# 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 21/3079, 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