335edo

← 334edo

335edo

336edo →

Prime factorization	5 × 67
Step size	3.58209 ¢
Fifth	196\335 (702.09 ¢)
Semitones (A1:m2)	32:25 (114.6 ¢ : 89.55 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

335et only is consistent to the 5-odd-limit. Using the patent val, it tempers out the parakleisma in the 5-limit; 4375/4374 and 3136/3125 in the 7-limit, supporting turan, quintosec, tricot, pseudotrillium, lifthrasir, tritomere, counterwürschmidt and gaster. Using the 335d val (⟨335 531 778 ‚‘‘991‘‘‘]), it tempers out 6144/6125, 16875/16807 and 14348907/14336000 in the 7-limit, supporting grendel.

Prime harmonics

Approximation of prime harmonics in 335edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.13	+0.55	-1.66	+0.32	+1.26	-1.07	-0.20	-1.41	-1.52	+1.23
	Relative (%)	+0.0	+3.8	+15.4	-46.4	+9.0	+35.3	-30.0	-5.6	-39.3	-42.4	+34.4
Steps (reduced)		335 (0)	531 (196)	778 (108)	940 (270)	1159 (154)	1240 (235)	1369 (29)	1423 (83)	1515 (175)	1627 (287)	1660 (320)

Subsets and supersets

335 factors into 5 × 67 with 5edo and 67edo as its subset edos. 670edo, which doubles it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[531 -335⟩	[⟨335 531]]	-0.0424	0.0424	1.18
2.3.5	[8 14 -13⟩, [47 -15 -10⟩	[⟨335 531 778]]	-0.1075	0.0984	2.75

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	88\335	315.22	6/5	Parakleismic
1	158\335	565.97	104/75	Tricot
5	232\335 (31\335)	831.04 (111.04)	80/49 (16/15)	Qintosec

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct