Landscape microtemperaments: Difference between revisions
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== Sextile == | == Sextile == | ||
Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the 12 & 270 temperament. | Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the 12 & 270 temperament. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness: 0.014915 | Badness: 0.014915 | ||
== Slendscape == | |||
Slendscape tempers out the [[slendrisma]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of 1＼15. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 250047/250000, 12884901888/12867859375 | |||
{{Mapping|legend=1| 15 0 17 54 | 0 4 3 -2 }} | |||
: Mapping generators: ~8575/8192, ~1152/875 | |||
[[Optimal tuning]] ([[CTE]]): ~8575/8192 = 1＼15, ~1152/875 = 475.4847 (~6/5 = 315.4847 or ~21/20 = 84.5153) | |||
{{Optimal ET sequence|legend=1| 255, 270, 525, 795, 1065 }} | |||
[[Badness]]: 0.058002 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 102487/102400, 180224/180075 | |||
Mapping: {{Mapping| 15 0 17 54 40 | 0 4 3 -2 2 }} | |||
Optimal tuning (CTE): ~22/21 = 1＼15, ~968/735 = 475.4912 (~6/5 = 315.4912 or ~21/20 = 84.5088) | |||
Optimal ET sequence: {{EDOs| 255, 270, 525, 795, 1065 }} | |||
Badness: 0.026246 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625 | |||
Mapping: {{Mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }} | |||
Optimal tuning (CTE): ~22/21 = 1＼15, ~154/117 = 475.4935 (~6/5 = 315.4935 or ~21/20 = 84.5065) | |||
Optimal ET sequence: {{EDOs| 255, 270, 795, 1065 }} | |||
Badness: 0.021230 | |||
== Akjayland == | == Akjayland == | ||
{{See also| 21st-octave temperaments }} | {{See also| 21st-octave temperaments }} | ||
Akjayland tempers out the [[akjaysma]] in addition to landscape comma, and thereby features a period of | Akjayland tempers out the [[akjaysma]] in addition to landscape comma, and thereby features a period of 1＼21. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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: mapping generators: ~1323/1280, ~131072/91875 | : mapping generators: ~1323/1280, ~131072/91875 | ||
[[Optimal tuning]] ([[CTE]]): ~1323/1280 = | [[Optimal tuning]] ([[CTE]]): ~1323/1280 = 1＼21, ~131072/91875 = 614.9354 | ||
{{Optimal ET sequence|legend=1| 84, 273, 357, 441, 966, 1407, 1848, 7833, 9681, 11529, 13377c }} | {{Optimal ET sequence|legend=1| 84, 273, 357, 441, 966, 1407, 1848, 7833, 9681, 11529, 13377c }} | ||
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=== Vasca === | === Vasca === | ||
Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of twenty-one [[23/16]]'s equal with eleven octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo. | Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of twenty-one [[23/16]]'s equal with eleven octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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: mapping generators: ~1323/1280, ~6615/5632 | : mapping generators: ~1323/1280, ~6615/5632 | ||
Optimal tuning (CTE): ~1323/1280 = | Optimal tuning (CTE): ~1323/1280 = 1＼21, ~6615/5632 = 278.8998 | ||
{{Optimal ET sequence|legend=1| 168, 357, 525, 882, 1407, 2289e }} | {{Optimal ET sequence|legend=1| 168, 357, 525, 882, 1407, 2289e }} | ||
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Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }} | Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }} | ||
Optimal tuning (CTE): ~336/325 = | Optimal tuning (CTE): ~336/325 = 1＼21, ~168/143 = 278.9058 | ||
{{Optimal ET sequence|legend=1| 168, 357, 525, 882 }} | {{Optimal ET sequence|legend=1| 168, 357, 525, 882 }} | ||
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Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }} | Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }} | ||
Optimal tuning (CTE): ~336/325 = | Optimal tuning (CTE): ~336/325 = 1＼21, ~168/143 = 278.9036 | ||
{{Optimal ET sequence|legend=1| 168, 357, 525, 882 }} | {{Optimal ET sequence|legend=1| 168, 357, 525, 882 }} | ||
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Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }} | Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }} | ||
Optimal tuning (CTE): ~336/325 = | Optimal tuning (CTE): ~336/325 = 1＼21, ~168/143 = 278.9036 | ||
{{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }} | {{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }} | ||
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Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 -6 -2 8 -3 6 7 -15 0 }} | Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 -6 -2 8 -3 6 7 -15 0 }} | ||
Optimal tuning (CTE): ~336/325 = | Optimal tuning (CTE): ~336/325 = 1＼21, ~168/143 = 278.8971 | ||
{{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }} | {{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }} | ||