11edo

11edo, or 11 equal divisions of the octave, is the equal tuning featuring steps of (1200/11) ~= 109.09 cents, 11 of which stack to the perfect octave 2/1. It does not approximate many small prime harmonics well at all. But approximates 11/8 very well for it's size and also approximates the interval 9/7 with only ~1 cent of error. It has 2 fifths at 654.55c and 763.64c.

Theory

Edostep interpretations

11edo's edostep has the following interpretations in the 2.7.11.17 subgroup:

• 128/121 (the interval between 11/8 and 16/11)
• 121/112 (the interval between 11/8 and 14/11)
• 17/16 (the 17th harmonic)
• 128/119 (the interval between 17/16 and 8/7)

JI Approximation

11edo does not approximate harmonics 3 or 5 at all. Unless one considers ~50c of error acceptable. However, 11edo approximates 7/4 acceptably well and approximates 11/8 very well. As well as the supermajor third 9/7 exceptionally well.

Chords

11edo has numerous xenharmonic sounding chords. An approach to chords in 11edo is stacking the interval 9/7 for very accurate 14:18:23 chords. Another is to take advantage of the duel fifths.

Scales

Arguably the main MOS scale in 11edo is the smitonic Scale 2-1-2-2-1-2-1. The smitonic scale is melodically rather similar in some regards to the 12edo diatonic scale. However, it is harmonically totally different due to the absence of harmonics 3 and 5 in 11edo.

There are others including the Checkertonic scale 2-1-1-2-1-1-2-1.