No-sevens subgroup temperaments: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 7. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 7. | ||
== Mavila == | |||
Subgroup: 2.3.5.11 | |||
[[Comma list]]: 33/32, 45/44 | |||
[[Gencom]]: [2 4/3; 33/32, 45/44] | |||
[[Gencom|Gencom mapping]]: [{{val|1 2 1 0 3}}, {{val|0 -1 3 0 1}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 2 1 3}}, {{val|0 -1 3 1}}] | |||
[[Tp tuning|POL2 generator]]: ~4/3 = 520.212 | |||
{{Val list|legend=1| 7, 16, 23e, 30bce }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 4.705 cents | |||
Related temperaments: [[Pelogic family #Mavila|mavila]], [[Pelogic family #Pelogic|pelogic]], [[Pelogic family #Armodue|armodue]] | |||
== Porkypine == | == Porkypine == | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 16: | Line 33: | ||
[[Tp tuning|POL2 generator]]: ~11/10 = 164.078 | [[Tp tuning|POL2 generator]]: ~11/10 = 164.078 | ||
{{Val list|legend=1| 7, 15, 22, 37, | {{Val list|legend=1| 7, 15, 22, 37, 73ce, 95ce, 117bce }} | ||
[[Tp tuning #T2 tuning|RMS error]]: 2.287 cents | [[Tp tuning #T2 tuning|RMS error]]: 2.287 cents | ||
Related temperament: [[Porcupine]] | |||
== Mohaha == | == Mohaha == | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 35: | Line 52: | ||
[[Tp tuning|POL2 generator]]: ~11/9 = 348.094 | [[Tp tuning|POL2 generator]]: ~11/9 = 348.094 | ||
{{Val list|legend=1| 7, 10, 17, 24, 31, 55, | {{Val list|legend=1| 7, 10, 17, 24, 31, 55, 69e, 100e, 131be }} | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.392 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.392 cents | ||
Related temperament: [[mohajira]], [[Meantone family #Migration|migration]] | |||
; Music | ; Music | ||
| Line 57: | Line 76: | ||
[[Tp tuning|POL2 generator]]: ~10/9 = 175.985 | [[Tp tuning|POL2 generator]]: ~10/9 = 175.985 | ||
{{Val list|legend=1| 7, | {{Val list|legend=1| 7, 27e, 34, 41, 75e }} | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.182 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.182 cents | ||
Related temperaments: [[Tetracot family #Monkey|monkey]], [[Tetracot family #Bunya|bunya]], [[Tetracot family #Modus|modus]], [[Tetracot family #Wollemia|wollemia]] | |||
=== 2.3.5.11.13 === | === 2.3.5.11.13 === | ||
| Line 74: | Line 95: | ||
[[Tp tuning|POL2 generator]]: ~10/9 = 176.196 | [[Tp tuning|POL2 generator]]: ~10/9 = 176.196 | ||
{{Val list|legend=1| 7, | {{Val list|legend=1| 7, 27e, 34, 41, 75e }} | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.140 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.140 cents | ||
| Line 82: | Line 103: | ||
[[Comma list]]: 243/242, 4000/3993 | [[Comma list]]: 243/242, 4000/3993 | ||
[[Gencom]]: [2 40/27; 243/242 4000/3993] | [[Gencom]]: [2 40/27; 243/242 4000/3993] | ||
| Line 96: | Line 115: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents | ||
Related temperaments: [[Gravity family|gravity]], [[Gravity family #Harry|harry]] | |||
== Twentcufo == | == Twentcufo == | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
| Line 115: | Line 134: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2393 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2393 cents | ||
Related temperament: [[Hemimean clan #Undetrita|undetrita]] | |||
== Emka == | == Emka == | ||
| Line 189: | Line 210: | ||
== Photia == | == Photia == | ||
Subgroup: 2.3.5.17 | Subgroup: 2.3.5.17 | ||
| Line 206: | Line 225: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.4842 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.4842 cents | ||
Related temperament: [[Schismatic family|Schismic]] | |||
=== 2.3.5.17.19 === | === 2.3.5.17.19 === | ||
| Line 333: | Line 354: | ||
== Nestoria == | == Nestoria == | ||
Subgroup: 2.3.5.19 | Subgroup: 2.3.5.19 | ||
| Line 350: | Line 369: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1763 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1763 cents | ||
Related temperament: [[Schismatic family|Schismic]] | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 11:07, 22 January 2022
This is a collection of subgroup temperaments which omit the prime harmonic of 7.
