112edo

← 111edo

112edo

113edo →

Prime factorization	24 × 7
Step size	10.7143 ¢
Fifth	66\112 (707.143 ¢) (→ 33\56)
Semitones (A1:m2)	14:6 (150 ¢ : 64.29 ¢)
Dual sharp fifth	66\112 (707.143 ¢) (→ 33\56)
Dual flat fifth	65\112 (696.429 ¢)
Dual major 2nd	19\112 (203.571 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

112edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the patent fifth- is identical to the perfect fifth of 56edo, a great inverse gentle fifth where +5 fifths gives a near-just 28:27 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 17:21.

One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from 17edo, but sharing a similar structure.

Odd harmonics

Approximation of odd harmonics in 112edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+5.19	-0.60	-4.54	-0.34	-4.89	-4.81	+4.59	+2.19	+2.49	+0.65	+3.87
	Relative (%)	+48.4	-5.6	-42.4	-3.2	-45.6	-44.9	+42.8	+20.4	+23.2	+6.0	+36.1
Steps (reduced)		178 (66)	260 (36)	314 (90)	355 (19)	387 (51)	414 (78)	438 (102)	458 (10)	476 (28)	492 (44)	507 (59)

Music

• Circulating 2.3.7.11.13 Floaty Piano Improv by Cam Taylor