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 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 [[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 ==

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Mapping generators: ~36/35, ~3

~~{{Multival|legend=1|26 52 0 22 -73 -146}}~~

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

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

~~Vals:~~ {{~~EDOs~~|130, 364, 494, 624}}, ...

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

=== 11-limit ===

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

~~Vals:~~ 130, 364, 494, 624, ...

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

=== 13-limit ===

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Optimal tuning (CTE): ~3/2 = 702.018

~~Vals:~~ 130, 364, 494, 624,...

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

[[Category:26edo]]

~~[[Category:Temperament collections]]~~

~~[[Category:Rank 2]]~~

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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 that of [[26edo]]. However, 7/4 is, as is 11/8 in the Bosonic 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.
-edo 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).
+edo 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 ==
@@ Line 13: / Line 15: @@
 Mapping generators: ~36/35, ~3
-{{Multival|legend=1|26 52 0 22 -73 -146}}
 [[POTE generator]]: ~3/2 = 701.250
@@ Line 87: / Line 87: @@
 [[Optimal tuning]] ([[CTE]]):  ~3/2 = 702.017
-Vals: {{EDOs|130, 364, 494, 624}}, ...
+{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ...
 === 11-limit ===
@@ Line 100: / Line 100: @@
 Optimal tuning (CTE):  ~3/2 = 702.017
-Vals: 130, 364, 494, 624, ...
+{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ...
 === 13-limit ===
@@ Line 113: / Line 113: @@
 Optimal tuning (CTE):  ~3/2 = 702.018
-Vals: 130, 364, 494, 624,...
+{{Optimal ET sequence|legend=1|130, 364, 494, 624}}, ...
+{{Navbox fractional-octave}}
 [[Category:26edo]]
-[[Category:Temperament collections]]
-[[Category:Rank 2]]