2081edo

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2081edo

2082edo →

Prime factorization	2081 (prime)
Step size	0.576646 ¢
Fifth	1217\2081 (701.778 ¢)
Semitones (A1:m2)	195:158 (112.4 ¢ : 91.11 ¢)
Consistency limit	7
Distinct consistency limit	7

2081 equal divisions of the octave (abbreviated 2081edo or 2081ed2), also called 2081-tone equal temperament (2081tet) or 2081 equal temperament (2081et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2081 equal parts of about 0.577 ¢ each. Each step represents a frequency ratio of 2^1/2081, or the 2081st root of 2.

Theory

2081edo is consistent to the 7-odd-limit, tempering out 2460375/2458624, 1312993546389/1310720000000 and [24 13 -18 -1⟩. It is strong in the 2.5.7.11.17.19 subgroup, tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625.

Odd harmonics

Approximation of odd harmonics in 2081edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.177	+0.039	-0.061	+0.223	-0.045	+0.222	-0.138	-0.006	+0.036	-0.238	+0.270
	Relative (%)	-30.7	+6.8	-10.6	+38.6	-7.7	+38.5	-23.9	-1.0	+6.3	-41.3	+46.8
Steps (reduced)		3298 (1217)	4832 (670)	5842 (1680)	6597 (354)	7199 (956)	7701 (1458)	8130 (1887)	8506 (182)	8840 (516)	9140 (816)	9414 (1090)

Subsets and supersets

2081edo is the 313th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-3298 2081⟩	[⟨2081 3298]]	0.0558	0.0558	9.68
2.3.5	[-68 18 17⟩, [-30 79 -41⟩	[⟨2081 3298 4832]]	0.0316	0.0570	9.88
2.3.5.7	2460375/2458624, [-24 13 -7 7⟩, [24 13 -18 -1⟩	[⟨2081 3298 4832 5842]]	0.0291	0.0496	8.60
2.3.5.7.11	160083/160000, 2460375/2458624, 3750705/3748096, 204073344/203809375	[⟨2081 3298 4832 5842 7199]]	0.0259	0.0448	7.77

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	194\2081	111.869	16/15	Vavoom

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

Music

Francium

• "Fluffy Pants" from Microtonal Six-Dimensional Cats (2025) – Spotify | Bandcamp | YouTube