26th-octave temperaments: Difference between revisions
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All temperaments on this page have a period that is [[Fractional-octave temperaments|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 | All temperaments on this page have a period that is [[Fractional-octave temperaments|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 == | == Bosonic == | ||
{{ | {{See also| High badness temperaments #Tridecatonic }} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Comma list]]: 321489/320000, 589824/588245 | [[Comma list]]: 321489/320000, 589824/588245 | ||
[[Mapping]]: [{{val|26 0 -22 73}}, {{val|0 1 2 0}}] | [[Mapping]]: [{{val| 26 0 -22 73 }}, {{val| 0 1 2 0 }}] | ||
Mapping generators: ~36/35, ~3 | Mapping generators: ~36/35, ~3 | ||
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Comma list: 441/440, 8019/8000, 65536/65219 | Comma list: 441/440, 8019/8000, 65536/65219 | ||
Mapping: [{{val|26 0 -22 73 90}}, {{val|0 1 2 0 0}}] | Mapping: [{{val| 26 0 -22 73 90 }}, {{val| 0 1 2 0 0 }}] | ||
POTE generator: ~3/2 = 701.559 | POTE generator: ~3/2 = 701.559 | ||
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Badness: 0.065219 | Badness: 0.065219 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | 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 | ||
Mapping: [{{val|26 0 -22 73 90 55}}, {{val|0 1 2 0 0 1}}] | Mapping: [{{val| 26 0 -22 73 90 55 }}, {{val| 0 1 2 0 0 1 }}] | ||
POTE generator: ~3/2 = 701.546 | POTE generator: ~3/2 = 701.546 | ||
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Badness: 0.032946 | Badness: 0.032946 | ||
== Fermionic == | === Fermionic === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 540/539, 78408/78125, 177147/176000 | Comma list: 540/539, 78408/78125, 177147/176000 | ||
Mapping: [{{val|26 0 -22 73 -116}}, {{val|0 1 2 0 5}}] | Mapping: [{{val| 26 0 -22 73 -116 }}, {{val| 0 1 2 0 5 }}] | ||
POTE generator: ~3/2 = 701.077 | POTE generator: ~3/2 = 701.077 | ||
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Badness: 0.090642 | Badness: 0.090642 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | 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 | ||
Mapping: [{{val|26 0 -22 73 -116 55}}, {{val|0 1 2 0 5 1}}] | Mapping: [{{val| 26 0 -22 73 -116 55 }}, {{val| 0 1 2 0 5 1 }}] | ||
POTE generator: ~3/2 = 701.038 | POTE generator: ~3/2 = 701.038 | ||
Revision as of 16:05, 8 January 2022
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]]
Mapping generators: ~36/35, ~3
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