Mavila
Subgroup: 2.3.5.11
Comma list: 33/32, 45/44
Gencom: [2 4/3; 33/32, 45/44]
Gencom mapping: [⟨1 2 1 0 3], ⟨0 -1 3 0 1]]
Sval mapping: [⟨1 2 1 3], ⟨0 -1 3 1]]
POL2 generator: ~4/3 = 520.212
RMS error: 4.705 cents
Related temperaments: mavila, pelogic, armodue
Porkypine
Subgroup: 2.3.5.11
Comma list: 55/54, 100/99
Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [⟨1 2 3 0 4], ⟨0 -3 -5 0 -4]]
Sval mapping: [⟨1 2 3 4], ⟨0 -3 -5 -4]]
POL2 generator: ~11/10 = 164.078
RMS error: 2.287 cents
Related temperament: Porcupine
Mohaha
Subgroup: 2.3.5.11
Comma list: 81/80, 121/120
Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 8 0 5]]
Sval mapping: [⟨1 1 0 2], ⟨0 2 8 5]]
POL2 generator: ~11/9 = 348.094
RMS error: 1.392 cents
Related temperament: mohajira, migration
- Music
Mohaha10ping2 by Billy Stiltner
Tetracot
- For full 11- and 13-limit extensions, see Tetracot family.
Subgroup: 2.3.5.11
Comma list: 100/99, 243/242
Gencom: [2 10/9; 100/99 243/242]
Gencom mapping: [⟨1 1 1 0 2], ⟨0 4 9 0 10]]
Sval mapping: [⟨1 1 1 2], ⟨0 4 9 10]]
POL2 generator: ~10/9 = 175.985
RMS error: 1.182 cents
Related temperaments: monkey, bunya, modus, wollemia
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 mapping: [⟨1 1 1 0 2 4], ⟨0 4 9 0 10 -2]]
Sval mapping: [⟨1 1 1 2 4], ⟨0 4 9 10 -2]]
POL2 generator: ~10/9 = 176.196
RMS error: 1.140 cents
Larry
Subgroup: 2.3.5.11
Comma list: 243/242, 4000/3993
Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [⟨1 5 12 0 12], ⟨0 -6 -17 0 -15]]
Sval mapping: [⟨1 5 12 12], ⟨0 -6 -17 -15]]
POL2 generator: ~40/27 = 683.166
RMS error: 0.3025 cents
Related temperaments: gravity, harry
Twentcufo
Subgroup: 2.3.5.11
Comma list: 8019/8000, 14641/14580
Gencom: [2 400/363; 8019/8000 14641/14580]
Gencom mapping: [⟨1 0 -2 0 0], ⟨0 11 30 0 24]]
Sval mapping: [⟨1 0 -2 0], ⟨0 11 30 24]]
POL2 generator: ~400/363 = 172.8796
RMS error: 0.2393 cents
Related temperament: undetrita
Emka
- For full 11- and 13-limit extensions, see Hemimean clan #Emka or Horwell temperaments #Emkay.
Subgroup: 2.3.5.11
Comma list: 4000/3993, 9453125/9437184
Gencom: [2 11/8; 4000/3993 9453125/9437184]
Gencom mapping: [⟨1 14 6 0 3], ⟨0 -27 -8 0 1]]
Sval mapping: [⟨1 14 6 3], ⟨0 -27 -8 1]]
POL2 generator: ~11/8 = 551.7778
RMS error: 0.1188 cents
2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 625/624, 2200/2197, 4000/3993
Gencom: [2 11/8; 625/624 2200/2197 4000/3993]
Gencom mapping: [⟨1 14 6 0 3 6], ⟨0 -27 -8 0 1 -5]]
Sval mapping: [⟨1 14 6 3 6], ⟨0 -27 -8 1 -5]]
POL2 generator: ~11/8 = 551.7753
RMS error: 0.1250 cents
Majvam
- For full 13- and 17-limit extensions, see Parkleiness temperaments #Majvamic or Cataharry temperaments #Majvamoid.
