26th-octave temperaments
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All temperaments on this page have a period that is 1/26th of an octave. However, the [-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 ([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 26, 130, 286 or 546 EDO).
Bosonic
- See also: High badness temperaments #Tridecatonic
Subgroup: 2.3.5.7
Comma list: 321489/320000, 589824/588245
Mapping: [⟨26 0 -22 73], ⟨0 1 2 0]]
Mapping generators: ~36/35, ~3
Wedgie: ⟨⟨26 52 0 22 -73 -146]]
POTE generator: ~3/2 = 701.250
Optimal ET sequence: 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: [⟨26 0 -22 73 90], ⟨0 1 2 0 0]]
POTE generator: ~3/2 = 701.559
Optimal ET sequence: 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: [⟨26 0 -22 73 90 55], ⟨0 1 2 0 0 1]]
POTE generator: ~3/2 = 701.546
Optimal ET sequence: 26, 104c, 130
Badness: 0.032946
Fermionic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 78408/78125, 177147/176000
Mapping: [⟨26 0 -22 73 -116], ⟨0 1 2 0 5]]
POTE generator: ~3/2 = 701.077
Optimal ET sequence: 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: [⟨26 0 -22 73 -116 55], ⟨0 1 2 0 5 1]]
POTE generator: ~3/2 = 701.038
Optimal ET sequence: 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: [⟨26 26 106 73], ⟨0 1 -3 0]]
Mapping generators: ~17280/16807 = 1\26, ~3/2 = 702.017
Optimal tuning (CTE): ~3/2 = 702.017
Optimal ET sequence: 130, 364, 494, 624, ...
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 131072/130977, 759375/758912
Mapping: [⟨26 26 106 73 166], ⟨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: 130, 364, 494, 624, ...
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 4096/4095, 91125/91091
Mapping: [⟨26 26 106 73 166 81]], ⟨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: 130, 364, 494, 624, ...