65edt: Difference between revisions
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Line 5: | Line 5: | ||
! | degree | ! | degree | ||
! | cents value | ! | cents value | ||
!hekts | |||
! | corresponding <br>JI intervals | ! | corresponding <br>JI intervals | ||
! | comments | ! | comments | ||
|- | |- | ||
| | 0 | | | 0 | ||
| | | | colspan="2"| 0 | ||
| | '''exact [[1/1]]''' | | | '''exact [[1/1]]''' | ||
| | | | | | ||
Line 15: | Line 16: | ||
| | 1 | | | 1 | ||
| | 29.2608 | | | 29.2608 | ||
|20 | |||
| | 57/56, 56/55 | | | 57/56, 56/55 | ||
| | | | | | ||
Line 20: | Line 22: | ||
| | 2 | | | 2 | ||
| | 58.5217 | | | 58.5217 | ||
|40 | |||
| | 30/29 | | | 30/29 | ||
| | | | | | ||
Line 25: | Line 28: | ||
| | 3 | | | 3 | ||
| | 87.7825 | | | 87.7825 | ||
|60 | |||
| | [[21/20]], [[20/19]] | | | [[21/20]], [[20/19]] | ||
| | | | | | ||
Line 30: | Line 34: | ||
| | 4 | | | 4 | ||
| | 117.0434 | | | 117.0434 | ||
|80 | |||
| | [[15/14]] | | | [[15/14]] | ||
| | | | | | ||
Line 35: | Line 40: | ||
| | 5 | | | 5 | ||
| | 146.3042 | | | 146.3042 | ||
|100 | |||
| | 49/45, [[12/11]] | | | 49/45, [[12/11]] | ||
| | | | | | ||
Line 40: | Line 46: | ||
| | 6 | | | 6 | ||
| | 175.5651 | | | 175.5651 | ||
|120 | |||
| | [[21/19]], 87/80, 72/65 | | | [[21/19]], 87/80, 72/65 | ||
| | pseudo-[[10/9]] | | | pseudo-[[10/9]] | ||
Line 45: | Line 52: | ||
| | 7 | | | 7 | ||
| | 204.8259 | | | 204.8259 | ||
|140 | |||
| | [[9/8]] | | | [[9/8]] | ||
| | | | | | ||
Line 50: | Line 58: | ||
| | 8 | | | 8 | ||
| | 234.0868 | | | 234.0868 | ||
|160 | |||
| | [[8/7]] | | | [[8/7]] | ||
| | | | | | ||
Line 55: | Line 64: | ||
| | 9 | | | 9 | ||
| | 263.3476 | | | 263.3476 | ||
|180 | |||
| | [[7/6]] | | | [[7/6]] | ||
| | | | | | ||
Line 60: | Line 70: | ||
| | 10 | | | 10 | ||
| | 292.6085 | | | 292.6085 | ||
|200 | |||
| | 45/38, [[32/27]] | | | 45/38, [[32/27]] | ||
| | | | | | ||
Line 65: | Line 76: | ||
| | 11 | | | 11 | ||
| | 321.8693 | | | 321.8693 | ||
|220 | |||
| | 65/54 | | | 65/54 | ||
| | pseudo-[[6/5]] | | | pseudo-[[6/5]] | ||
Line 70: | Line 82: | ||
| | 12 | | | 12 | ||
| | 351.1302 | | | 351.1302 | ||
|240 | |||
| | [[11/9]], 27/22 | | | [[11/9]], 27/22 | ||
| | | | | | ||
|- | |- | ||
| | 13 | | | 13 | ||
| | 380. | | | 380.391 | ||
|260 | |||
| | 56/45, 81/65 | | | 56/45, 81/65 | ||
| | pseudo-[[5/4]] | | | pseudo-[[5/4]] | ||
Line 80: | Line 94: | ||
| | 14 | | | 14 | ||
| | 409.6518 | | | 409.6518 | ||
|280 | |||
| | [[19/15]] | | | [[19/15]] | ||
