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| All temperaments on this page have a period that is 1/26th of an octave. However, the {{monzo| -41 26 }} comma is not tempered out. Thus the 3/2 is not that of [[26edo]]. However, 7/4 is, as is 11/8 in the bosonic temperaments. | | All temperaments on this page have a period that is 1/26th of an octave. However, the {{monzo| -41 26 }} comma is not tempered out. Thus the 3/2 is not that of [[26edo]]. However, 7/4 is, as is 11/8 in the bosonic temperaments. |
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| 26edo is very accurate for 7th harmonic, the [[26-7-comma]] ({{monzo| 73 0 0 -26 }}, the amount by which 26 septimal whole tones ([[8/7]]) exceed 5 octaves) is tempered out by 26-fold multiple edos up to 1456 (such as [[26edo|26-]], [[130edo|130-]], [[286edo|286-]] or [[546edo|546edo]]). | | 26edo is very accurate for 7th harmonic, the [[26-7-comma]] ({{monzo| 73 0 0 -26 }}, the amount by which 26 septimal whole tones ([[8/7]]) exceed 5 octaves) is tempered out by 26-fold multiple edos up to 1456 (such as [[26edo|26-]], [[130edo|130-]], [[286edo|286-]] or [[546edo|546edo]]). |
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| == Bosonic ==
| | Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron. |
| : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tridecatonic]].''
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 321489/320000, 589824/588245
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| {{Mapping|legend=1| 26 0 -22 73 | 0 1 2 0 }}
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| : mapping generators: ~36/35, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~36/35 = 46.1534{{c}}, ~3/2 = 701.2433{{c}}
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| : [[error map]]: {{val| -0.012 -0.723 +0.775 +0.372 }}
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| * [[CWE]]: ~36/35 = 46.1538{{c}}, ~3/2 = 701.2451{{c}}
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| : error map: {{val| 0.000 -0.710 +0.792 +0.405 }}
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| {{Optimal ET sequence|legend=1| 26, …, 104c, 130, 546, 676, 806c }}
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| [[Badness]] (Sintel): 3.94
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 441/440, 8019/8000, 65536/65219
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| Mapping: {{mapping| 26 0 -22 73 90 | 0 1 2 0 0 }}
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| Optimal tunings:
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| * WE: ~36/35 = 46.1443{{c}}, ~3/2 = 701.4143{{c}}
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| * CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.4791{{c}}
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| {{Optimal ET sequence|legend=0| 26, …, 104c, 130 }}
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| Badness (Sintel): 2.16
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 351/350, 364/363, 441/440, 15379/15360
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| Mapping: {{mapping| 26 0 -22 73 90 55 | 0 1 2 0 0 1 }}
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| Optimal tunings:
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| * WE: ~36/35 = 46.1469{{c}}, ~3/2 = 701.4410{{c}}
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| * CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.4873{{c}}
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| {{Optimal ET sequence|legend=0| 26, …, 104c, 130 }}
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| Badness (Sintel): 1.36
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| === Fermionic ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 540/539, 78408/78125, 177147/176000
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| Mapping: {{mapping| 26 0 -22 73 -116 | 0 1 2 0 5 }}
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| Optimal tunings:
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| * WE: ~36/35 = 46.1550{{c}}, ~3/2 = 701.0945{{c}}
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| * CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.0853{{c}}
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| {{Optimal ET sequence|legend=0| 130, 286, 416, 546 }}
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| Badness (Sintel): 3.00
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 351/350, 540/539, 40656/40625, 142884/142805
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| Mapping: {{mapping| 26 0 -22 73 -116 55 | 0 1 2 0 5 1 }}
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| Optimal tunings:
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| * WE: ~36/35 = 46.1573{{c}}, ~3/2 = 701.0904{{c}}
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| * CWE: ~36/35 = 46.1538{{c}}, ~3/2 = 701.0603{{c}}
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| {{Optimal ET sequence|legend=0| 130, 286, 416, 546 }}
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| Badness (Sintel): 1.80
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| == Iron == | | == Iron == |