241200edo

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

← 241199edo

241200edo

241201edo →

Prime factorization	24 × 32 × 52 × 67
Step size	0.00497512 ¢
Fifth	141093\241200 (701.955 ¢) (→ 15677\26800)
Semitones (A1:m2)	22851:18135 (113.7 ¢ : 90.22 ¢)
Consistency limit	39
Distinct consistency limit	39

241200 equal divisions of the octave (abbreviated 241200edo or 241200ed2), also called 241200-tone equal temperament (241200tet) or 241200 equal temperament (241200et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 241200 equal parts of about 0.00498 ¢ each. Each step represents a frequency ratio of 2^1/241200, or the 241200th root of 2.

241200edo is the 60th zeta peak edo and the first one that 1200 divides, making it compatible with cents. It is also a zeta peak integer edo. It is a strong 37-limit system, distinctly consistent in the 39-odd-limit, with a lower 37-limit relative error than any previous equal temperaments.

Prime harmonics

Approximation of prime harmonics in 241200edo

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+0.00000	+0.00022	-0.00028	-0.00004	+0.00047	-0.00030	-0.00019	-0.00058	-0.00072
	Relative (%)	+0.0	+4.5	-5.6	-0.7	+9.4	-6.0	-3.7	-11.6	-14.4
Steps (reduced)		241200 (0)	382293 (141093)	560049 (77649)	677134 (194734)	834415 (110815)	892546 (168946)	985896 (21096)	1024600 (59800)	1091083 (126283)

Approximation of prime harmonics in 241200edo (continued)

Harmonic		29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	-0.00008	-0.00075	-0.00076	+0.00227	-0.00029	+0.00084	-0.00206	+0.00247	+0.00077
	Relative (%)	-1.6	-15.0	-15.2	+45.6	-5.9	+16.9	-41.4	+49.6	+15.4
Steps (reduced)		1171745 (206945)	1194952 (230152)	1256520 (50520)	1292242 (86242)	1308815 (102815)	1339767 (133767)	1381574 (175574)	1418894 (212894)	1430494 (224494)

Approximation of prime harmonics in 241200edo (continued)

Harmonic		67	71	73	79	83	89	97	101	103
Error	Absolute (¢)	+0.00143	-0.00003	+0.00157	+0.00042	+0.00243	+0.00048	+0.00011	+0.00194	+0.00036
	Relative (%)	+28.7	-0.5	+31.6	+8.4	+48.9	+9.6	+2.2	+39.0	+7.3
Steps (reduced)		1463141 (15941)	1483319 (36119)	1492986 (45786)	1520472 (73272)	1537660 (90460)	1561947 (114747)	1591899 (144699)	1605961 (158761)	1612784 (165584)