Subgroup: 2.3.5.13
Comma list: 676/675, 127401984/126953125
Gencom: [2 125/96; 676/675 127401984/126953125]
Gencom mapping: [⟨1 10 5 0 0 19], ⟨0 -22 -7 0 0 -40]]
Sval mapping: [⟨1 10 5 19], ⟨0 -22 -7 -40]]
POL2 generator: ~125/96 = 458.988
RMS error: 0.1171 cents
2.3.5.13.17
Subgroup: 2.3.5.13.17
Comma list: 676/675, 2601/2600, 24576/24565
Gencom: [2 125/96; 676/675 2601/2600 24576/24565]
Gencom mapping: [⟨1 10 5 0 0 19 6], ⟨0 -22 -7 0 0 -40 -5]]
Sval mapping: [⟨1 10 5 19 6], ⟨0 -22 -7 -40 -5]]
POL2 generator: ~125/96 = 458.991
RMS error: 0.1129 cents
Photia
Subgroup: 2.3.5.17
Comma list: 256/255, 1458/1445
Gencom: [2 4/3; 256/255 1458/1445]
Gencom mapping: [⟨1 2 -1 0 0 0 7], ⟨0 -1 8 0 0 0 -7]]
Sval mapping: [⟨1 2 -1 7], ⟨0 -1 8 -7]]
POL2 generator: ~3/2 = 701.491
RMS error: 0.4842 cents
Related temperament: Schismic
2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 171/170, 256/255, 324/323
Gencom: [2 4/3; 171/170 256/255 324/323]
Gencom mapping: [⟨1 2 -1 0 0 0 7 3], ⟨0 -1 8 0 0 0 -7 3]]
Sval mapping: [⟨1 2 -1 7 3], ⟨0 -1 8 -7 3]]
POL2 generator: ~3/2 = 701.470
RMS error: 0.5374 cents
Quintaleap
- For full 17- and 19-limit extensions, see Quintaleap family.
Subgroup: 2.3.5.17
Comma list: 256/255, 1419857/1417176
Gencom: [2 18/17; 256/255 1419857/1417176]
Gencom mapping: [⟨1 2 1 0 0 0 5], ⟨0 -5 16 0 0 0 -11]]
Sval mapping: [⟨1 2 1 5], ⟨0 -5 16 -11]]
POL2 generator: ~18/17 = 99.272
RMS error: 0.3051 cents
2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 256/255, 361/360, 4624/4617
Gencom: [2 18/17; 256/255 361/360 4624/4617]
Gencom mapping: [⟨1 2 1 0 0 0 5 4], ⟨0 -5 16 0 0 0 -11 3]]
Sval mapping: [⟨1 2 1 5 4], ⟨0 -5 16 -11 3]]
POL2 generator: ~18/17 = 99.276
RMS error: 0.3427 cents
Quindromeda
- For full 17- and 19-limit extensions, see Quindromeda family.
Subgroup: 2.3.5.17
Comma list: 24576/24565, 295936/295245
Gencom: [2 18/17; 24576/24565 295936/295245]
Gencom mapping: [⟨1 2 0 0 0 0 5], ⟨0 -5 28 0 0 0 -11]]
Sval mapping: [⟨1 2 0 5], ⟨0 -5 28 -11]]
POL2 generator: ~18/17 = 99.524
RMS error: 0.0757 cents
2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 1216/1215, 1445/1444, 6144/6137
Gencom: [2 18/17; 1216/1215 1445/1444 6144/6137]
Gencom mapping: [⟨1 2 0 0 0 0 5 4], ⟨0 -5 28 0 0 0 -11 3]]
Sval mapping: [⟨1 2 0 5 4], ⟨0 -5 28 -11 3]]
POL2 generator: ~18/17 = 99.524
RMS error: 0.0813 cents
Quintilischis
- For full 17- and 19-limit extensions, see Schismatic family #Quintilipyth or Schismatic family #Quintaschis.
Subgroup: 2.3.5.17
Comma list: 32805/32768, 1419857/1417176
Gencom: [2 18/17; 32805/32768 1419857/1417176]
Gencom mapping: [⟨1 2 -1 0 0 0 5], ⟨0 -5 40 0 0 0 -11]]
Sval mapping: [⟨1 2 -1 5], ⟨0 -5 40 -11]]
POL2 generator: ~18/17 = 99.649
RMS error: 0.0719 cents
2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 4624/4617, 6144/6137, 6885/6859
Gencom: [2 18/17; 4624/4617 6144/6137 6885/6859]
Gencom mapping: [⟨1 2 -1 0 0 0 5 4], ⟨0 -5 40 0 0 0 -11 3]]
Sval mapping: [⟨1 2 -1 5 4], ⟨0 -5 40 -11 3]]
POL2 generator: ~18/17 = 99.652
RMS error: 0.1636 cents
Nestoria
Subgroup: 2.3.5.19
Comma list: 361/360, 513/512
Gencom: [2 4/3; 361/360 513/512]
Gencom mapping: [⟨1 2 -1 0 0 0 0 3], ⟨0 -1 8 0 0 0 0 3]]
Sval mapping: [⟨1 2 -1 3], ⟨0 -1 8 3]]
POL2 generator: ~3/2 = 701.746
RMS error: 0.1763 cents
Related temperament: Schismic