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 [[26edo]]~~'s 3/2~~. 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]], 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.

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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POTE generator: ~3/2 = 701.559

~~Vals~~: {{Val list| 26, 104c, 130 }}

Optimal GPV sequence: {{Val list| 26, 104c, 130 }}

Badness: 0.065219

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POTE generator: ~3/2 = 701.546

~~Vals~~: {{Val list| 26, 104c, 130 }}

Optimal GPV sequence: {{Val list| 26, 104c, 130 }}

Badness: 0.032946

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POTE generator: ~3/2 = 701.077

~~Vals~~: {{Val list| 130, 286, 416, 546, 1508bcd }}

Optimal GPV sequence: {{Val list| 130, 286, 416, 546, 1508bcd }}

Badness: 0.090642

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POTE generator: ~3/2 = 701.038

~~Vals~~: {{Val list| 130, 286, 416, 546, 962bf }}

Optimal GPV sequence: {{Val list| 130, 286, 416, 546, 962bf }}

Badness: 0.043581

@@ Line 1: / Line 1: @@
-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 [[26edo]]'s 3/2. 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]], 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.
+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 29: / Line 31: @@
 POTE generator: ~3/2 = 701.559
-Vals: {{Val list| 26, 104c, 130 }}
+Optimal GPV sequence: {{Val list| 26, 104c, 130 }}
 Badness: 0.065219
@@ Line 42: / Line 44: @@
 POTE generator: ~3/2 = 701.546
-Vals: {{Val list| 26, 104c, 130 }}
+Optimal GPV sequence: {{Val list| 26, 104c, 130 }}
 Badness: 0.032946
@@ Line 55: / Line 57: @@
 POTE generator: ~3/2 = 701.077
-Vals: {{Val list| 130, 286, 416, 546, 1508bcd }}
+Optimal GPV sequence: {{Val list| 130, 286, 416, 546, 1508bcd }}
 Badness: 0.090642
@@ Line 68: / Line 70: @@
 POTE generator: ~3/2 = 701.038
-Vals: {{Val list| 130, 286, 416, 546, 962bf }}
+Optimal GPV sequence: {{Val list| 130, 286, 416, 546, 962bf }}
 Badness: 0.043581