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Subgroup temperaments: Difference between revisions

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= Fractional subgroup temperaments =
= Fractional subgroup temperaments =
== 2.5/3… subgroups ==


== 3/2.5/2… subgroup ==
=== Greeley ===
{{Main|Half-prime subgroup}}
Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]


=== Hemihemi ===
[[Subgroup]]: 2.5/3.7/3.11/3
[[Subgroup]]: 3/2.5/2.7/2


[[Comma list]]: [[10976/10935]]
[[Comma list]]: 121/120, 126/125


{{Mapping|legend=2| 1 2 3 | 0 3 1 }}
{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}


[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909
{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}


[[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]
: [[gencom]]: [2 11/10; 121/120 126/125]


=== Halftone ===
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~11/10 = 155.776
{{Main| Halftone }}


[[Subgroup]]: 3/2.5/2.7/2
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131†, 208*† }}


[[Comma list]]: 9604/9375
<nowiki>*</nowiki> wart for 5/3


{{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
<nowiki>†</nowiki> wart for 11/3


: sval mapping generators: ~3/2, ~15/14
[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents


[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 128.783
== 2.3.7/5… subgroups ==
=== Hydrothermal ===
A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.


Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49
[[Subgroup]]: 2.3.7/5


<nowiki>*</nowiki> wart for 3/2
[[Comma list]]: [[50/49]]


==== 3/2.5/2.7/2.11/2 ====
{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
[[Subgroup]]: 3/2.5/2.7/2.11/2


[[Comma list]]: 1232/1215, 27783/27500
[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962


{{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}


: sval mapping generators: ~3/2, ~15/14
=== Historical ===
{{distinguish|Historical temperaments}}
[[Subgroup]]: 2.3.7/5.11/5.13/5


[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.186
[[Comma list]]: 364/363, 441/440, 1001/1000


[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]
{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}


<nowiki>*</nowiki> wart for 3/2
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016


==== 3/2.5/2.7/2.11/2.13/2 ====
{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
[[Subgroup]]: 3/2.5/2.7/2.11/2.13/2


[[Comma list]]: 275/273, 1232/1215, 1323/1300
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents


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


[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.381
== 2.5.9/7… subgroups ==


[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
=== 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.


<nowiki>*</nowiki> wart for 3/2
[[Subgroup]]: 2.5.9/7


=== Semiwolf ===
[[Comma list]]: 225/224
[[Subgroup]]: 3/2.5/2.7/4


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


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


: sval mapping generators: ~3/2, ~9/7
: [[gencom]]: [2 5/4; 225/224]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 262.1728
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638


[[Optimal ET sequence]]: [[3edf]], [[5edf]], [[8edf]]
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}


==== Semilupine ====
<nowiki>*</nowiki> wart for 9/7
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: 100/99, 245/243
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


{{Mapping|legend=2| 1 1 2 0 | 0 2 -1 4 }}
==== Sulis ====
Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771
[[Subgroup]]: 2.5.9/7.11/9


[[Optimal ET sequence]]: [[8edf]], [[13edf]]
[[Comma list]]: 99/98, 176/175


==== Hemilycan ====
{{Mapping|legend=2| 1 2 1 -1 | 0 1 -2 4 }}]
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Comma list]]: 245/243, 441/440
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558


{{Mapping|legend=2| 1 1 2 5 | 0 2 -1 -4 }}
{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents


[[Optimal ET sequence]]: [[8edf]], [[11edf]]
== 2.3.11/5… subgroups ==
=== Hypnosis ===
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]


<!-- name conflict
[[Subgroup]]: 2.3.7.11/5.13
== 3/2.5/4 subgroup ==
=== Poseidon ===
[[Subgroup]]: 3/2.5/4.11/8


[[Comma list]]: 121/120
[[Comma list]]: 169/168, 540/539, 729/728


{{Mapping|legend=2| 1 1 1 | 0 2 -1 }}]
{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}


: [[gencom]]: [3/2 12/11; 121/120]
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2, [12/11 = 158.29
{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}


{{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}}
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-->


== 5/3.7/3… subgroup ==
== 2.3.11/7… subgroups ==
=== Pepperoni ===
{{Main| Parapyth }}


=== Greeley ===
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.
Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]


[[Subgroup]]: 2.5/3.7/3.11/3
[[Subgroup]]: 2.3.11/7.13/7


[[Comma list]]: 121/120, 126/125
[[Comma list]]: 352/351, 364/363


{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}


{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}


: [[gencom]]: [2 11/10; 121/120 126/125]
: [[gencom]]: [2 3/2; 352/351 364/363]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~11/10 = 155.776
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856


{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131†, 208*† }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}


