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Subgroup temperaments: Difference between revisions

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Cleanup (3/)
→Fractional subgroup temperaments: cleanup (4/); comment out temperaments with name conflict
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[[Comma list]]: 364/363, 441/440, 1001/1000
[[Comma list]]: 364/363, 441/440, 1001/1000


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


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
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=== Hypnosis ===
=== Hypnosis ===
Related temperaments: [[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


[[Sval]] [[mapping]]: [{{val| 1 0 -3 8 0 }}, {{val| 0 3 11 -13 7 }}]
{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518


{{Optimal ET sequence|legend=1| 17, 36, 118e, 125e, 161e, 197e }}
{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents


Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
=== Oceanfront ===
Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]


=== Oceanfront ===
[[Subgroup]]: 2.3.7.13/5
[[Subgroup]]: 2.3.7.13/5


[[Comma list]]: 64/63, 91/90
[[Comma list]]: 64/63, 91/90


[[Sval]] [[mapping]]: [{{val| 1 0 6 -5 }}, {{val| 0 1 -2 4 }}]
{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
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[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents


Related temperament: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
=== Marveltri ===
Marveltri, the 3 & 13 temperament in the 2.5.9/7 subgroup, is related to marvel, magic, and the unnamed 22 & 47 temperament.


=== Marveltri ===
[[Subgroup]]: 2.5.9/7
[[Subgroup]]: 2.5.9/7


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


Sval name: 3&13
{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}


Related temperaments: marvel, 22&47, magic
{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
 
: [[gencom]]: [2 5/4; 225/224]


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


[[Gencom|Gencom]]: [2 5/4; 225/224]
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}


Gencom mapping: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]
<nowiki>*</nowiki> wart for 9/7
 
[[Sval]] [[mapping]]: [{{val| 1 2 1 }}, {{val| 0 1 -2 }}]
 
{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


==== Sulis ====
==== Sulis ====
Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]
[[Subgroup]]: 2.5.9/7.11/9
[[Subgroup]]: 2.5.9/7.11/9


[[Comma list]]: 99/98, 176/175
[[Comma list]]: 99/98, 176/175


[[Sval]] [[mapping]]: [{{val| 1 2 1 -1 }}, {{val| 0 1 -2 4 }}]
{{Mapping|legend=2| 1 2 1 -1 | 0 1 -2 4 }}]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
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[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
<!-- name conflict
=== Breedsmic ===
Related temperament: [[hemithirds]], [[newt]]


Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]
=== Breedsmic ===
[[Subgroup]]: 2.3.49/5
[[Subgroup]]: 2.3.49/5


[[Comma list]]: 2401/2400
[[Comma list]]: 2401/2400


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


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
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[[Tp tuning #T2 tuning|RMS error]]: ?
[[Tp tuning #T2 tuning|RMS error]]: ?
 
-->
Related temperament: [[hemithirds]], [[newt]]
 
=== Semiwolf ===
=== Semiwolf ===
[[Subgroup]]: 3/2.7/4.5/2
[[Subgroup]]: 3/2.7/4.5/2
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[[Comma list]]: 245/243
[[Comma list]]: 245/243


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


[[Optimal tuning]] ([[POL2]]): ~7/6 = 262.1728
[[Optimal tuning]] ([[POL2]]): ~7/6 = 262.1728
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[[Comma list]]: 100/99, 245/243
[[Comma list]]: 100/99, 245/243


[[Sval]] [[mapping]]: [{{val| 1 1 3 4 }}, {{val| 0 1 -2 -4 }}]
{{Mapping|legend=2| 1 1 3 4 | 0 1 -2 -4 }}


[[POL2]] generator: ~7/6 = 264.3771
[[Optimal tuning]] ([[POL2]]): ~7/6 = 264.3771


[[Optimal ET sequence]]: [[8edf]], [[13edf]]
[[Optimal ET sequence]]: [[8edf]], [[13edf]]
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[[Comma list]]: 245/243, 441/440
[[Comma list]]: 245/243, 441/440


[[Sval]] [[mapping]]: [{{val| 1 1 3 1 }}, {{val| 0 1 -2 4 }}]
{{Mapping|legend=2| 1 1 3 1 | 0 1 -2 4 }}


[[Optimal tuning]] ([[POL2]]): ~7/6 = 261.5939
[[Optimal tuning]] ([[POL2]]): ~7/6 = 261.5939
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=== Greeley ===
=== Greeley ===
Subgroup: 2.5/3.7/3.11/3
Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]


Commas: 121/120, 126/125
[[Subgroup]]: 2.5/3.7/3.11/3


Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]
[[Comma list]]: 121/120, 126/125


[[Tp_tuning|POT2 generator]]: ~11/10 = 155.776
{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}


[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}


Gencom mapping: &lt;1 -5/4 -1/4 3/4 3/4|, &lt;0 9/4 1/4 -15/4 5/4|]
: [[gencom]]: [2 11/10; 121/120 126/125]


Mapping: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]
[[Optimal tuning]] ([[POL2]]): ~11/10 = 155.776


EDOs: {{EDOs|8, 15, 23, 54, 77, 100, 131d, 208bd}}
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }}


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


=== Pepperoni ===
=== Pepperoni ===
Subgroup: 2.3.11/7.13/7
{{Main| Parapyth }}


Commas: 352/351, 364/363
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.


Sval name: 5&amp;12
[[Subgroup]]: 2.3.11/7.13/7


Related temperament: The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
[[Comma list]]: 352/351, 364/363


[[Tp_tuning|POT2 generator]]: ~3/2 = 703.856
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}


[[Gencom|Gencom]]: [2 3/2; 352/351 364/363]
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}


Gencom mapping: [&lt;1 1 0 -8/3 1/3 7/3|, &lt;0 1 0 11/3 -1/3 -10/3|]
: [[gencom]]: [2 3/2; 352/351 364/363]


Mapping: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]
[[Optimal tuning]] ([[POL2]]): ~3/2 = 703.856


EDOs: {{EDOs|5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd}}
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd }}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.3789 cents


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
<!-- name conflict
<!-- name conflict
=== Poseidon ===
=== Poseidon ===
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{{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}}
{{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 ===
=== Hyperion ===
[[Subgroup]]: 5/2.7.11
[[Subgroup]]: 5/2.7.11
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