400th-octave temperaments

Fractional-octave temperaments

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Centismic

Main article: Centisma

Centismic maps 289/288 into 1\200, and tritones 24/17 and 17/12 respectively into 597 and 603 cents exactly.

Subgroup: 2.3.5.7.11.13.17

Comma list: [-1001 -400 0 0 0 0 400⟩

Mapping: [⟨400 0 0 0 0 0 1001], ⟨0 1 0 0 0 0 1], ⟨0 0 1 0 0 0 0], ⟨0 0 0 1 0 0 0]]

mapping generators: ~[498 199 -199⟩ = 1\400, ~3, ~5, ~7, ~11, ~13

Supporting ETs: 400, 13400, ...

Centic

Subgroup: 2.3.17

Comma list: [-1001 -400 0 0 0 0 400⟩

Sval mapping: [⟨400 0 1001], ⟨0 1 1]]

mapping generators: ~[498 199 -199⟩ = 1\400, ~3,

Supporting ETs: 400, 13400, ...