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Subgroup temperaments: Difference between revisions

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[[Badness]]: 0.0215 × 10<sup>-3</sup>
[[Badness]]: 0.0215 × 10<sup>-3</sup>


== Fractional subgroup temperaments ==
= Fractional subgroup temperaments =
=== Historical ===
 
{{distinguish|Historical temperaments}}
== 2.3 subgroup==
[[Subgroup]]: 2.3.7/5.11/5.13/5


[[Comma list]]: 364/363, 441/440, 1001/1000
=== Hydrothermal ===
[[Subgroup]]: 2.3.7/5


{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
[[Comma list]]: [[50/49]]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
{{Mapping|legend=2| 2 3 1 | 0 1 0 }}


{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962


[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
[[Support]]ing [[ET]]s: *2, *4, *6, *8, *10, *12, *14


=== Hypnosis ===
=== Barbados ===
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
[[Subgroup]]: 2.3.13/5


[[Subgroup]]: 2.3.7.11/5.13
[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}


[[Comma list]]: 169/168, 540/539, 729/728
[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]


{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}


{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
[[Badness]]: 0.002335


[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
<nowiki>*</nowiki> wart for 3/2


=== Oceanfront ===
=== Oceanfront ===
Line 556: Line 556:
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents


=== Marveltri ===
=== Hypnosis ===
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to marvel, magic, and the unnamed 22 &amp; 47 temperament.  
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
 
[[Subgroup]]: 2.3.7.11/5.13
 
[[Comma list]]: 169/168, 540/539, 729/728
 
{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
 
{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
 
=== Historical ===
{{distinguish|Historical temperaments}}
[[Subgroup]]: 2.3.7/5.11/5.13/5
 
[[Comma list]]: 364/363, 441/440, 1001/1000
 
{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}


[[Subgroup]]: 2.5.9/7
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016


[[Comma list]]: 225/224
{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}


{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents


{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
=== Pepperoni ===
{{Main| Parapyth }}


: [[gencom]]: [2 5/4; 225/224]
Pepperoni is the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638
[[Subgroup]]: 2.3.11/7.13/7


{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
[[Comma list]]: 352/351, 364/363


<nowiki>*</nowiki> wart for 9/7
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}


==== Sulis ====
: [[gencom]]: [2 3/2; 352/351 364/363]
Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]


[[Subgroup]]: 2.5.9/7.11/9
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856


[[Comma list]]: 99/98, 176/175
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}


{{Mapping|legend=2| 1 2 1 -1 | 0 1 -2 4 }}]
<nowiki>*</nowiki> wart for 11/7


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
<nowiki>†</nowiki> wart for 13/7


{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents


[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
<!-- name conflict
<!-- name conflict
=== Breedsmic ===
=== Breedsmic ===
Line 607: Line 626:
[[Tp tuning #T2 tuning|RMS error]]: ?
[[Tp tuning #T2 tuning|RMS error]]: ?
-->
-->
=== Semiwolf ===
== Other octave-period ==
[[Subgroup]]: 3/2.5/2.7/4
 
=== Marveltri ===
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to marvel, magic, and the unnamed 22 &amp; 47 temperament.
 
[[Subgroup]]: 2.5.9/7


[[Comma list]]: 245/243
[[Comma list]]: 225/224


{{Mapping|legend=2| 1 1 2 | 0 2 -1 }}
{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}


: sval mapping generators: ~3/2, ~9/7
{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 262.1728
: [[gencom]]: [2 5/4; 225/224]


[[Optimal ET sequence]]: [[3edf]], [[5edf]], [[8edf]]
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638


==== Semilupine ====
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: 100/99, 245/243
<nowiki>*</nowiki> wart for 9/7


{{Mapping|legend=2| 1 1 2 0 | 0 2 -1 4 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771
==== Sulis ====
Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]


[[Optimal ET sequence]]: [[8edf]], [[13edf]]
[[Subgroup]]: 2.5.9/7.11/9


==== Hemilycan ====
[[Comma list]]: 99/98, 176/175
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: 245/243, 441/440
{{Mapping|legend=2| 1 2 1 -1 | 0 1 -2 4 }}]


{{Mapping|legend=2| 1 1 2 5 | 0 2 -1 -4 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939
{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}


[[Optimal ET sequence]]: [[8edf]], [[11edf]]
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents


=== Greeley ===
=== Greeley ===
Line 665: Line 687:
[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents


=== Pepperoni ===
=== Poggers ===
{{Main| Parapyth }}
Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]


Pepperoni is the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
[[Subgroup]]: 2.9.7.15/11.13


[[Subgroup]]: 2.3.11/7.13/7
[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]


[[Comma list]]: 352/351, 364/363
{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}


{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888


{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105


: [[gencom]]: [2 3/2; 352/351 364/363]
== 3/2.7 subgroup ==


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
=== Auk ===
[[Subgroup]]: 3/2.7.13


{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}
[[Comma list]]: 87808/85293


