View source for 26th-octave temperaments

{{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).

== Bosonic ==
{{See also| High badness temperaments #Tridecatonic }}

Subgroup: 2.3.5.7

[[Comma list]]: 321489/320000, 589824/588245

[[Mapping]]: [{{val| 26 0 -22 73 }}, {{val| 0 1 2 0 }}]

Mapping generators: ~36/35, ~3

[[POTE generator]]: ~3/2 = 701.250

{{Optimal ET sequence|legend=1| 26, 130, 546, 676, 806c }}

[[Badness]]: 0.155827

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 441/440, 8019/8000, 65536/65219

Mapping: [{{val| 26 0 -22 73 90 }}, {{val| 0 1 2 0 0 }}]

POTE generator: ~3/2 = 701.559

{{Optimal ET sequence|legend=1| 26, 104c, 130 }}

Badness: 0.065219

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

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 }}]

POTE generator: ~3/2 = 701.546

{{Optimal ET sequence|legend=1| 26, 104c, 130 }}

Badness: 0.032946

=== Fermionic ===
Subgroup: 2.3.5.7.11

Comma list: 540/539, 78408/78125, 177147/176000

Mapping: [{{val| 26 0 -22 73 -116 }}, {{val| 0 1 2 0 5 }}]

POTE generator: ~3/2 = 701.077

{{Optimal ET sequence|legend=1| 130, 286, 416, 546, 1508bcd }}

Badness: 0.090642

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

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 }}]

POTE generator: ~3/2 = 701.038

{{Optimal ET sequence|legend=1| 130, 286, 416, 546, 962bf }}

Badness: 0.043581

== Iron ==
''Iron'' is named after the 26th element.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 2460375/2458624, 2147483648/2144153025

[[Mapping]]: [{{val|26 26 106 73}}, {{val|0 1 -3 0}}]

[[Mapping]] [[generators]]: ~17280/16807 = 1\26, ~3/2 = 702.017

[[Optimal tuning]] ([[CTE]]):  ~3/2 = 702.017

{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ...

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977, 759375/758912

Mapping: [{{val|26 26 106 73 166}}, {{val|0 1 -3 0 -5}}]

Mapping generators: ~77/75 = 1\26, ~3/2 = 702.017

Optimal tuning (CTE):  ~3/2 = 702.017

{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ...

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 4096/4095, 91125/91091

Mapping: [{{val|26 26 106 73 166 81}}], {{val|0 1 -3 0 -5 1}}]

Mapping generators: ~77/75 = 1\26, ~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]]