| | | | | | ||
Line 85: | Line 100: | ||
| | 15 | | | 15 | ||
| | 438.9127 | | | 438.9127 | ||
|300 | |||
| | [[9/7]] | | | [[9/7]] | ||
| | | | | | ||
Line 90: | Line 106: | ||
| | 16 | | | 16 | ||
| | 468.1735 | | | 468.1735 | ||
|320 | |||
| | [[21/16]] | | | [[21/16]] | ||
| | | | | | ||
Line 95: | Line 112: | ||
| | 17 | | | 17 | ||
| | 497.4344 | | | 497.4344 | ||
|340 | |||
| | [[4/3]] | | | [[4/3]] | ||
| | | | | | ||
Line 100: | Line 118: | ||
| | 18 | | | 18 | ||
| | 526.6952 | | | 526.6952 | ||
|360 | |||
| | [[19/14]] | | | [[19/14]] | ||
| | | | | | ||
Line 105: | Line 124: | ||
| | 19 | | | 19 | ||
| | 555.9561 | | | 555.9561 | ||
|380 | |||
| | 40/29 | | | 40/29 | ||
| | | | | | ||
Line 110: | Line 130: | ||
| | 20 | | | 20 | ||
| | 585.2169 | | | 585.2169 | ||
|400 | |||
| | [[7/5]] | | | [[7/5]] | ||
| | | | | | ||
Line 115: | Line 136: | ||
| | 21 | | | 21 | ||
| | 614.4778 | | | 614.4778 | ||
|420 | |||
| | [[10/7]] | | | [[10/7]] | ||
| | | | | | ||
Line 120: | Line 142: | ||
| | 22 | | | 22 | ||
| | 643.7386 | | | 643.7386 | ||
|440 | |||
| | 29/20 | | | 29/20 | ||
| | | | | | ||
Line 125: | Line 148: | ||
| | 23 | | | 23 | ||
| | 672.9995 | | | 672.9995 | ||
|460 | |||
| | [[28/19]] | | | [[28/19]] | ||
| | | | | | ||
Line 130: | Line 154: | ||
| | 24 | | | 24 | ||
| | 702.2603 | | | 702.2603 | ||
|480 | |||
| | [[3/2]] | | | [[3/2]] | ||
| | | | | | ||
Line 135: | Line 160: | ||
| | 25 | | | 25 | ||
| | 731.5212 | | | 731.5212 | ||
|500 | |||
| | [[32/21]] | | | [[32/21]] | ||
| | | | | | ||
|- | |- | ||
| | 26 | | | 26 | ||
| | 760. | | | 760.782 | ||
|520 | |||
| | 45/29 | | | 45/29 | ||
| | | | | | ||
Line 145: | Line 172: | ||
| | 27 | | | 27 | ||
| | 790.0428 | | | 790.0428 | ||
|540 | |||
| | [[30/19]] | | | [[30/19]] | ||
| | | | | | ||
Line 150: | Line 178: | ||
| | 28 | | | 28 | ||
| | 819.3037 | | | 819.3037 | ||
|560 | |||
| | 45/28 | | | 45/28 | ||
| | pseudo-[[8/5]] | | | pseudo-[[8/5]] | ||
Line 155: | Line 184: | ||
| | 29 | | | 29 | ||
| | 848.5645 | | | 848.5645 | ||
|580 | |||
| | [[18/11]] | | | [[18/11]] | ||
| | | | | | ||
Line 160: | Line 190: | ||
| | 30 | | | 30 | ||
| | 877.8254 | | | 877.8254 | ||
|600 | |||
| | 108/65 | | | 108/65 | ||
| | pseudo-[[5/3]] | | | pseudo-[[5/3]] | ||
Line 165: | Line 196: | ||
| | 31 | | | 31 | ||
| | 907.0862 | | | 907.0862 | ||
|620 | |||
| | [[27/16]] | | | [[27/16]] | ||
| | | | | | ||
Line 170: | Line 202: | ||
| | 32 | | | 32 | ||
| | 936.3471 | | | 936.3471 | ||
|640 | |||
