3079edo

← 3078edo

3079edo

3080edo →

Prime factorization	3079 (prime)
Step size	0.389737¢
Fifth	1801\3079 (701.916¢)
Semitones (A1:m2)	291:232 (113.4¢ : 90.42¢)
Consistency limit	9
Distinct consistency limit	9

3079 equal divisions of the octave (abbreviated 3079edo or 3079ed2), also called 3079-tone equal temperament (3079tet) or 3079 equal temperament (3079et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3079 equal parts of about 0.39 ¢ each. Each step represents a frequency ratio of 2^1/3079, or the 3079th root of 2.

Theory

3079edo is consistent to the 9-odd-limit. The equal temperament tempers out 43046721/43025920, 1220703125/1219784832 and [51 -13 -1 -10⟩ in the 7-limit. It supports acrosextilififths.

Prime harmonics

Approximation of prime harmonics in 3079edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.039	-0.084	+0.060	+0.160	+0.135	-0.116	-0.144	-0.018	+0.108	+0.012
	Relative (%)	+0.0	-10.0	-21.7	+15.4	+41.0	+34.6	-29.8	-36.9	-4.7	+27.7	+3.0
Steps (reduced)		3079 (0)	4880 (1801)	7149 (991)	8644 (2486)	10652 (1415)	11394 (2157)	12585 (269)	13079 (763)	13928 (1612)	14958 (2642)	15254 (2938)

Subsets and supersets

3079edo is the 440th prime edo.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-4880 3079⟩	[⟨3079 4880]]	0.0122	0.0122	3.13
2.3.5	[-69 45 -1⟩, [-50 -71 70⟩	[⟨3079 4880 7149]]	0.0203	0.0151	3.87
2.3.5.7	43046721/43025920, 1220703125/1219784832, [51 -13 -1 -10⟩	[⟨3079 4880 7149 8644]]	0.0099	0.0223	5.72

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	1278\3079	498.084	4/3	Counterschismic

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

Music

Francium

• "mfdreamshoppedfashionforyou" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube – acrosextilififths[13] in 3079edo tuning