500edo

← 499edo

500edo

501edo →

Prime factorization	22 × 53
Step size	2.4 ¢
Fifth	292\500 (700.8 ¢) (→ 73\125)
Semitones (A1:m2)	44:40 (105.6 ¢ : 96 ¢)
Dual sharp fifth	293\500 (703.2 ¢)
Dual flat fifth	292\500 (700.8 ¢) (→ 73\125)
Dual major 2nd	85\500 (204 ¢) (→ 17\100)
Consistency limit	3
Distinct consistency limit	3

Theory

500et is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used in the 2.9.5.7.11.13.17.19.23.29.31.37.41.43 subgroup, tempering out 936/935, 4096/4095, 12376/12375, 2025/2024, 3328/3325, 9801/9800, 35750/35721, 46592/46575, 5104/5103, 12555/12544, 1296/1295, 1376/1375 and 6273/6272.

Odd harmonics

Approximation of odd harmonics in 500edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.16	+0.09	+0.77	+0.09	+0.68	-0.53	-1.07	+0.64	+0.09	-0.38	+0.53
	Relative (%)	-48.1	+3.6	+32.3	+3.7	+28.4	-22.0	-44.5	+26.9	+3.6	-15.9	+21.9
Steps (reduced)		792 (292)	1161 (161)	1404 (404)	1585 (85)	1730 (230)	1850 (350)	1953 (453)	2044 (44)	2124 (124)	2196 (196)	2262 (262)

Subsets and supersets

500 factors into 2² * 5³, with subset edos 2, 4, 5, 10, 20, 25, 50, 100, 125, and 250. 1000edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[317 -100⟩	[⟨500 1585]]	-0.0142	0.0142	0.59
2.9.5	[38 -1 -15⟩, [55 -32 20⟩	[⟨500 1585 1161]]	-0.0219	0.0159	0.66
2.9.5.7	703125/702464, 589824/588245, 31381059609/31360000000	[⟨500 1585 1161 1404]]	-0.0853	0.1108	4.62
2.9.5.7.11	9801/9800, 46656/46585, 2252800/2250423, 703125/702464	[⟨500 1585 1161 1404 1730]]	-0.1077	0.1087	4.53
2.9.5.7.11.13	4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091	[⟨500 1585 1161 1404 1730 1850]]	-0.0660	0.1362	5.68
2.9.5.7.11.13.17	936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011	[⟨500 1585 1161 1404 1730 1850 2044]]	-0.0791	0.1301	5.42

Music

Francium

• loveyouforever (2024)