2072edo
| ← 2071edo | 2072edo | 2073edo → |
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
| 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.