24th-octave temperaments: Difference between revisions
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== Chromium (5-limit) == | == Chromium (5-limit) == | ||
{{Main|Chromium}} | {{Main| Chromium }} | ||
: ''For extensions, see [[Landscape microtemperaments #Chromium]].'' | |||
The chromium temperament is defined by equating a stack of twenty-four [[250/243|porcupine commas]] with the octave. | |||
[[Subgroup]]: 2.3.5 | |||
{{ | [[Comma list]]: {{monzo| -23 120 -72 }} | ||
: mapping generators: ~ | {{mapping|legend=1| 24 1 -6 | 0 3 5 }} | ||
: mapping generators: ~250/243, ~{{monzo| -8 42 -25 }} | |||
[[ | [[Optimal tuning]]s: | ||
* [[WE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}} | |||
: [[error map]]: {{val| +0.007 -0.093 +0.120 }} | |||
* [[CWE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}} | |||
: error map: {{val| 0.000 -0.099 +0.112 }} | |||
Badness: | {{Optimal ET sequence|legend=1| 72, …, 480, 552, 624, 1320, 1944 }} | ||
[[Badness]] (Sintel): 169 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
Latest revision as of 11:47, 15 May 2026
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:
Chromium (5-limit)
- 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⟩
- 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