26th-octave temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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 546edo).
Bosonic
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
Optimal tunings (POTE): ~36/35 = 46.154 ¢, ~3/2 = 701.250 ¢
Optimal ET sequence: 26, 130, 546, 676, 806c
Badness (Smith): 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]]
Optimal tuning (POTE): ~36/35 = 46.154 ¢, ~3/2 = 701.559 ¢
Optimal ET sequence: 26, 104c, 130
Badness (Smith): 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]]
Optimal tuning (POTE): ~36/35 = 46.154 ¢, ~3/2 = 701.546 ¢
Optimal ET sequence: 26, 104c, 130
Badness (Smith): 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]]
Optimal tuning (POTE): ~36/35 = 46.154 ¢, ~3/2 = 701.077 ¢
Optimal ET sequence: 130, 286, 416, 546, 1508bcd
Badness (Smith): 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]]
Optimal tuning (POTE): ~36/35 = 46.154 ¢, ~3/2 = 701.038 ¢
Optimal ET sequence: 130, 286, 416, 546, 962bf
Badness (Smith): 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, ~3/2
Optimal tunings (CTE): ~17280/16807 = 46.154 ¢, ~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]]
Optimal tuning (CTE): ~77/75 = 46.154 ¢, ~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]]
Optimal tuning (CTE): ~77/75 = 46.154 ¢, ~3/2 = 702.018 ¢