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]] | {{Technical data page}} | ||
{{Infobox fractional-octave|26}} | |||
All temperaments on this page have a period that is [[Fractional-octave temperaments|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. | |||
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|546]] EDO). | 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|546]] EDO). | ||
== Bosonic == | == Bosonic == | ||
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Mapping generators: ~36/35, ~3 | Mapping generators: ~36/35, ~3 | ||
[[POTE generator]]: ~3/2 = 701.250 | [[POTE generator]]: ~3/2 = 701.250 | ||
{{ | {{Optimal ET sequence|legend=1| 26, 130, 546, 676, 806c }} | ||
[[Badness]]: 0.155827 | [[Badness]]: 0.155827 | ||
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POTE generator: ~3/2 = 701.559 | POTE generator: ~3/2 = 701.559 | ||
Optimal | {{Optimal ET sequence|legend=1| 26, 104c, 130 }} | ||
Badness: 0.065219 | Badness: 0.065219 | ||
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POTE generator: ~3/2 = 701.546 | POTE generator: ~3/2 = 701.546 | ||
Optimal | {{Optimal ET sequence|legend=1| 26, 104c, 130 }} | ||
Badness: 0.032946 | Badness: 0.032946 | ||
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POTE generator: ~3/2 = 701.077 | POTE generator: ~3/2 = 701.077 | ||
Optimal | {{Optimal ET sequence|legend=1| 130, 286, 416, 546, 1508bcd }} | ||
Badness: 0.090642 | Badness: 0.090642 | ||
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POTE generator: ~3/2 = 701.038 | POTE generator: ~3/2 = 701.038 | ||
Optimal | {{Optimal ET sequence|legend=1| 130, 286, 416, 546, 962bf }} | ||
Badness: 0.043581 | Badness: 0.043581 | ||
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[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.017 | [[Optimal tuning]] ([[CTE]]): ~3/2 = 702.017 | ||
{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ... | |||
=== 11-limit === | === 11-limit === | ||
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Optimal tuning (CTE): ~3/2 = 702.017 | Optimal tuning (CTE): ~3/2 = 702.017 | ||
{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ... | |||
=== 13-limit === | === 13-limit === | ||
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Optimal tuning (CTE): ~3/2 = 702.018 | Optimal tuning (CTE): ~3/2 = 702.018 | ||
{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ... | |||
{{Navbox fractional-octave}} | |||
[[Category:26edo]] | [[Category:26edo]] | ||