456edo

← 455edo

456edo

457edo →

Prime factorization	23 × 3 × 19
Step size	2.63158¢
Fifth	267\456 (702.632¢) (→89\152)
Semitones (A1:m2)	45:33 (118.4¢ : 86.84¢)
Consistency limit	7
Distinct consistency limit	7

456 equal divisions of the octave (abbreviated 456edo or 456ed2), also called 456-tone equal temperament (456tet) or 456 equal temperament (456et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 456 equal parts of about 2.63 ¢ each. Each step represents a frequency ratio of 2^1/456, or the 456th root of 2.

456edo is enfactored in the 5-limit, with the same tuning as 152edo, defined by tempering out 1600000/1594323 (amity comma) and [32 -7 -9⟩ (escapade comma), as well as [23 6 -14⟩ (vishnuzma), [41 -20 -4⟩ (undim comma), and [-14 -19 19⟩ (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the optimal patent val for the chromat temperament.

Odd harmonics

Approximation of odd harmonics in 456edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.68	+0.53	-0.40	-1.28	+1.31	-1.05	+1.20	+0.31	-0.14	+0.27	+0.67
	Relative (%)	+25.7	+20.1	-15.4	-48.6	+49.9	-40.1	+45.8	+11.7	-5.5	+10.3	+25.6
Steps (reduced)		723 (267)	1059 (147)	1280 (368)	1445 (77)	1578 (210)	1687 (319)	1782 (414)	1864 (40)	1937 (113)	2003 (179)	2063 (239)

Subsets and supersets

Since 456 factors into 2³ × 3 × 19, 456edo has subset edos 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, and 228.