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User:Eliora/33rd-octave temperaments

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Revision as of 20:28, 29 July 2026 by Eliora (talk | contribs) (Created page with "Arsenic is named after the 33rd element and was discovered by Xenllium in 2026. While its harmonics, 2.11.13.17.19, are a bit high - arsenic is of notably low complexity and can be reached with 66 or 99-tone MOS scales. It reaches 11th, 13th, 17th, 19th harmonics all in just one step. The 66-tone mos contains just 11, 13, 19, while the 99-tone mos adds 17. Subgroup: 2.11.13.17.19 Comma list: 2432/2431, 7086244/7054567, 33698267/33554432 {{Mapping|legend=2| 3...")
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Arsenic is named after the 33rd element and was discovered by Xenllium in 2026.

While its harmonics, 2.11.13.17.19, are a bit high - arsenic is of notably low complexity and can be reached with 66 or 99-tone MOS scales. It reaches 11th, 13th, 17th, 19th harmonics all in just one step. The 66-tone mos contains just 11, 13, 19, while the 99-tone mos adds 17.


Subgroup: 2.11.13.17.19

Comma list: 2432/2431, 7086244/7054567, 33698267/33554432

Subgroup-val mapping: [⟨33 0 8 249 26], ⟨0 1 1 -1 1]]

mapping generators: ~247/242, ~11

Optimal tunings:

  • WE: ~247/242 = 36.3676 ¢, ~11/8 = 550.4246 ¢
  • CWE: ~247/242 = 36.3636 ¢, ~11/8 = 550.4187 ¢

Optimal ET sequence: 33, 165, 198, 231, 495h

Badness (Sintel): 2.30

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