2072edo

 ← 2071edo 2072edo 2073edo →
Prime factorization 23 × 7 × 37
Step size 0.579151¢
Fifth 1212\2072 (701.931¢) (→303\518)
Semitones (A1:m2) 196:156 (113.5¢ : 90.35¢)
Consistency limit 17
Distinct consistency limit 17

2072 equal divisions of the octave (abbreviated 2072edo or 2072ed2), also called 2072-tone equal temperament (2072tet) or 2072 equal temperament (2072et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2072 equal parts of about 0.579 ¢ each. Each step represents a frequency ratio of 21/2072, or the 2072nd root of 2.

2072edo is consistent in the 17-odd-limit, as well as a strong 5-limit tuning, tempering out kwazy, [-53 10 16, [-33 97 -52, and barium comma, [-225 224 -56, equating 81/80 to 1/56th of the octave. It provides the optimal patent val for the barium temperament in the 13-limit. It tempers out the euzenius comma in the 7-limit.

2072edo contains the 2.7.11 mapping of 296edo.

Prime harmonics

Approximation of prime harmonics in 2072edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.024 -0.020 +0.093 +0.033 -0.180 -0.129 +0.170 +0.104 +0.153 -0.055
Relative (%) +0.0 -4.2 -3.5 +16.1 +5.8 -31.1 -22.3 +29.4 +18.0 +26.3 -9.5
Steps
(reduced)
2072
(0)
3284
(1212)
4811
(667)
5817
(1673)
7168
(952)
7667
(1451)
8469
(181)
8802
(514)
9373
(1085)
10066
(1778)
10265
(1977)

Subsets and supersets

Since 2072 factors as 23 × 7 × 37, 2072edo has subset edos 1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036.