10edo

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10edo, or 10 equal divisions of the octave, is the equal tuning featuring steps of (1200/10) = 120 cents, 10 of which stack to the perfect octave 2/1. It is notable for its good approximation of the 2.7.13 subgroup and for being possibly the smallest edo in the same class as 12edo.

Theory

Chords

See also: Oneirotonic#Chords_of_oneirotonic

Detempers

Due to its small size and unique melodic character, it is very easy to detemper 10edo. Example tunings are shown in parenthesis.

Full octave, neutral third generator

• Sharp (13\43), 3L7s
  • Mainly oneirotonic fifth
  • Good approximation of 19:22:25:27:29
  • Similar to Submajor/Interpental temperament
• Flat (11\37), 7L3s
  • Mainly diatonic fifth
  • General 13-limit, especially 2.7.13

Half octave, fifth generator

• Flat (3\32)
  • Mainly diatonic fifth
  • Oceanfront temperament with added 17/14
• Sharp (4\38)
  • Mainly oneirotonic fifth