509edo

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509edo

510edo →

Prime factorization	509 (prime)
Step size	2.35756 ¢
Fifth	298\509 (702.554 ¢)
Semitones (A1:m2)	50:37 (117.9 ¢ : 87.23 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

509et tempers out 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit and 1073741824/1071794405, 1019215872/1019046875, 151263/151250, 226492416/226474325, 2359296/2358125, 1953125/1948617, 172032/171875, 4302592/4296875, 5767168/5764801, 180224/180075, 5632/5625, 422576/421875, 3025/3024, 41503/41472, 1362944/1361367, 42592/42525, 456533/455625, 322102/321489 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the temperaments Eir, Petrtri and Orthocanousmic.

Odd harmonics

Approximation of odd harmonics in 509edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.60	+0.33	+0.13	-1.16	+0.35	+1.12	+0.93	+1.13	-0.46	+0.73	-1.16
	Relative (%)	+25.4	+13.9	+5.6	-49.2	+14.9	+47.6	+39.3	+48.1	-19.5	+31.0	-49.3
Steps (reduced)		807 (298)	1182 (164)	1429 (411)	1613 (86)	1761 (234)	1884 (357)	1989 (462)	2081 (45)	2162 (126)	2236 (200)	2302 (266)

Subsets and supersets

509 is the 97th prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[807 -509⟩	⟨509 807]	-0.1890	0.1889	8.01
2.3.5	[9 -13 5⟩, [93 -3 -38⟩	⟨509 807 1182]	-0.1729	0.1559	6.61
2.3.5.7	2401/2400, 1600000/1594323, 4802000/4782969	⟨509 807 1182 1429]	-0.1415	0.1456	6.18
2.3.5.7.11	2401/2400, 3025/3024, 5632/5625, 41503/41472	⟨509 807 1182 1429 1761]	-0.1335	0.1312	5.57
2.3.5.7.11.13	2080/2079, 2200/2197, 3025/3024, 4459/4455, 5632/5625	⟨509 807 1182 1429 1761 1884]	-0.1618	0.1354	5.74
2.3.5.7.11.13.17	1225/1224, 2080/2079, 2431/2430, 7744/7735, 12376/12375, 14161/14157	⟨509 807 1182 1429 1761 1884 2081]	-0.1784	0.1318	5.59

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	36\509	84.87	21/20	Amicable
1	115\509	271.12	1024/875	Quasiorwell
1	144\509	339.49	243/200	Amity