8th-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.

Fractional-octave temperaments

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← 7th-octave • 8th-octave • 9th-octave →

An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.

Temperaments discussed elsewhere include:

• Octant → Schismatic family
• Octoid → Ragismic microtemperaments

Octatonic

12/11 is very close to 1 step of 8edo, and hence this temperament tempers out the undecimal octatonic comma, the difference between a stack of eight 12/11's and the octave.

Subgroup: 2.3.11

Comma list: 214990848/214358881

Subgroup-val mapping: [⟨8 0 15], ⟨0 1 1]]

mapping generators: ~12/11, ~3

Optimal tunings:

• WE: ~12/11 = 149.9917 ¢, ~3/2 = 701.9324 ¢

error map: ⟨-0.066 -0.089 +0.424]

• CWE: ~12/11 = 150.0000 ¢, ~3/2 = 701.9147 ¢

error map: ⟨0.000 -0.040 +0.597]

Optimal ET sequence: 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e

Badness (Sintel): 0.515