118edo

118edo is the equal division of the octave into 118 parts of 10.1695 cents each.

118edo represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, [-15 8 1⟩ and the parakleisma, [8 14 -13⟩, as well as the vishnuzma, [23 6 -14⟩, the hemithirds comma, [38 -2 -15⟩, and the kwazy, [-53 10 16⟩. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.

In the 7-limit, it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelan temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but 99edo does better with that.

In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.

118edo is the 17th zeta peak edo.

Just approximation

		prime 2	prime 3	prime 5	prime 7	prime 11	prime 13	prime 17	prime 19
Error	absolute (¢)	0.00	-0.26	+0.13	-2.72	-2.17	+3.54	-3.26	-2.60
	relative (%)	0.0	-2.6	+1.2	-26.8	-21.3	+34.8	-32.1	-25.5