52edt
| ← 51edt | 52edt | 53edt → |
The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 11-limit, so that it tempers out the same commas as 26edt in the 11-limit and 13edt in the 7-limit. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh no-twos zeta peak edt.
Intervals
| Steps | Cents | Hekts | BP nonatonic degree | Diatonic degree | Corresponding JI intervals | Comments | Generator for... |
|---|---|---|---|---|---|---|---|
| 1 | 36.6 | 25 | Qa1/3d2 | Sa1 | 50/49~33/32~49/48 | ||
| 2 | 73.15 | 50 | Sa1/sd2 | A1/dd2 | 25/24~28/27~22/21~27/26~24/23~21/20~29/28 | ||
| 3 | 109.7 | 75 | 3A1/qd2 | A+1/d-2 | 15/14~16/15~29/27~121/112 | ||
| 4 | 146.3 | 100 | A1/m2 | AA1/sm2 | 27/25~25/23~49/45~13/12~14/13~11/10~169/162 | ||
| 5 | 182.9 | 125 | Sm2 | sm+2 | 10/9 | ||
| 6 | 219.5 | 150 | N2 | m2 | 9/8~8/7~44/39 | ||
| 7 | 256.0 | 175 | sM2 | N2 | 147/128~7/6 | ||
| 8 | 292.6 | 200 | M2/d3 | M2 | 32/27~25/21~13/11~27/23 | ||
| 9 | 329.2 | 225 | Qa2/3d3 | SM-2/d-2 | 6/5 | 11/9- | |
| 10 | 365.8 | 250 | Sa2/sd3 | SM2/dd3 | 5/4~16/13 | 11/9+ | |
| 11 | 402.3 | 275 | 3A3/qd3 | SM+2 | 81/64~63/50~33/26~23/18 | ||
| 12 | 438.9 | 300 | A2/P3/d4 | AA2/sm3 | 32/25~9/7~14/11~104/81~13/10 | ||
| 13 | 475.5 | 325 | Qa3/3d4 | sm+3 | 21/16~98/75 | ||
| 14 | 512.1 | 350 | Sa3/sd4 | m3 | 4/3~27/20~162/121 | ||
| 15 | 548.6 | 375 | 3A3/qd4 | N3 | 11/8~243/169 | 18/13- | |
| 16 | 585.2 | 400 | A3/m4/d5 | M3 | 7/5~25/18~112/81~88/63~32/23~29/21 | 18/13+ | |
| 17 | 621.8 | 425 | Sm4/3d5 | SM-3 | 10/7~36/25~81/56~63/44~23/16~42/29 | 13/9- | |
| 18 | 658.4 | 450 | N4/sd5 | SM3/dd4 | 16/11~338/243 | 13/9+ | |
| 19 | 694.95 | 475 | sM4/qd5 | SM+3/d-4 | 3/2~40/27~121/81 | ||
| 20 | 731.5 | 500 | M4/m5 | AA3/d4 | 32/21~75/49 | ||
| 21 | 768.1 | 525 | Qa4/Sm5 | d+4 | 25/16~14/9~11/7~81/52 | ||
| 22 | 804.7 | 550 | Sa4/N5 | P4 | 8/5~36/23 | ||
| 23 | 841.25 | 575 | 3A4/sM5 | A-4 | 13/8 | ||
| 24 | 877.8 | 600 | A4/M5/d6 | A4 | 5/3 | ||
| 25 | 914.4 | 625 | Qa5/3d6 | A+4 | 27/16~42/25~22/13~46/27 | ||
| 26 | 951 | 650 | Sa5/sd6 | AA4/dd5 | 125/72 | ||
| 27 | 987.55 | 675 | 3A5/qd6 | d-5 | 16/9~8/7~39/22~75/46 | ||
| 28 | 1024.1 | 700 | A5/m6/d7 | d5 | 9/5 | ||
| 29 | 1060.7 | 725 | Sm6/3d7 | d+5 | 50/27~46/25~90/49~24/13~13/7~20/11 | ||
| 30 | 1097.3 | 750 | N6/sd7 | P5 | 15/8 | ||
| 31 | 1133.9 | 775 | sM6/qd7 | A-5 | 48/25~27/14~21/11~52/27~23/12~40/21~56/29 | ||
| 32 | 1170.4 | 800 | M6/m7 | A5/dd6 | 49/25~64/33~96/49 | ||
| 33 | 1207.0 | 825 | Qa6/Sm7 | A+5 | 2/1 | ||
| 34 | 1243.6 | 850 | Sa6/N7 | AA5/sm6 | 33/16~100/49~49/24~729/338 | ||
| 35 | 1280.2 | 875 | 3A6/sM7 | sm+6 | 25/12~56/27~44/21~27/13 | ||
| 36 | 1316.7 | 900 | A6/M7/d8 | m6 | 15/7~32/15~58/27 | ||
| 37 | 1353.3 | 925 | Qa7/3d8 | N6 | 54/25~50/23~98/45~13/6~169/81 | ||
| 38 | 1389.9 | 950 | Sa7/sd8 | M6 | 20/9~9/4- | ||
| 39 | 1426.5 | 975 | 3A7/qd8 | SM-6 | 9/4+~16/7 | ||
| 40 | 1463.0 | 1000 | A7/P8/d9 | SM6/dd7 | 147/64~7/3 | ||
| 41 | 1499.6 | 1025 | Qa8/3d9 | SM+6/sm-7 | 64/27~50/21~26/11~81/23 | ||
| 42 | 1536.2 | 1050 | Sa8/sd9 | AA6/sm7 | 12/5 | 22/9- | |
| 43 | 1572.7 | 1075 | 3A8/qd9 | sm-7 | 5/2~32/13 | 22/9+ | |
| 44 | 1609.3 | 1100 | A8/m9 | m7 | 81/32~63/25~33/13~23/9 | ||
| 45 | 1645.9 | 1125 | Sm9 | N7 | 64/45~18/7~28/11~208/81~13/5 | ||
| 46 | 1682.5 | 1150 | N9 | M7 | 21/8~196/75 | ||
| 47 | 1719.1 | 1175 | sM9 | SM-7 | 8/3~27/10 | ||
| 48 | 1755.65 | 1200 | M9/d10 | SM7/dd8 | 69/25~135/49 | 36/13- | |
| 49 | 1792.2 | 1225 | Qa9/3d10 | SM+7/d-8 | 14/5~25/9~224/81~176/63~64/23~58/21 | 36/13+ | |
| 50 | 1828.8 | 1250 | Sa9/sd10 | A7/d8 | 20/7~72/25~81/28~63/22~23/8~84/29 | 26/9- | |
| 51 | 1865.4 | 1275 | 3A9/qd10 | P-8 | 147/50~32/11~338/81~144/49 | 26/9+ | |
| 52 | 1902.0 | 1300 | A9/P10 | P8 | 3/1 | Tritave |
It is a weird coincidence how 52edt intones any 52edo intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:
| 52edt | 52edo | Discrepancy |
|---|---|---|
| 365.761 | 369.231 | -3.47 |
| 512.065 | 507.692 | +4.373 |
| 877.825 | 876.923 | +0.902 |
| 1243.586 | 1246.154 | -2.168 |
| 1389.89 | 1384.615 | +5.275 |
| 1755.651 | 1753.846 | +1.805 |
| 2121.411 | 2123.077 | -1.666 |
| 2633.476 | 2630.769 | +2.647 |
…and so on