26th-octave temperaments

Fractional-octave temperaments

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← 25th-octave • 26th-octave • 27th-octave →

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, ...