Irrational-subgroup temperaments: Difference between revisions
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This page is a list of temperaments which have an irrational subgroup that cannot be expressed in surds. | This page is a list of temperaments which have an irrational subgroup that cannot be expressed in surds. | ||
==Polyraider== | == 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. | ||
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[[Badness]] (Sintel): 0.655 | [[Badness]] (Sintel): 0.655 | ||
[[Category:Catalogs of subgroup temperaments]] | |||
[[Category:Catalogs of rank-2 temperaments]] | |||
Revision as of 09:27, 17 October 2026
This page is a list of temperaments which have an irrational subgroup that cannot be expressed in surds.
Polyraider
The temperament below can also be written with 34ed30 nominals and cent-deviation (1\1171) accidentals. This temperament was found by 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.f2.f3 where f2, f3 are the second and third modes of an ideal unsupported bar.
Comma list: 1771561/1771470, 1310730070806386550964611/1310720000000000000000000, [-8 6 -3 2 -1 0>, [-11 10 -7 4 0 -1>
Mapping: [⟨1 65 172 148 162 27], ⟨0 −111 −297 −253 −281 −43]]
- mapping generators: ~2, ~10460353203/7040000000
- WE: ~2 = 1199.999 ¢, ~10460353203/7040000000 = 685.567 ¢
- error map: ⟨-0.001 -0.001 -0.002 -0.017 -0.024 0.122]
- CWE: ~2 = 1200.000 ¢, ~10460353203/7040000000 = 685.568 ¢
- error map: ⟨0.000 0.000 -0.001 -0.014 -0.023 0.125]
Optimal ET sequence: 7, 1164, 1171, 1178, 1185, 2335, 2349, 3506, 3520, 3527, 4691
Badness (Sintel): 0.655