31920edo

The 31920 division divides the octave into 31920 equal parts of 0.03759 cents each. It is distinctly consistent through the 41 limit, with a smaller 41-limit relative error than any smaller distinctly consistent division. It is also an atomic temperament, tempering out the Kirnberger atom, |161 -84 -12>. It is a very "smooth" number, with many divisors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920. These facts make it a good candidate for an interval size measure, and one step of it may be called an imp, so that the cent is 26.6 imps, and a 12edo semitone is 2660 imps. A single step of 15edo is 2128 imps, of 19edo 1680 imps, of 84edo 380 imps, of 140edo 228 imps, of 152edo 210 imps, of 190edo 168 imps, and of 665edo 48 imps. The simplest of the commas under the 43 limit it tempers out are 47916/47915, 52480/52479, 58311/58310, 60516/60515, 67600/67599, 68783/68782, 72501/72500, 75141/75140, 76875/76874, 81549/81548, 81796/81795, 82944/82943, 88320/88319, 93093/93092, 93500/93499, 96876/96875 and 98736/98735.