415edt

← 414edt

415edt

416edt →

Prime factorization	5 × 83
Step size	4.58302¢
Octave	262\415edt (1200.75¢)
Consistency limit	7
Distinct consistency limit	7

415edt is the equal division of the third harmonic into 415 parts of 4.5830 cents each, corresponding to 261.8358 edo. It is notable for its impressive consistency records in very high no-evens throdd limits: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 add-77 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their patent val approximation. This makes it a potential candidate for the tritave-based version of 311edo, although its performance is not quite as spectacular as that miracle edo.

Harmonics

Approximation of odd harmonics in 415edt

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27	29	31	33	35
Error	Absolute (¢)	+0.00	+0.16	-0.30	+0.00	+0.90	+0.42	+0.16	-1.12	-1.19	-0.30	-1.97	+0.33	+0.00	+0.03	-0.85	+0.90	-0.14
	Relative (%)	+0.0	+3.6	-6.6	+0.0	+19.7	+9.2	+3.6	-24.4	-26.0	-6.6	-43.1	+7.2	+0.0	+0.6	-18.6	+19.7	-3.0
Steps (reduced)		415 (0)	608 (193)	735 (320)	830 (0)	906 (76)	969 (139)	1023 (193)	1070 (240)	1112 (282)	1150 (320)	1184 (354)	1216 (386)	1245 (0)	1272 (27)	1297 (52)	1321 (76)	1343 (98)

Approximation of odd harmonics in 415edt (continued)

Harmonic		37	39	41	43	45	47	49	51	53	55	57	59	61	63	65	67	69	71	73	75	77	79
Error	Absolute (¢)	-0.10	+0.42	+0.92	+0.96	+0.16	-1.79	-0.61	-1.12	+1.03	+1.07	-1.19	-1.31	+0.55	-0.30	+0.59	-1.46	-1.97	-1.03	+1.29	+0.33	+0.60	+2.04
	Relative (%)	-2.2	+9.2	+20.1	+20.9	+3.6	-39.0	-13.2	-24.4	+22.5	+23.3	-26.0	-28.7	+12.0	-6.6	+12.8	-32.0	-43.1	-22.4	+28.2	+7.2	+13.1	+44.4
Steps (reduced)		1364 (119)	1384 (139)	1403 (158)	1421 (176)	1438 (193)	1454 (209)	1470 (225)	1485 (240)	1500 (255)	1514 (269)	1527 (282)	1540 (295)	1553 (308)	1565 (320)	1577 (332)	1588 (343)	1599 (354)	1610 (365)	1621 (376)	1631 (386)	1641 (396)	1651 (406)