13th-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.
A 13th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 13. Although 13edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are.
Aluminium
- For extensions, see Ragismic microtemperaments #Aluminium.
Aluminium tempers out [92 -39 -13⟩ in the 5-limit, and sets 135/128 to 1/13 of an octave.
Subgroup: 2.3.5
Comma list: [92 -39 -13⟩
Mapping: [⟨13 0 92], ⟨0 1 -3]]
- mapping generators: ~135/128, ~3
- WE: ~135/128 = 92.3068 ¢, ~3/2 = 701.9791 ¢
- error map: ⟨-0.012 +0.012 +0.009]
- CWE: ~135/128 = 92.3077 ¢, ~3/2 = 701.9897 ¢
- error map: ⟨0.000 +0.032 +0.033]
Optimal ET sequence: 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc
Badness (Sintel): 2.89
Tridecatonic
- For extensions, see Octagar temperaments #Tridecatonic, Ragismic microtemperaments #Trideci, and Varunismic temperaments #Bosonic.
Tridecatonic tempers out the devil's tridecalimma, the comma which associates the 10/9 minor tone with 2\13.
Subgroup: 2.3.5
Comma list: [-11 26 -13⟩
Mapping: [⟨13 0 -11], ⟨0 1 2]]
- mapping generators: ~531441/500000, ~3
- WE: ~531441/500000 = 92.3166 ¢, ~3/2 = 701.2353 ¢
- error map: ⟨+0.116 -0.688 +0.737]
- CWE: ~531441/500000 = 92.3077 ¢, ~3/2 = 701.2353 ¢
- error map: ⟨0.000 -0.797 +0.617]
Optimal ET sequence: 26, 39, 65, 286, 351, 416, 481, 546
Badness (Sintel): 10.3
Triskaidekic
- For extensions, see Orwellismic temperaments #Triskaidekic.
Subgroup: 2.3.5
Comma list: 1220703125/1073741824
Mapping: [⟨13 0 30], ⟨0 1 0]]
- Mapping generators: ~128/125, ~3
- WE: ~128/125 = 92.589 ¢, ~3/2 = 698.263 ¢
- error map: ⟨+3.656 -0.036 -8.647]
- CWE: ~128/125 = 92.308 ¢, ~3/2 = 698.068 ¢
- error map: ⟨0.000 -3.887 -17.083]
Optimal ET sequence: 13, 26, 91cc
Badness (Sintel): 52.6