140edo

← 139edo

140edo

141edo →

Prime factorization	22 × 5 × 7
Step size	8.57143 ¢
Fifth	82\140 (702.857 ¢) (→ 41\70)
Semitones (A1:m2)	14:10 (120 ¢ : 85.71 ¢)
Consistency limit	9
Distinct consistency limit	9

The 140 equal divisions of the octave (140edo), or the 140(-tone) equal temperament (140tet, 140et) when viewed from a regular temperament perspective, divides the octave into 140 parts of about 8.57 cents each.

Theory

In the 5-limit, 140et tempers out 15625/15552, making it a kleismic system, and the kwazy comma, [-53 10 16⟩. It is most notable, however, in the 7-limit, where it tempers out 2401/2400, 5120/5103, 10976/10935 and 65625/65536. It supports the 7-limit rank-2 temperaments tertiaseptal, hemififths, countercata and bisupermajor, and is a good tuning recommendation for countercata, the 53&140 temperament tempering out 15625/15552 and 5120/5103, and provides the optimal patent val for 13-limit countercata. In the 11-limit it tempers out 385/384, 1331/1323, 1375/1372, 5632/5625, 6250/6237 and 9801/9800, and in the 13-limit 325/324, 352/351, 625/624, 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.

If we use the val ⟨140 223 325 394] (140bbd) we obtain a tuning for porcupine temperament; the generator 19\140 is 0.023 cents flat of the POTE generator.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	15625/15552, [35 -25 2⟩	[⟨140 222 325]]	-0.104	0.346	4.03
2.3.5.7	2401/2400, 5120/5103, 15625/15552	[⟨140 222 325 393]]	-0.055	0.311	3.63
2.3.5.7.11	385/384, 1331/1323, 1375/1372, 2200/2187	[⟨140 222 325 393 484]]	+0.115	0.439	5.12
2.3.5.7.11.13	325/324, 352/351, 385/384, 625/624, 1331/1323	[⟨140 222 325 393 484 518]]	+0.119	0.401	4.68

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	9\140	77.14	22/21	Tertiaseptal / tertia
1	13\140	111.43	16/15	Stockhausenic
1	37\140	317.14	6/5	Hanson / countercata
1	41\140	351.43	49/40	Hemififths
1	53\140	454.29	13/10	Fibo
1	59\140	505.71	75/56	Marfifths
2	3\140	25.71	64/63	Ketchup
2	19\140	162.86	11/10	Kwazy / bisupermajor
2	41\140 (29\140)	351.43 (248.57)	49/40 (15/13)	Semihemi
4	37\140 (2\140)	317.14 (17.14)	6/5 (126/125)	Quadritikleismic
4	58\140 (12\140)	497.14 (102.86)	4/3 (35/33)	Undim
5	43\140 (13\140)	368.57 (111.43)	10125/8192 (16/15)	Qintosec
10	29\140 (1\140)	248.57 (8.57)	15/13 (176/175)	Decoid
20	54\140 (2\140)	497.14 (17.14)	4/3 (126/125)	Degrees
28	54\140 (2\140)	497.14 (17.14)	4/3 (126/125)	Oquatonic