<nowiki>*</nowiki> wart for 5/3
<nowiki>*</nowiki> wart for 11/7


<nowiki>†</nowiki> wart for 11/3
<nowiki>†</nowiki> wart for 13/7


[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents


== 7/5.11/5… subgroup ==


=== Historical ===
== 2.3.13/5… subgroups ==
{{distinguish|Historical temperaments}}
=== Barbados ===
[[Subgroup]]: 2.3.7/5.11/5.13/5
[[Subgroup]]: 2.3.13/5


[[Comma list]]: 364/363, 441/440, 1001/1000
[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}


{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621


{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
[[Badness]]: 0.002335


== 11/7.13/7… subgroup ==
<nowiki>*</nowiki> wart for 3/2


=== Pepperoni ===
=== Oceanfront ===
{{Main| Parapyth }}
Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]


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]]: 2.3.7.13/5


[[Subgroup]]: 2.3.11/7.13/7
[[Comma list]]: 64/63, 91/90


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


{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910


{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}


: [[gencom]]: [2 3/2; 352/351 364/363]
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
Scales: [[Oceanfront scales]]


{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}
=== Pakkanian hemipyth ===


<nowiki>*</nowiki> wart for 11/7
[[Subgroup]]: 2.3.11.13/5.17


<nowiki>†</nowiki> wart for 13/7
[[Comma list]]: 221/220, 243/242, 289/288


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}


== Other 3/2 subgroups ==
[[Optimal tuning]]s:
* [[Tp tuning|subgroup CTE]]: ~17/12 = 1\2, ~26/15 = 950.7656 (~15/13 = 249.2344)
* [[Tp tuning|subgroup CWE]]: ~17/12 = 1\2, ~26/15 = 950.6011 (~15/13 = 249.3989)


=== Auk ===
{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
[[Subgroup]]: 3/2.7.13


[[Comma list]]: 87808/85293
<nowiki>*</nowiki> wart for 13/5


{{Mapping|legend=2| 1 0 -8 | 0 1 3 }}
== 2.15/11… subgroups ==


: sval mapping generators: ~3/2, ~7
=== Poggers ===
Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]


[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~28/9 = 1950.859
[[Subgroup]]: 2.9.7.15/11.13


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]
[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]


<nowiki>*</nowiki> wart for 3/2
{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}


=== Doubleton ===
[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
[[Subgroup]]: 3/2.7.13


[[Comma list]]: 1352/1323
[[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


{{Mapping|legend=2| 2 0 3 | 0 1 1 }}
<!-- name conflict
== 2.49/5… subgroups ==
=== Breedsmic ===
Related temperament: [[hemithirds]], [[newt]]


: sval mapping generators: ~26/21, ~7
[[Subgroup]]: 2.3.49/5


[[Optimal tuning]] (subgroup [[CTE]]): ~26/21 = 1\2edf, ~28/9 = 1971.772
[[Comma list]]: 2401/2400


Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]
{{Mapping|legend=2| 1 1 3 | 0 2 1 }}


<nowiki>*</nowiki> wart for 3/2
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966


== Other 5/2 subgroups ==
{{Optimal ET sequence|legend=1|?}}


=== Hyperion ===
[[Tp tuning #T2 tuning|RMS error]]: ?
[[Subgroup]]: 5/2.7.11
-->


[[Comma list]]: {{monzo| 11 1 -5 }}


{{Mapping|legend=2| 1 4 3 | 0 -5 -1 }}
== 3/2.5/2… subgroups ==
{{Main|Half-prime subgroup}}


: [[gencom]]: [5/2 125/88; 341796875/329832448]
=== Hemihemi ===
[[Subgroup]]: 3/2.5/2.7/2


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/2 = 1586.3137, ~125/88 = 593.6668
[[Comma list]]: [[10976/10935]]


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]
{{Mapping|legend=2| 1 2 3 | 0 3 1  }}


<nowiki>*</nowiki> wart for 5/2
[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909


== Other 7/5 subgroups ==
[[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]


=== Hydrothermal ===
=== Halftone ===
A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
{{Main| Halftone }}


[[Subgroup]]: 2.3.7/5
[[Subgroup]]: 3/2.5/2.7/2


[[Comma list]]: [[50/49]]
[[Comma list]]: 9604/9375


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


[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
: sval mapping generators: ~3/2, ~15/14


[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 128.783


== Other 11/5 subgroups ==
Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49


=== Hypnosis ===
<nowiki>*</nowiki> wart for 3/2
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]


[[Subgroup]]: 2.3.7.11/5.13
==== 3/2.5/2.7/2.11/2 ====
[[Subgroup]]: 3/2.5/2.7/2.11/2


[[Comma list]]: 169/168, 540/539, 729/728
[[Comma list]]: 1232/1215, 27783/27500


{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
{{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
: sval mapping generators: ~3/2, ~15/14


{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.186


[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]


== Other 13/5 subgroups ==
<nowiki>*</nowiki> wart for 3/2
=== Barbados ===
[[Subgroup]]: 2.3.13/5


[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
==== 3/2.5/2.7/2.11/2.13/2 ====
[[Subgroup]]: 3/2.5/2.7/2.11/2.13/2


