665th-octave temperaments

Fractional-octave temperaments

---

← 664th-octave • 665th-octave • 666th-octave →

665edo is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. Satanic temperaments are a notable subset of 665th-octave temperaments which have a page of their own.

Satanic

Subgroup: 2.3.5

Comma list: [-1054 665⟩ (satanic comma)

Mapping: [⟨665 1054 0], ⟨0 0 1]]

Mapping generators: ~[485 -306⟩, ~5

Optimal tuning (CTE): ~[485 -306⟩ = 1＼665, ~5/4 = 386.31371386

Optimal ET sequence: 665, …, 4655, 5320, 5985, 6650, 7315, 7980, 24605, 32585

Badness: 0.935807

Monzosatanic

Subgroup: 2.3.5.7

Comma list: 19073486328125/19042491875328, 450359962737049600/450283905890997363

Mapping: [⟨665 1054 1544 0], ⟨0 0 0 1]]

Mapping generators: ~[485 -306⟩, ~7

Optimal tuning (CTE): ~[485 -306⟩ = 1＼665, ~7/4 = 968.826

Optimal ET sequence: 665, 3325, 3990, 4655c, 5320c, 5985c

Badness: 1.492380

Neosatanic

Subgroup: 2.3.5.7.13.17.19

Comma list: 4200/4199, 6860/6859, 285719/285610, 369664/369603, 781250/780759

Mapping: [⟨665 1054 1544 0 594 4585 958], ⟨0 0 0 1 1 -1 1]]

Mapping generators: ~[485 -306⟩, ~7

Optimal tuning (POTE): ~[485 -306⟩ = 1＼665, ~7/4 = 968.7358

Optimal ET sequence: 665, 3325, 3990