| | [[12/7]] | | | [[12/7]] | ||
| | | | | | ||
Line 175: | Line 208: | ||
| | 33 | | | 33 | ||
| | 965.6079 | | | 965.6079 | ||
|660 | |||
| | [[7/4]] | | | [[7/4]] | ||
| | | | | | ||
Line 180: | Line 214: | ||
| | 34 | | | 34 | ||
| | 994.8688 | | | 994.8688 | ||
|680 | |||
| | [[16/9]] | | | [[16/9]] | ||
| | | | | | ||
Line 185: | Line 220: | ||
| | 35 | | | 35 | ||
| | 1024.1296 | | | 1024.1296 | ||
|700 | |||
| | 65/36 | | | 65/36 | ||
| | pseudo-[[9/5]] | | | pseudo-[[9/5]] | ||
Line 190: | Line 226: | ||
| | 36 | | | 36 | ||
| | 1053.3905 | | | 1053.3905 | ||
|720 | |||
| | [[11/6]] | | | [[11/6]] | ||
| | | | | | ||
Line 195: | Line 232: | ||
| | 37 | | | 37 | ||
| | 1082.6513 | | | 1082.6513 | ||
|740 | |||
| | [[28/15]] | | | [[28/15]] | ||
| | | | | | ||
Line 200: | Line 238: | ||
| | 38 | | | 38 | ||
| | 1111.9122 | | | 1111.9122 | ||
|760 | |||
| | [[19/10]] | | | [[19/10]] | ||
| | | | | | ||
|- | |- | ||
| | 39 | | | 39 | ||
| | 1141. | | | 1141.173 | ||
|780 | |||
| | 29/15 | | | 29/15 | ||
| | | | | | ||
Line 210: | Line 250: | ||
| | 40 | | | 40 | ||
| | 1170.4338 | | | 1170.4338 | ||
|800 | |||
| | 55/28 | | | 55/28 | ||
| | | | | | ||
Line 215: | Line 256: | ||
| | 41 | | | 41 | ||
| | 1199.6947 | | | 1199.6947 | ||
|820 | |||
| | [[Octave|2/1]] | | | [[Octave|2/1]] | ||
| | | | | | ||
Line 220: | Line 262: | ||
| | 42 | | | 42 | ||
| | 1228.9555 | | | 1228.9555 | ||
|840 | |||
| | 57/28 | | | 57/28 | ||
| | | | | | ||
Line 225: | Line 268: | ||
| | 43 | | | 43 | ||
| | 1258.2164 | | | 1258.2164 | ||
|860 | |||
| | 60/29 | | | 60/29 | ||
| | | | | | ||
Line 230: | Line 274: | ||
| | 44 | | | 44 | ||
| | 1287.4772 | | | 1287.4772 | ||
|880 | |||
| | 21/10 | | | 21/10 | ||
| | | | | | ||
Line 235: | Line 280: | ||
| | 45 | | | 45 | ||
| | 1316.7381 | | | 1316.7381 | ||
|900 | |||
| | [[15/7]] | | | [[15/7]] | ||
| | | | | | ||
Line 240: | Line 286: | ||
| | 46 | | | 46 | ||
| | 1345.9989 | | | 1345.9989 | ||
|920 | |||
| | 87/40 | | | 87/40 | ||
| | | | | | ||
Line 245: | Line 292: | ||
| | 47 | | | 47 | ||
| | 1375.2598 | | | 1375.2598 | ||
|940 | |||
| | 42/19 | | | 42/19 | ||
| | | | | | ||
Line 250: | Line 298: | ||
| | 48 | | | 48 | ||
| | 1404.5206 | | | 1404.5206 | ||
|960 | |||
| | [[9/4]] | | | [[9/4]] | ||
| | | | | | ||
Line 255: | Line 304: | ||
| | 49 | | | 49 | ||
| | 1433.7815 | | | 1433.7815 | ||
|980 | |||
| | [[16/7]] | | | [[16/7]] | ||
| | | | | | ||
Line 260: | Line 310: | ||
| | 50 | | | 50 | ||
| | 1463.0423 | | | 1463.0423 | ||
