26th-octave temperaments: Difference between revisions
No edit summary |
mNo edit summary |
||
| Line 1: | Line 1: | ||
All temperaments on this page have a period that is 1/26th of an octave, i.e. their [[pergen]] is (P8/26, P5). However, the {{monzo|-41 26}} comma is not tempered out. Thus the 3/2 is not | All temperaments on this page have a period that is 1/26th of an octave, i.e. their [[pergen]] is (P8/26, P5). However, the {{monzo|-41 26}} comma is not tempered out. Thus the 3/2 is not [[26EDO]]'s 3/2. However, 7/4 is, as is 11/8 in the Bosonic temperaments. | ||
== Bosonic == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 321489/320000, 589824/588245 | [[Comma list]]: 321489/320000, 589824/588245 | ||
| Line 14: | Line 16: | ||
[[Badness]]: 0.155827 | [[Badness]]: 0.155827 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 8019/8000, 65536/65219 | Comma list: 441/440, 8019/8000, 65536/65219 | ||
| Line 25: | Line 29: | ||
Badness: 0.065219 | Badness: 0.065219 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 364/363, 441/440, 15379/15360 | Comma list: 351/350, 364/363, 441/440, 15379/15360 | ||
| Line 36: | Line 42: | ||
Badness: 0.032946 | Badness: 0.032946 | ||
= Fermionic = | == Fermionic == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 78408/78125, 177147/176000 | Comma list: 540/539, 78408/78125, 177147/176000 | ||
| Line 47: | Line 55: | ||
Badness: 0.090642 | Badness: 0.090642 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 540/539, 40656/40625, 142884/142805 | Comma list: 351/350, 540/539, 40656/40625, 142884/142805 | ||
| Line 58: | Line 68: | ||
Badness: 0.043581 | Badness: 0.043581 | ||
[[Category:26edo]] | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Temperament collection]] | [[Category:Temperament collection]] | ||
Revision as of 22:31, 11 June 2021
All temperaments on this page have a period that is 1/26th of an octave, i.e. their pergen is (P8/26, P5). However, the [-41 26⟩ comma is not tempered out. Thus the 3/2 is not 26EDO's 3/2. However, 7/4 is, as is 11/8 in the Bosonic temperaments.
Bosonic
Subgroup: 2.3.5.7
Comma list: 321489/320000, 589824/588245
Mapping: [⟨26 0 -22 73], ⟨0 1 2 0]]
Wedgie: ⟨⟨ 26 52 0 22 -73 -146 ]]
POTE generator: ~3/2 = 701.250
Badness: 0.155827
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 65536/65219
Mapping: [⟨26 0 -22 73 90], ⟨0 1 2 0 0]]
POTE generator: ~3/2 = 701.559
Vals: Template:Val list
Badness: 0.065219
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 15379/15360
Mapping: [⟨26 0 -22 73 90 55], ⟨0 1 2 0 0 1]]
POTE generator: ~3/2 = 701.546
Vals: Template:Val list
Badness: 0.032946
Fermionic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 78408/78125, 177147/176000
Mapping: [⟨26 0 -22 73 -116], ⟨0 1 2 0 5]]
POTE generator: ~3/2 = 701.077
Vals: Template:Val list
Badness: 0.090642
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 40656/40625, 142884/142805
Mapping: [⟨26 0 -22 73 -116 55], ⟨0 1 2 0 5 1]]
POTE generator: ~3/2 = 701.038
Vals: Template:Val list
Badness: 0.043581