<nowiki>*</nowiki> wart for 11/7
{{Mapping|legend=2| 1 0 -8 | 0 1 3 }}


<nowiki>†</nowiki> wart for 13/7
: sval mapping generators: ~3/2, ~7


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~28/9 = 1950.859
<!-- name conflict
=== Poseidon ===
[[Subgroup]]: 3/2.5/4.11/8


[[Comma list]]: 121/120
Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]


{{Mapping|legend=2| 1 1 1 | 0 2 -1 }}]
<nowiki>*</nowiki> wart for 3/2
 
: [[gencom]]: [3/2 12/11; 121/120]
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2, [12/11 = 158.29
 
{{Optimal ET sequence|legend=1|9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49}}
-->
=== Hyperion ===
[[Subgroup]]: 5/2.7.11
 
[[Comma list]]: {{monzo| 11 1 -5 }}
 
{{Mapping|legend=2| 1 4 3 | 0 -5 -1 }}
 
: [[gencom]]: [5/2 125/88; 341796875/329832448]
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/2 = 1586.3137, ~125/88 = 593.6668
 
Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]
 
<nowiki>*</nowiki> wart for 5/2


=== Doubleton ===
=== Doubleton ===
Line 733: Line 732:
<nowiki>*</nowiki> wart for 3/2
<nowiki>*</nowiki> wart for 3/2


=== Auk ===
== 3/2.5/2 subgroup ==
[[Subgroup]]: 3/2.7.13
 
[[Comma list]]: 87808/85293
 
{{Mapping|legend=2| 1 0 -8 | 0 1 3 }}
 
: sval mapping generators: ~3/2, ~7
 
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~28/9 = 1950.859
 
Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]
 
<nowiki>*</nowiki> wart for 3/2


=== Halftone ===
=== Halftone ===
Line 793: Line 779:
<nowiki>*</nowiki> wart for 3/2
<nowiki>*</nowiki> wart for 3/2


=== Hemihemi ===
[[Subgroup]]: 3/2.5/2.7/2


=== Poggers ===
[[Comma list]]: [[10976/10935]]
Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
 
{{Mapping|legend=2| 1 2 3 | 0 3 1  }}
 
[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909
 
[[Support]]ing [[ET]]s: *23, *12, *11, *35, *34, *10, *13, *47, *9[+5/2], *14[-5/2], *45, *25, *21[+5/2], *8[+5/2]
 
=== Semiwolf ===
[[Subgroup]]: 3/2.5/2.7/4
 
[[Comma list]]: 245/243
 
{{Mapping|legend=2| 1 1 2 | 0 2 -1 }}
 
: sval mapping generators: ~3/2, ~9/7
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 262.1728
 
[[Optimal ET sequence]]: [[3edf]], [[5edf]], [[8edf]]


[[Subgroup]]: 2.9.7.15/11.13
==== Semilupine ====
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
[[Comma list]]: 100/99, 245/243


{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
{{Mapping|legend=2| 1 1 2 0 | 0 2 -1 4 }}


[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771


[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105
[[Optimal ET sequence]]: [[8edf]], [[13edf]]


=== Hemihemi ===
==== Hemilycan ====
[[Subgroup]]: 3/2.5/2.7/2
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: [[10976/10935]]
[[Comma list]]: 245/243, 441/440


{{Mapping|legend=2| 1 2 3 | 0 3 1 }}
{{Mapping|legend=2| 1 1 2 5 | 0 2 -1 -4 }}


[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939


[[Support]]ing [[ET]]s: *23, *12, *11, *35, *34, *10, *13, *47, *9[+5/2], *14[-5/2], *45, *25, *21[+5/2], *8[+5/2]
[[Optimal ET sequence]]: [[8edf]], [[11edf]]


=== Barbados ===
== Other nonoctave ==
[[Subgroup]]: 2.3.13/5
<!-- name conflict
=== Poseidon ===
[[Subgroup]]: 3/2.5/4.11/8


[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
[[Comma list]]: 121/120


[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
{{Mapping|legend=2| 1 1 1 | 0 2 -1 }}]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
: [[gencom]]: [3/2 12/11; 121/120]


{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2, [12/11 = 158.29


[[Badness]]: 0.002335
{{Optimal ET sequence|legend=1|9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49}}
-->
=== Hyperion ===
[[Subgroup]]: 5/2.7.11


<nowiki>*</nowiki> wart for 3/2
[[Comma list]]: {{monzo| 11 1 -5 }}


=== Hydrothermal ===
{{Mapping|legend=2| 1 4 3 | 0 -5 -1 }}
[[Subgroup]]: 2.3.7/5


[[Comma list]]: [[50/49]]
: [[gencom]]: [5/2 125/88; 341796875/329832448]


{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/2 = 1586.3137, ~125/88 = 593.6668


[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]


[[Support]]ing [[ET]]s: *2, *4, *6, *8, *10, *12, *14
<nowiki>*</nowiki> wart for 5/2


<!-- main article -->
<!-- main article -->
[[Category:Temperament collections]][[Category:Subgroup]]
[[Category:Temperament collections]][[Category:Subgroup]]
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