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, 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.
+{{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).
 == 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]]: [{{val| 26 0 -22 73 }}, {{val| 0 1 2 0 }}]
-{{Multival|legend=1|26 52 0 22 -73 -146}}
+Mapping generators: ~36/35, ~3
 [[POTE generator]]: ~3/2 = 701.250
-{{Val list|legend=1| 26, 130, 546, 676, 806c }}
+{{Optimal ET sequence|legend=1| 26, 130, 546, 676, 806c }}
 [[Badness]]: 0.155827
@@ Line 21: / Line 27: @@
 Comma list: 441/440, 8019/8000, 65536/65219
-Mapping: [{{val|26 0 -22 73 90}}, {{val|0 1 2 0 0}}]
+Mapping: [{{val| 26 0 -22 73 90 }}, {{val| 0 1 2 0 0 }}]
 POTE generator: ~3/2 = 701.559
-Vals: {{Val list| 26, 104c, 130 }}
+{{Optimal ET sequence|legend=1| 26, 104c, 130 }}
 Badness: 0.065219
-=== 13-limit ===
+==== 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}}]
+Mapping: [{{val| 26 0 -22 73 90 55 }}, {{val| 0 1 2 0 0 1 }}]
 POTE generator: ~3/2 = 701.546
-Vals: {{Val list| 26, 104c, 130 }}
+{{Optimal ET sequence|legend=1| 26, 104c, 130 }}
 Badness: 0.032946
-== Fermionic ==
+=== 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}}]
+Mapping: [{{val| 26 0 -22 73 -116 }}, {{val| 0 1 2 0 5 }}]
 POTE generator: ~3/2 = 701.077
-Vals: {{Val list| 130, 286, 416, 546, 1508bcd }}
+{{Optimal ET sequence|legend=1| 130, 286, 416, 546, 1508bcd }}
 Badness: 0.090642
-=== 13-limit ===
+==== 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}}]
+Mapping: [{{val| 26 0 -22 73 -116 55 }}, {{val| 0 1 2 0 5 1 }}]
 POTE generator: ~3/2 = 701.038
-Vals: {{Val list| 130, 286, 416, 546, 962bf }}
+{{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]]
-[[Category:Temperament]]
-[[Category:Temperament collection]]