Irrational-subgroup temperaments: Difference between revisions
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This page is a list of temperaments | This page is a list of [[regular temperament|temperaments]] of irrational subgroups that cannot be expressed in surds. | ||
== | == Photosynthesis == | ||
Photosynthesis is a [[nonoctave]] temperament tempering out the comma 243/(5⋅ϕ<sup>8</sup>) in the ϕ.3.5 subgroup, equating five [[3/1]] with [[5/1]]. It has a period of [[acoustic phi]] and a generator of a major second just flat of 3/(ϕ<sup>2</sup>), the "phi-reduced 3rd harmonic". It possesses mos scales of the families 3L 1s<ϕ>, 4L 3s<ϕ>, 4L 7s<ϕ>, and 11L 4s<ϕ>. | |||
[[Subgroup]]: ϕ.3.5 | |||
[[Comma list]]: 243/(5⋅ϕ<sup>8</sup>) | |||
{{Mapping|legend=3| 1 0 -8 | 0 1 5 }} | |||
: mapping generators: ~ϕ, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ϕ = 833.0903{{c}}, ~3/ϕ = 1057.989{{c}}{{confirm}} | |||
[[Edφ|Edϕ]]s: 11, 15, 7[+5], 19[-5], 26, 5[--5], 18[+5], 23[-3, -5], 34[-3, -5], 37, 41[-3], 27[-3, -5], 49[-3, -5], 31[-3, --5] | |||
== Polyraider == | |||
The temperament below can also be written with [[34ed30]] nominals and cent-deviation (1\1171) accidentals. This temperament was found by [[User:2^67-1|2^67-1 (alias Cole Whitewood)]] in an attempt to figure out how to expand [[11edt]]'s approximations of this subgroup. | The temperament below can also be written with [[34ed30]] nominals and cent-deviation (1\1171) accidentals. This temperament was found by [[User:2^67-1|2^67-1 (alias Cole Whitewood)]] in an attempt to figure out how to expand [[11edt]]'s approximations of this subgroup. | ||
[[Subgroup]]: 2.3.5.11. | [[Subgroup]]: 2.3.5.11.''f''<sub>2</sub>.''f''<sub>3</sub> * | ||
: <nowiki/>* ''f''<sub>2</sub>, ''f''<sub>3</sub> are the 2nd and 3rd modes of an ideal unsupported bar. | |||
[[Comma list]]: [[1771561/1771470]], 1310730070806386550964611/1310720000000000000000000, | [[Comma list]]: [[1771561/1771470]], 1310730070806386550964611/1310720000000000000000000, {{monzo| -8 6 -3 2 -1 0 }}, {{monzo| -11 10 -7 4 0 -1 }} | ||
{{Mapping|legend=1|1 65 172 148 162 27 | 0 −111 −297 −253 −281 −43}} | {{Mapping|legend=1| 1 65 172 148 162 27 | 0 −111 −297 −253 −281 −43 }} | ||
: mapping generators: ~2, ~10460353203/7040000000 | : mapping generators: ~2, ~10460353203/7040000000 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.999{{c}}, ~10460353203/7040000000 = 685.567{{c}} | * [[WE]]: ~2 = 1199.999{{c}}, ~10460353203/7040000000 = 685.567{{c}}{{confirm}} | ||
: [[error map]]: {{val| -0.001 -0.001 -0.002 -0.017 -0.024 0.122 | : [[error map]]: {{val| -0.001 -0.001 -0.002 -0.017 -0.024 0.122 }} | ||
* [[CWE]]: ~2 = 1200.000{{c}}, ~10460353203/7040000000 = 685.568{{c}} | * [[CWE]]: ~2 = 1200.000{{c}}, ~10460353203/7040000000 = 685.568{{c}}{{confirm}} | ||
: error map: {{val|0.000 0.000 -0.001 -0.014 -0.023 0.125 }} | : error map: {{val|0.000 0.000 -0.001 -0.014 -0.023 0.125 }} | ||
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[[Badness]] (Sintel): 0.655 | [[Badness]] (Sintel): 0.655 | ||
[[Category:Catalogs of subgroup temperaments]] | |||
[[Category:Catalogs of rank-2 temperaments]] | |||