13th-octave temperaments
Although 13edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.
Discussed elsewhere are:
- Aluminium, → Ragismic microtemperaments, which is notable as 135/128 is a semiconvergent to 1\13 as well as a 5-limit interval.
Tridecatonic
- See also: Octagar temperaments #Tridecatonic, Ragismic microtemperaments #Trideci, and 26th-octave temperaments
Tridecatonic tempers out the devil's tridecalimma, the comma which associates the 10/9 minor tone with 2 steps of 13edo.
Subgroup: 2.3.5
Comma: 2541865828329/2500000000000
Mapping: [⟨13 21 31], ⟨0 -1 -2]]
POTE generator: ~3/2 = 701.0837
Optimal ET sequence: 26, 39, 65, 286, 351, 416, 481, 546
Badness: 0.437494