26th-octave temperaments: Difference between revisions

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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.

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]]).

The [[26-comma]], {{monzo| -41 26 }}, is technically usable for regular temperament purposes, however it makes a very imprecise temperament, only supported by 26edo itself and [[52edo]]. Thus, 26th-octave temperaments which are of musical interest typically do not inherit the flattone approximation of 3/2 which is found in [[26edo]].

However, 7/4 is frequently inherited, as 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]]).

Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.

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

~~Mapping:~~ {{~~mapping~~| 26 0 184 73 296 | 0 1 -3 0 -5 }}

Optimal tunings:

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

~~Mapping:~~ {{~~mapping~~| 26 0 184 73 296 55 | 0 1 -3 0 -5 1 }}

Optimal tunings:

@@ Line 1: / Line 1: @@
 {{Technical data page}}
 {{Infobox fractional-octave|26}}
-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.
-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|546edo]]).
+The [[26-comma]], {{monzo| -41 26 }}, is technically usable for regular temperament purposes, however it makes a very imprecise temperament, only supported by 26edo itself and [[52edo]]. Thus, 26th-octave temperaments which are of musical interest typically do not inherit the flattone approximation of 3/2 which is found in [[26edo]].
+However, 7/4 is frequently inherited, as 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]]).
 Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.
@@ Line 32: / Line 34: @@
 Comma list: 9801/9800, 131072/130977, 759375/758912
-Mapping: {{mapping| 26 0 184 73 296 | 0 1 -3 0 -5 }}
+{{Mapping|legend=0| 26 0 184 73 296 | 0 1 -3 0 -5 }}
 Optimal tunings:
@@ Line 47: / Line 49: @@
 Comma list: 1716/1715, 2080/2079, 4096/4095, 91125/91091
-Mapping: {{mapping| 26 0 184 73 296 55 | 0 1 -3 0 -5 1 }}
+{{Mapping|legend=0| 26 0 184 73 296 55 | 0 1 -3 0 -5 1 }}
 Optimal tunings:

26th-octave temperaments: Difference between revisions

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