# 13th-octave temperaments

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**Fractional-octave temperaments**

← 12th-octave temperaments 13th-octave temperaments 14th-octave temperaments →

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