = | == 2.9.15.7 subgroup == | ||
== Stacks (aka 2magic) == | === Stacks (aka 2magic) === | ||
Subgroup: 2.9.15.7 | Subgroup: 2.9.15.7 | ||
| Line 825: | Line 825: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents | ||
=== 2.9.15.7.11 === | ==== 2.9.15.7.11 ==== | ||
Subgroup: 2.9.15.7.11 | Subgroup: 2.9.15.7.11 | ||
| Line 842: | Line 842: | ||
RMS error: 1.226 cents | RMS error: 1.226 cents | ||
=== 2.9.15.7.11.13 === | ==== 2.9.15.7.11.13 ==== | ||
Subgroup: 2.9.15.7.11.13 | Subgroup: 2.9.15.7.11.13 | ||
| Line 859: | Line 859: | ||
RMS error: 1.540 cents | RMS error: 1.540 cents | ||
= 2.9.21 subgroup = | == 2.9.21 subgroup == | ||
== A-team == | === A-team === | ||
Subgroup: 2.9.21 | Subgroup: 2.9.21 | ||
| Line 878: | Line 878: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents | ||
= Miscellaneous subgroup temperaments = | == Miscellaneous subgroup temperaments == | ||
== Historical == | === Historical === | ||
Subgroup: 2.3.7/5.11/5.13/5 | Subgroup: 2.3.7/5.11/5.13/5 | ||
| Line 893: | Line 893: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents | ||
== Hypnosis == | === Hypnosis === | ||
Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]] | Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]] | ||