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33rd-octave temperaments

Revision as of 02:39, 4 July 2026 by Xenllium (talk | contribs) (Created page with "{{Infobox fractional-octave|33}} 33edo might not be immediately recognizable for fractional-octave potential, but its step is in direct proximity to 48/47. == Arsenic == Arsenic is named after the 33rd chemical element. Conceptualized as a no-threes subgroup temperament. Subgroup: 2.11.13.17.19 Comma list: 2432/2431, 7086244/7054567, 33698267/33554432 {{Mapping|legend=2| 33 0 8 249 26 | 0 1 1 -1 1 }} : mapping generators: ~247/242, ~11 Optimal tun...")
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33edo might not be immediately recognizable for fractional-octave potential, but its step is in direct proximity to 48/47.

Arsenic

Arsenic is named after the 33rd chemical element. Conceptualized as a no-threes subgroup temperament.

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:

  • CTE: ~247/242 = 36.3636¢ (1 ⧵ 33), ~11/8 = 550.632¢
  • CWE: ~247/242 = 36.3636¢ (1 ⧵ 33), ~11/8 = 550.419¢

Optimal ET sequence: 33, 132fg, 165, 198, 231

Badness (Sintel): 2.300

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