Subgroup temperaments: Difference between revisions
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Cleanup (6/) |
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[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents | ||
=== Oceanfront === | |||
Related temperaments: [[archytas clan #Superpyth|superpyth]], [[archytas clan #Ultrapyth|ultrapyth]] | |||
[[Subgroup]]: 2.3.7.13/5 | |||
[[Comma list]]: 64/63 ({{monzo| 6 -2 -1 0 }}), 91/90 ({{monzo| -1 -2 1 1 }}) | |||
{{Mapping|legend=3| 1 0 6 -5 | 0 1 -2 4 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1197.2656{{c}}, ~3/2 = 710.1993{{c}} | |||
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.7413{{c}} | |||
{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 32, 59 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents | |||
Scales: [[Oceanfront scales]] | |||
=== Darian calendar === | === Darian calendar === | ||
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[[Subgroup]]: 2.3.35.11.19 | [[Subgroup]]: 2.3.35.11.19 | ||
[[Comma list]]: 29282/29241 ({{monzo| 1 -4 0 4 -2 }}), 42875/42768 ({{monzo| -4 -5 3 -1 | [[Comma list]]: 29282/29241 ({{monzo| 1 -4 0 4 -2 }}), 42875/42768 ({{monzo| -4 -5 3 -1 0 }}), 885115/884736 ({{monzo| -15 -3 1 3 1 }}) | ||
{{Mapping|legend=3| 4 5 18 13 18 | 0 8 15 5 -6 }} | {{Mapping|legend=3| 4 5 18 13 18 | 0 8 15 5 -6 }} | ||
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{{See also| Chromatic pairs #Haumea }} | {{See also| Chromatic pairs #Haumea }} | ||
Haumea is the add-7/5 extension of [[#Bridgetown|bridgetown]], which is in turn the add-11/5 extension of [[#Barbados|barbados]]. Other related temperamnets include [[schismatic family #Hemigari|hemigari]], [[the Archipelago #Parizekmic|parizekmic]], and [[aberschismic family #Namaka|namaka]]. | |||
[[Subgroup]]: 2.3.7/5.11/5.13/5 | [[Subgroup]]: 2.3.7/5.11/5.13/5 | ||
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<nowiki/>* Wart for 49/5 | <nowiki/>* Wart for 49/5 | ||
==== Tobago ==== | |||
{{See also| Chromatic pairs #Tobago }} | |||
Tobago, the 10 & 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]]. | |||
[[Subgroup]]: 2.3.11.13/5 | |||
[[Comma list]]: [[243/242]] ({{monzo| -1 5 -2 0 }}), [[676/675]] ({{monzo| 2 -3 0 2 }}) | |||
{{Mapping|legend=3| 2 0 -1 -2 | 0 2 5 3 }} | |||
{{Mapping|legend=5| 2 0 -5 0 -1 -1 | 0 2 -3/2 0 5 3/2 }} | |||
: mapping generators: ~55/39, ~26/15 | |||
[[Optimal tuning]]s: | |||
* [[Tp tuning|subgroup]] [[WE]]: ~55/39 = 599.9845{{c}}, ~26/15 = 950.6637{{c}} | |||
* [[Tp tuning|subgroup]] [[CWE]]: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6776{{c}} | |||
{{Optimal ET sequence|legend=1| 10, 14, 24, 82, 106, 130, 154 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents | |||
==== Pakkanian hemipyth ==== | |||
[[Subgroup]]: 2.3.11.13/5.17 | |||
[[Comma list]]: 221/220 ({{monzo| -2 0 -1 1 1 }}), 243/242 ({{monzo| -1 5 -2 0 0 }}), 289/288 ({{monzo| -5 -2 0 0 2 }}) | |||
{{Mapping|legend=3| 2 0 -1 -2 5 | 0 2 5 3 2 }} | |||
[[Optimal tuning]]s: | |||
* [[Tp tuning|subgroup WE]]: ~17/12 = 600.1781{{c}}, ~26/15 = 950.7656{{c}} (~15/13 = 249.2344{{c}}) | |||
* [[Tp tuning|subgroup CWE]]: ~17/12 = 600.0000{{c}}, ~26/15 = 950.6011{{c}} (~15/13 = 249.3989{{c}}) | |||
{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }} | |||
: <nowiki/>* wart for 13/5 | |||
=== Bridgetown === | === Bridgetown === | ||
{{See also| Chromatic pairs #Bridgetown }} | {{See also| Chromatic pairs #Bridgetown }} | ||
Bridgetown, the 5 & 24 temperament in the 2.3.11/5.13/5 subgroup, is | Bridgetown, the 5 & 24 temperament in the 2.3.11/5.13/5 subgroup, is the no-7/5 restriction of [[#Haumea|haumea]] and the add-11/5 [[extension]] of [[#Barbados|barbados]]. | ||
[[Subgroup]]: 2.3.11/5.13/5 | [[Subgroup]]: 2.3.11/5.13/5 | ||
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[[Subgroup]]: 2.3.11/7 | [[Subgroup]]: 2.3.11/7 | ||
[[Comma list]]: 256/243 ({{monzo| 8 -5 }}) | [[Comma list]]: 256/243 ({{monzo| 8 -5 0 }}) | ||
{{Mapping|legend=3| 5 8 0 | 0 0 1 }} | {{Mapping|legend=3| 5 8 0 | 0 0 1 }} | ||
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=== Barbados === | === Barbados === | ||
The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. | Barbados is the restriction of [[#Bridgetown|bridgetown]] to the 2.3.13/5 subgroup. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. | ||
[[Subgroup]]: 2.3.13/5 | [[Subgroup]]: 2.3.13/5 | ||
[[Comma list]]: 676/675 | [[Comma list]]: 676/675 ({{monzo| 2 -3 2 }}) | ||
{{Mapping|legend=3| 1 0 -1 | 0 2 3 }} | |||
: mapping generators: ~2, ~26/15 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[Tp tuning|subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}} | |||
* [[Tp tuning|subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}} | |||
{{Optimal ET sequence|legend=1| 5 | {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }} | ||
[[Badness]]: 0.002335 | [[Badness]] (Smith): 0.002335 | ||
; Music | ; Music | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 | * ''[[Desert Island Rain]]'' by [[Sevish]] – [https://web.archive.org/web/20201127013711/http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 play] | [https://sevish.bandcamp.com/track/desert-island-rain Bandcamp] | [https://soundcloud.com/sevish/desert-island-rain SoundCloud] | [https://www.youtube.com/watch?v=Gcgawrr2xao YouTube] – in 313edo tuned Barbados[9] | ||
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=== Seventeen-cot === | === Seventeen-cot === | ||