327edo

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327edo

328edo →

Prime factorization	3 × 109
Step size	3.66972 ¢
Fifth	191\327 (700.917 ¢)
Semitones (A1:m2)	29:26 (106.4 ¢ : 95.41 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

327et tempers out 283115520/282475249, 156250000/155649627, 16875/16807, 19683/19600, 95703125/95551488, 250047/250000 and 2100875/2097152 in the 7-limit; 95703125/95664294, 56723625/56689952, 55296000/55240493, 20155392/20131375, 46656/46585, 2734375/2725888, 104162436/103984375, 226492416/226474325, 540/539, 9765625/9732096, 137781/137500, 5767168/5764801, 85937500/85766121, 1375/1372, 8019/8000, 134775333/134217728, 47265625/47258883, 3025/3024, 160083/160000, 35937/35840, 202397184/201768035, 102487/102400, 20614528/20588575, 805255/802816, 1771561/1769472 and 526153617/524288000 in the 11-limit. It supports petrtri.

Odd harmonics

Approximation of odd harmonics in 327edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.04	-0.99	-0.02	+1.59	-0.86	-0.16	+1.64	+1.47	-0.27	-1.06	-0.75
	Relative (%)	-28.3	-27.0	-0.5	+43.5	-23.4	-4.4	+44.7	+40.0	-7.2	-28.8	-20.5
Steps (reduced)		518 (191)	759 (105)	918 (264)	1037 (56)	1131 (150)	1210 (229)	1278 (297)	1337 (29)	1389 (81)	1436 (128)	1479 (171)

Subsets and supersets

327 factors into 3 × 109, with 3edo and 109edo as its subset EDOs.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-518 327⟩	[⟨327 518]]	0.3273	0.3274	8.92
2.3.5	2109375/2097152, [-20 39 -18⟩	[⟨327 518 759]]	0.3608	0.2715	7.40
2.3.5.7	19683/19600, 16875/16807, 2109375/2097152	[⟨327 518 759 918]]	0.2722	0.2807	7.65
2.3.5.7.11	540/539, 3025/3024, 8019/8000, 5788125/5767168	[⟨327 518 759 918 1131]]	0.2674	0.2512	6.85
2.3.5.7.11.13	540/539, 625/624, 3025/3024, 8019/8000, 4225/4224	[⟨327 518 759 918 1131 1210]]	0.2301	0.2441	6.65

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	74\327	271.56	75/64	Orson
3	44\327	161.47	192/175	Pnict
3	50\327	183.49	10/9	Mirkat

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