[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
[[Comma list]]: 275/273, 1232/1215, 1323/1300


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
{{Mapping|legend=2| 1 3 4 4 5 | 0 -4 -5 1 -2 }}


{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.381


[[Badness]]: 0.002335
[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]


<nowiki>*</nowiki> wart for 3/2
<nowiki>*</nowiki> wart for 3/2


=== Oceanfront ===
=== Semiwolf ===
Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
[[Subgroup]]: 3/2.5/2.7/4
 
[[Comma list]]: 245/243


[[Subgroup]]: 2.3.7.13/5
{{Mapping|legend=2| 1 1 2 | 0 2 -1 }}


[[Comma list]]: 64/63, 91/90
: sval mapping generators: ~3/2, ~9/7


{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 262.1728


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
[[Optimal ET sequence]]: [[3edf]], [[5edf]], [[8edf]]


{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
==== Semilupine ====
[[Subgroup]]: 3/2.5/2.7/4.11/4


[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
[[Comma list]]: 100/99, 245/243


Scales: [[Oceanfront scales]]
{{Mapping|legend=2| 1 1 2 0 | 0 2 -1 4 }}


=== Pakkanian hemipyth ===
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771


[[Subgroup]]: 2.3.11.13/5.17
[[Optimal ET sequence]]: [[8edf]], [[13edf]]


[[Comma list]]: 221/220, 243/242, 289/288
==== Hemilycan ====
[[Subgroup]]: 3/2.5/2.7/4.11/4


{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
[[Comma list]]: 245/243, 441/440


[[Optimal tuning]]s:
{{Mapping|legend=2| 1 1 2 5 | 0 2 -1 -4 }}
* [[Tp tuning|subgroup CTE]]: ~17/12 = 1\2, ~26/15 = 950.7656 (~15/13 = 249.2344)
* [[Tp tuning|subgroup CWE]]: ~17/12 = 1\2, ~26/15 = 950.6011 (~15/13 = 249.3989)


{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939


<nowiki>*</nowiki> wart for 13/5
[[Optimal ET sequence]]: [[8edf]], [[11edf]]


<!-- name conflict
<!-- name conflict
== Other 49/5 subgroups ==
== 3/2.5/4… subgroups ==
=== Breedsmic ===
=== Poseidon ===
Related temperament: [[hemithirds]], [[newt]]
[[Subgroup]]: 3/2.5/4.11/8


[[Subgroup]]: 2.3.49/5
[[Comma list]]: 121/120


[[Comma list]]: 2401/2400
{{Mapping|legend=2| 1 1 1 | 0 2 -1 }}]


{{Mapping|legend=2| 1 1 3 | 0 2 1 }}
: [[gencom]]: [3/2 12/11; 121/120]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2, [12/11 = 158.29


{{Optimal ET sequence|legend=1|?}}
{{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}}
 
[[Tp tuning #T2 tuning|RMS error]]: ?
-->
-->


== Other 9/7 subgroups ==
== Other 3/2-equave subgroups ==
=== Auk ===
[[Subgroup]]: 3/2.7.13


=== Marveltri ===
[[Comma list]]: 87808/85293
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
{{Mapping|legend=2| 1 0 -8 | 0 1 3 }}


[[Comma list]]: 225/224
: sval mapping generators: ~3/2, ~7


{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~28/9 = 1950.859


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


: [[gencom]]: [2 5/4; 225/224]
<nowiki>*</nowiki> wart for 3/2


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638
=== Doubleton ===
[[Subgroup]]: 3/2.7.13


{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
[[Comma list]]: 1352/1323


<nowiki>*</nowiki> wart for 9/7
{{Mapping|legend=2| 2 0 3 | 0 1 1 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
: sval mapping generators: ~26/21, ~7


==== Sulis ====
[[Optimal tuning]] (subgroup [[CTE]]): ~26/21 = 1\2edf, ~28/9 = 1971.772
Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]


[[Subgroup]]: 2.5.9/7.11/9
Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]


[[Comma list]]: 99/98, 176/175
<nowiki>*</nowiki> wart for 3/2


{{Mapping|legend=2| 1 2 1 -1 | 0 1 -2 4 }}]
== 5/2-equave subgroups ==


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
=== Hyperion ===
[[Subgroup]]: 5/2.7.11


{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
[[Comma list]]: {{monzo| 11 1 -5 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
{{Mapping|legend=2| 1 4 3 | 0 -5 -1 }}


== Other 15/11 subgroups ==
: [[gencom]]: [5/2 125/88; 341796875/329832448]


=== Poggers ===
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/2 = 1586.3137, ~125/88 = 593.6668
Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]


[[Subgroup]]: 2.9.7.15/11.13
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]


[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
<nowiki>*</nowiki> wart for 5/2
 
{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
 
[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
 
[[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


= Related temperament collections =
= Related temperament collections =
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"