24th-octave temperaments

Fractional-octave temperaments

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← 23rd-octave • 24th-octave • 25th-octave →

24edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.

Temperaments discussed elswhere include:

• Hours → Compton family
• Rabic → Rastmic rank-3 clan

Chromium (5-limit)

Main article: Chromium

For extensions, see Landscape microtemperaments #Chromium.

The chromium temperament is defined by equating a stack of twenty-four porcupine commas with the octave.

Subgroup: 2.3.5

Comma list: [-23 120 -72⟩

Mapping: [⟨24 1 -6], ⟨0 3 5]]

mapping generators: ~250/243, ~[-8 42 -25⟩

Optimal tunings:

• WE: ~250/243 = 50.0000 ¢, ~[-8 42 -25⟩ = 617.2852 ¢

error map: ⟨+0.007 -0.093 +0.120]

• CWE: ~250/243 = 50.0000 ¢, ~[-8 42 -25⟩ = 617.2852 ¢

error map: ⟨0.000 -0.099 +0.112]

Optimal ET sequence: 72, …, 480, 552, 624, 1320, 1944

Badness (Sintel): 169