499edt

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499edt

500edt →

Prime factorization	499 (prime)
Step size	3.81153 ¢
Octave	315\499edt (1200.63 ¢)
Consistency limit	7
Distinct consistency limit	7

499 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 499edt or 499ed3), is a nonoctave tuning system that divides the interval of 3/1 into 499 equal parts of about 3.81 ¢ each. Each step represents a frequency ratio of 3^1/499, or the 499th root of 3. It correspondes to 314.8342edo.

Theory

499edt is strong in the 3.5.7.11.13.17.23 subgroup, tempering out 2277/2275, 21879/21875, 104247/104125, 12397/12393, 9317/9315 and 584375/583443. Using the 3.5.11.13.17.23 subgroup, it tempers out 73125/73117.

Harmonics

Approximation of harmonics in 499edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.63	+0.00	+1.27	-0.08	+0.63	+0.57	+1.90	+0.00	+0.55	-0.56	+1.27
	Relative (%)	+16.6	+0.0	+33.2	-2.2	+16.6	+14.9	+49.8	+0.0	+14.4	-14.7	+33.2
Steps (reduced)		315 (315)	499 (0)	630 (131)	731 (232)	814 (315)	884 (385)	945 (446)	998 (0)	1046 (48)	1089 (91)	1129 (131)

Approximation of harmonics in 499edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
Error	Absolute (¢)	-0.09	+1.20	-0.08	-1.28	+0.49	+0.63	-1.49	+1.18	+0.57	+0.07	-0.65	+1.90	-0.17	+0.54	+0.00
	Relative (%)	-2.4	+31.5	-2.2	-33.6	+12.8	+16.6	-39.2	+31.0	+14.9	+2.0	-17.1	+49.8	-4.4	+14.2	+0.0
Steps (reduced)		1165 (167)	1199 (201)	1230 (232)	1259 (261)	1287 (289)	1313 (315)	1337 (339)	1361 (363)	1383 (385)	1404 (406)	1424 (426)	1444 (446)	1462 (464)	1480 (482)	1497 (0)

Music

Francium

• "dougalicious" from wiloliquy (2025) – Spotify | Bandcamp | YouTube – in Galeaclolusite, 499edt tuning