|1000 | |||
| | [[7/3]] | | | [[7/3]] | ||
| | | | | | ||
Line 265: | Line 316: | ||
| | 51 | | | 51 | ||
| | 1492.3032 | | | 1492.3032 | ||
|1020 | |||
| | 45/19 | | | 45/19 | ||
| | | | | | ||
|- | |- | ||
| | 52 | | | 52 | ||
| | 1521. | | | 1521.564 | ||
|1040 | |||
| | 65/27 | | | 65/27 | ||
| | pseudo-[[12/5]] | | | pseudo-[[12/5]] | ||
Line 275: | Line 328: | ||
| | 53 | | | 53 | ||
| | 1550.8248 | | | 1550.8248 | ||
|1060 | |||
| | 22/9, 27/11 | | | 22/9, 27/11 | ||
| | | | | | ||
Line 280: | Line 334: | ||
| | 54 | | | 54 | ||
| | 1580.0857 | | | 1580.0857 | ||
|1080 | |||
| | 162/65 | | | 162/65 | ||
| | pseudo-[[5/2]] | | | pseudo-[[5/2]] | ||
Line 285: | Line 340: | ||
| | 55 | | | 55 | ||
| | 1609.3465 | | | 1609.3465 | ||
|1100 | |||
| | 38/15 | | | 38/15 | ||
| | | | | | ||
Line 290: | Line 346: | ||
| | 56 | | | 56 | ||
| | 1638.6074 | | | 1638.6074 | ||
|1120 | |||
| | 18/7 | | | 18/7 | ||
| | | | | | ||
Line 295: | Line 352: | ||
| | 57 | | | 57 | ||
| | 1667.8682 | | | 1667.8682 | ||
|1140 | |||
| | 21/8 | | | 21/8 | ||
| | | | | | ||
Line 300: | Line 358: | ||
| | 58 | | | 58 | ||
| | 1697.1291 | | | 1697.1291 | ||
|1160 | |||
| | [[8/3]] | | | [[8/3]] | ||
| | | | | | ||
Line 305: | Line 364: | ||
| | 59 | | | 59 | ||
| | 1726.3899 | | | 1726.3899 | ||
|1180 | |||
| | 19/7 | | | 19/7 | ||
| | | | | | ||
Line 310: | Line 370: | ||
| | 60 | | | 60 | ||
| | 1755.6508 | | | 1755.6508 | ||
|1200 | |||
| | [[11/4]] | | | [[11/4]] | ||
| | | | | | ||
Line 315: | Line 376: | ||
| | 61 | | | 61 | ||
| | 1784.9116 | | | 1784.9116 | ||
|1220 | |||
| | [[14/5]] | | | [[14/5]] | ||
| | | | | | ||
Line 320: | Line 382: | ||
| | 62 | | | 62 | ||
| | 1814.1725 | | | 1814.1725 | ||
|1240 | |||
| | 20/7 | | | 20/7 | ||
| | | | | | ||
Line 325: | Line 388: | ||
| | 63 | | | 63 | ||
| | 1843.4333 | | | 1843.4333 | ||
|1260 | |||
| | 29/10 | | | 29/10 | ||
| | | | | | ||
Line 330: | Line 394: | ||
| | 64 | | | 64 | ||
| | 1872.6942 | | | 1872.6942 | ||
|1280 | |||
| | 56/19 | | | 56/19 | ||
| | | | | | ||
Line 335: | Line 400: | ||
| | 65 | | | 65 | ||
| | 1901.9550 | | | 1901.9550 | ||
|1300 | |||
| | '''exact [[3/1]]''' | | | '''exact [[3/1]]''' | ||
| | [[3/2|just perfect fifth]] plus an octave | | | [[3/2|just perfect fifth]] plus an octave |
Revision as of 14:24, 24 April 2019
Division of the third harmonic into 65 equal parts (65EDT) is almost identical to 41 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the 16-integer-limit.
