18edo

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18edo, or 18 equal divisions of the octave, is the equal tuning featuring steps of (1200/18) ~= 66.7 cents, 18 of which stack to the octave 2/1.

With the sharp fifth 733.3c and the flat fifth 666.7c almost equally detuned from the just fifth, 18edo is often considered the quintessential straddle-3 edo and the straddle-3 version of 12edo. It does not approximate low harmonics well, except 9 and debatably 5; it is also straddle-7, 13, 17, and 19.

Scales

• Straddle-3 diatonic (5L1m1s), 3331332 or 3332331, constructed by an alternating stack of flat and sharp fifths
• Oneirotonic (5L3s), 33133131 (compressed 17edo diatonic)
• Smitonic (4L3s), 3323232 (stretched 19edo diatonic)
• Taric (8L2s), 2222122221 and the altered MOS pentachordal taric, 2221222221
• Hexawood (6L6s) is a "straddle-3 chromatic scale", constructed by an alternating stack of flat and sharp fifths

DR theory

18edo has the following approximate DR chords (below 10c pairwise logarithmic least-squares error, bounding interval < 1200c, no 1\18 or 17\18):

+1+1

• [0 8 14]\18 (error 6.3c)
• [0 6 11]\18 (error 7.3c)

+1+2

• [0 6 15]\18 (error 1.3c)
• [0 3 8]\18 (error 4.8c)
• [0 5 13]\18 (error 8.6c)

+2+1

• [0 7 10]\18 (error 6.8c)
• [0 11 15]\18 (error 9.5c)

+1+?+1

• [0 4 8 11]\18 (error 0.2c)
• [0 3 11 13]\18 (error 0.2c)
• [0 7 10 15]\18 (error 3.3c)
• [0 6 12 16]\18 (error 5.2c)
• [0 6 11 15]\18 (error 6.8c)
• [0 5 7 11]\18 (error 7.8c)
• [0 4 7 10]\18 (error 8.6c)
• [0 4 9 12]\18 (error 8.8c)