26th-octave temperaments

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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 [-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 GPV sequence26, 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 GPV 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 GPV 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 GPV 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 GPV sequence: 130, 286, 416, 546, 962bf

Badness: 0.043581