111202edo

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.

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111202edo

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Prime factorization	2 × 7 × 132 × 47
Step size	0.0107912 ¢
Fifth	65049\111202 (701.955 ¢) (convergent)
Semitones (A1:m2)	10535:8361 (113.7 ¢ : 90.22 ¢)
Consistency limit	9
Distinct consistency limit	9

111202 equal divisions of the octave (abbreviated 111202edo or 111202ed2), also called 111202-tone equal temperament (111202tet) or 111202 equal temperament (111202et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 111202 equal parts of about 0.0108 ¢ each. Each step represents a frequency ratio of 2^1/111202, or the 111202nd root of 2. It is the denominator of the next convergent for log₂3 past 79335, before 190537.

111202edo has a consistency limit of only 9, and is a strong 5-limit system, with additional strengths in the 2.3.5.17.19.23 subgroup.

Prime harmonics

Approximation of prime harmonics in 111202edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00000	-0.00000	-0.00052	-0.00520	+0.00308	-0.00321	-0.00046	-0.00038	-0.00147	-0.00219	+0.00498
	Relative (%)	+0.0	-0.0	-4.8	-48.2	+28.5	-29.8	-4.3	-3.5	-13.7	-20.3	+46.2
Steps (reduced)		111202 (0)	176251 (65049)	258203 (35799)	312183 (89779)	384696 (51090)	411496 (77890)	454534 (9726)	472378 (27570)	503029 (58221)	540217 (95409)	550917 (106109)