733edo

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733edo

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Prime factorization	733 (prime)
Step size	1.63711¢
Fifth	429\733 (702.319¢)
Semitones (A1:m2)	71:54 (116.2¢ : 88.4¢)
Consistency limit	11
Distinct consistency limit	11

733 equal divisions of the octave (abbreviated 733edo or 733ed2), also called 733-tone equal temperament (733tet) or 733 equal temperament (733et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 733 equal parts of about 1.64 ¢ each. Each step represents a frequency ratio of 2^1/733, or the 733rd root of 2.

Theory

733edo is consistent to the 11-odd-limit, tempering out 3025/3024, 19712/19683, 180224/180075 and 1953125/1951488. It supports hemiluna and French decimal.

Prime harmonics

Approximation of prime harmonics in 733edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.364	+0.044	+0.342	+0.387	-0.691	-0.181	+0.441	+0.375	+0.164	-0.697
	Relative (%)	+0.0	+22.2	+2.7	+20.9	+23.7	-42.2	-11.0	+26.9	+22.9	+10.0	-42.6
Steps (reduced)		733 (0)	1162 (429)	1702 (236)	2058 (592)	2536 (337)	2712 (513)	2996 (64)	3114 (182)	3316 (384)	3561 (629)	3631 (699)

Subsets and supersets

733edo is the 130th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1162 -733⟩	[⟨733 1162]]	-0.1149	0.1149	7.02
2.3.5	[38 -2 -15⟩, [42 -47 14⟩	[⟨733 1162 1702]]	-0.0829	0.1042	6.36
2.3.5.7	420175/419904, 67108864/66976875, 48828125/48771072	[⟨733 1162 1702 2058]]	-0.0926	0.0918	5.61
2.3.5.7.11	3025/3024, 19712/19683, 180224/180075, 1953125/1951488	[⟨733 1162 1702 2058 2536]]	-0.0965	0.0824	5.03

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	118\733	193.179	262144/234375	Luna

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct