5th-octave temperaments: Difference between revisions
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Created page with "{{Fractional-octave navigation|5}} 5edo is the smallest xenharmonic system, as 1edo, 2edo, 3edo and 4edo are all subsets of 12edo. The most notable 5th-octave family..." |
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* [[Trisedodge family|Trisedodge temperaments]] | * [[Trisedodge family|Trisedodge temperaments]] | ||
== Pentonismic == | == Pentonismic (rank-5) == | ||
{{Main|Pentonisma}} | {{Main|Pentonisma}} | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 11:49, 26 August 2023
Template:Fractional-octave navigation 5edo is the smallest xenharmonic system, as 1edo, 2edo, 3edo and 4edo are all subsets of 12edo.
The most notable 5th-octave family is limmic temperaments - tempers out 256/243 and associates 3\5 to 3/2 as well as 1\5 to 9/8, producing temperaments like blackwood. Equally notable among small equal divisions are the cloudy temperaments - identifying 8/7 with one step of 5edo. Other families of 5-limit 5th-octave commas are:
- Pental temperaments - tempers out the [-28 25 -5⟩ comma which improves the 3/2 mapping for 5edo, producing a temperament with 3/2 as a generator and 1\5 as a period.
- Qintosec temperaments
- Trisedodge temperaments
Pentonismic (rank-5)
Subgroup: 2.3.5.7.11.13
Comma list: 281974669312/281950621875
Mapping: [⟨5 0 0 0 0 24], ⟨0 1 0 0 0 -1], ⟨0 0 1 0 0 -1], ⟨0 0 0 1 0 1]]
- mapping generators: ~224/195 = 1\5, ~3, ~5, ~7, ~11
Supporting ETs: 10, 50, 80, 120, 125, 270, 2000, 2460, 3125, 3395, 5585