degree | cents value | hekts | corresponding JI intervals |
comments |
---|---|---|---|---|
0 | 0 | exact 1/1 | ||
1 | 29.2608 | 20 | 57/56, 56/55 | |
2 | 58.5217 | 40 | 30/29 | |
3 | 87.7825 | 60 | 21/20, 20/19 | |
4 | 117.0434 | 80 | 15/14 | |
5 | 146.3042 | 100 | 49/45, 12/11 | |
6 | 175.5651 | 120 | 21/19, 87/80, 72/65 | pseudo-10/9 |
7 | 204.8259 | 140 | 9/8 | |
8 | 234.0868 | 160 | 8/7 | |
9 | 263.3476 | 180 | 7/6 | |
10 | 292.6085 | 200 | 45/38, 32/27 | |
11 | 321.8693 | 220 | 65/54 | pseudo-6/5 |
12 | 351.1302 | 240 | 11/9, 27/22 | |
13 | 380.391 | 260 | 56/45, 81/65 | pseudo-5/4 |
14 | 409.6518 | 280 | 19/15 | |
15 | 438.9127 | 300 | 9/7 | |
16 | 468.1735 | 320 | 21/16 | |
17 | 497.4344 | 340 | 4/3 | |
18 | 526.6952 | 360 | 19/14 | |
19 | 555.9561 | 380 | 40/29 | |
20 | 585.2169 | 400 | 7/5 | |
21 | 614.4778 | 420 | 10/7 | |
22 | 643.7386 | 440 | 29/20 | |
23 | 672.9995 | 460 | 28/19 | |
24 | 702.2603 | 480 | 3/2 | |
25 | 731.5212 | 500 | 32/21 | |
26 | 760.782 | 520 | 45/29 | |
27 | 790.0428 | 540 | 30/19 | |
28 | 819.3037 | 560 | 45/28 | pseudo-8/5 |
29 | 848.5645 | 580 | 18/11 | |
30 | 877.8254 | 600 | 108/65 | pseudo-5/3 |
31 | 907.0862 | 620 | 27/16 | |
32 | 936.3471 | 640 | 12/7 | |
33 | 965.6079 | 660 | 7/4 | |
34 | 994.8688 | 680 | 16/9 | |
35 | 1024.1296 | 700 | 65/36 | pseudo-9/5 |
36 | 1053.3905 | 720 | 11/6 | |
37 | 1082.6513 | 740 | 28/15 | |
38 | 1111.9122 | 760 | 19/10 | |
39 | 1141.173 | 780 | 29/15 | |
40 | 1170.4338 | 800 | 55/28 | |
41 | 1199.6947 | 820 | 2/1 | |
42 | 1228.9555 | 840 | 57/28 | |
43 | 1258.2164 | 860 | 60/29 | |
44 | 1287.4772 | 880 | 21/10 | |
45 | 1316.7381 | 900 | 15/7 | |
46 | 1345.9989 | 920 | 87/40 | |
47 | 1375.2598 | 940 | 42/19 | |
48 | 1404.5206 | 960 | 9/4 | |
49 | 1433.7815 | 980 | 16/7 | |
50 | 1463.0423 | 1000 | 7/3 | |
51 | 1492.3032 | 1020 | 45/19 | |
52 | 1521.564 | 1040 | 65/27 | pseudo-12/5 |
53 | 1550.8248 | 1060 | 22/9, 27/11 | |
54 | 1580.0857 | 1080 | 162/65 | pseudo-5/2 |
55 | 1609.3465 | 1100 | 38/15 | |
56 | 1638.6074 | 1120 | 18/7 | |
57 | 1667.8682 | 1140 | 21/8 | |
58 | 1697.1291 | 1160 | 8/3 | |
59 | 1726.3899 | 1180 | 19/7 | |
60 | 1755.6508 | 1200 | 11/4 | |
61 | 1784.9116 | 1220 | 14/5 | |
62 | 1814.1725 | 1240 | 20/7 | |
63 | 1843.4333 | 1260 | 29/10 | |
64 | 1872.6942 | 1280 | 56/19 | |
65 | 1901.9550 | 1300 | exact 3/1 | just perfect fifth plus an octave |