3558edo

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3558edo

3559edo →

Prime factorization	2 × 3 × 593
Step size	0.337268 ¢
Fifth	2081\3558 (701.855 ¢)
Semitones (A1:m2)	335:269 (113 ¢ : 90.73 ¢)
Consistency limit	5
Distinct consistency limit	5

3558 equal divisions of the octave (abbreviated 3558edo or 3558ed2), also called 3558-tone equal temperament (3558tet) or 3558 equal temperament (3558et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3558 equal parts of about 0.337 ¢ each. Each step represents a frequency ratio of 2^1/3558, or the 3558th root of 2.

Theory

3558edo is only consistent to the 5-odd-limit.

Odd harmonics

Approximation of odd harmonics in 3558edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.100	-0.142	+0.145	+0.137	+0.115	-0.055	+0.096	-0.065	-0.043	+0.045	+0.056
	Relative (%)	-29.7	-42.0	+43.1	+40.7	+34.2	-16.5	+28.3	-19.3	-12.6	+13.5	+16.7
Steps (reduced)		5639 (2081)	8261 (1145)	9989 (2873)	11279 (605)	12309 (1635)	13166 (2492)	13901 (3227)	14543 (311)	15114 (882)	15628 (1396)	16095 (1863)

Subsets and supersets

Since 3558 factors into 2 × 3 × 593, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779.

Scales

Some MOS scales:

• Terrain[9]
• Terrain[15]