User:Overthink/7200edo

← 7199edo

7200edo

7201edo →

Prime factorization	25 × 32 × 52
Step size	0.166667 ¢
Fifth	4212\7200 (702 ¢) (→ 117\200)
Semitones (A1:m2)	684:540 (114 ¢ : 90 ¢)
Consistency limit	7
Distinct consistency limit	7

7200 equal divisions of the octave (abbreviated 7200edo or 7200ed2), also called 7200-tone equal temperament (7200tet) or 7200 equal temperament (7200et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7200 equal parts of about 0.167 ¢ each. Each step represents a frequency ratio of 2^1/7200, or the 7200th root of 2.

Theory

The step size of this edo is the relative cent of 72edo. It is a strong system in the 2.5.7.11.13.17.19 subgroup.

Subsets and supersets

Since 7200 factors into 2⁵ * 3² * 5², it has subset edos 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, and 3600.

Approximation of prime harmonics in 7200edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	+0.0450	+0.0196	+0.0074	+0.0154	-0.0277	+0.0446	-0.0130	+0.0590	-0.0772	-0.0356
	Relative (%)	+0.0	+27.0	+11.8	+4.5	+9.2	-16.6	+26.8	-7.8	+35.4	-46.3	-21.3
Steps (reduced)		7200 (0)	11412 (4212)	16718 (2318)	20213 (5813)	24908 (3308)	26643 (5043)	29430 (630)	30585 (1785)	32570 (3770)	34977 (6177)	35670 (6870)