Subgroup temperaments: Difference between revisions
tried to sort the fractional subgroups a little better |
made labels a bit clearer? |
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[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents | [[Tp tuning#T2 tuning|RMS error]]: 1.034 cents | ||
== 2. | == 2.….9/7… subgroups == | ||
=== Marveltri === | === Marveltri === | ||
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Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]] | Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]] | ||
[[Subgroup]]: 2.5.9/7.11/ | [[Subgroup]]: 2.5.9/7.11/7 | ||
[[Comma list]]: 99/98, 176/175 | [[Comma list]]: 99/98, 176/175 | ||
{{Mapping|legend=2| 1 2 1 | {{Mapping|legend=2| 1 2 1 0 | 0 1 -2 2 }}] | ||
[[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 | ||
== 2.3.11/5… subgroups == | == 2.….15/11… subgroups == | ||
=== Poggers === | |||
Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]] | |||
[[Subgroup]]: 2.9.7.15/11.13 | |||
[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]] | |||
{{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 | |||
== 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. | |||
[[Subgroup]]: 2.3.7/5 | |||
[[Comma list]]: [[50/49]] | |||
{{Mapping|legend=2| 2 3 1 | 0 1 0 }} | |||
[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962 | |||
[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}} | |||
=== 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 }} | |||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016 | |||
{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents | |||
== 2.….11/5… subgroups == | |||
=== Hypnosis === | === Hypnosis === | ||
Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]] | Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]] | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents | ||
== 2. | == 2.….11/7… subgroups == | ||
=== Pepperoni === | === Pepperoni === | ||
{{Main| Parapyth }} | {{Main| Parapyth }} | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | ||
== 2.….13/5… subgroups == | |||
== 2. | |||
=== Barbados === | === Barbados === | ||
[[Subgroup]]: 2.3.13/5 | [[Subgroup]]: 2.3.13/5 | ||
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<nowiki>*</nowiki> wart for 13/5 | <nowiki>*</nowiki> wart for 13/5 | ||
<!-- name conflict | <!-- name conflict | ||
== 2.49/5… subgroups == | == 2.….49/5… subgroups == | ||
=== Breedsmic === | === Breedsmic === | ||
Related temperament: [[hemithirds]], [[newt]] | Related temperament: [[hemithirds]], [[newt]] | ||