47edo: Difference between revisions
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m Fixed non-standard title and bolded "47-EDO". |
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| Line 25: | Line 25: | ||
! | Degree | ! | Degree | ||
! | Size (Cents) | ! | Size (Cents) | ||
!pions | |||
!7mus | |||
! colspan="2" | relative notation | ! colspan="2" | relative notation | ||
! | absolute notation | ! | absolute notation | ||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| style="text-align:right;" | 0.0000 | | colspan="3" style="text-align:right;" | 0.0000 | ||
| style="text-align:center;" | perfect unison | | style="text-align:center;" | perfect unison | ||
| style="text-align:center;" | P1 | | style="text-align:center;" | P1 | ||
| Line 36: | Line 38: | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:right;" | 25.5319 | | style="text-align:right;" | 25.5319 | ||
|27.0638 | |||
|32.68085 (20.AE4C<sub>16</sub>) | |||
| style="text-align:center;" | aug 1sn | | style="text-align:center;" | aug 1sn | ||
| style="text-align:center;" | A1 | | style="text-align:center;" | A1 | ||
| Line 42: | Line 46: | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:right;" | 51.0638 | | style="text-align:right;" | 51.0638 | ||
|54.1277 | |||
|65.3617 (41.5C988<sub>16</sub>) | |||
| style="text-align:center;" | double-aug 1sn | | style="text-align:center;" | double-aug 1sn | ||
| style="text-align:center;" | AA1 | | style="text-align:center;" | AA1 | ||
| Line 48: | Line 54: | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:right;" | 76.5957 | | style="text-align:right;" | 76.5957 | ||
|81.1915 | |||
|98.04255 (62.0AE5<sub>16</sub>) | |||
| style="text-align:center;" | triple-aug 1sn, triple-dim 2nd | | style="text-align:center;" | triple-aug 1sn, triple-dim 2nd | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>1, d<span style="font-size: 90%; vertical-align: super;">3</span>2 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>1, d<span style="font-size: 90%; vertical-align: super;">3</span>2 | ||
| Line 54: | Line 62: | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:right;" | 102.1277 | | style="text-align:right;" | 102.1277 | ||
|108.2553 | |||
|130.7234 (82.B931<sub>16</sub>) | |||
| style="text-align:center;" | double-dim 2nd | | style="text-align:center;" | double-dim 2nd | ||
| style="text-align:center;" | dd2 | | style="text-align:center;" | dd2 | ||
| Line 60: | Line 70: | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:right;" | 127.6596 | | style="text-align:right;" | 127.6596 | ||
|135.31915 | |||
|163.4043 (A3.677D<sub>16</sub>) | |||
| style="text-align:center;" | dim 2nd | | style="text-align:center;" | dim 2nd | ||
| style="text-align:center;" | d2 | | style="text-align:center;" | d2 | ||
| Line 66: | Line 78: | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:right;" | 153.1915 | | style="text-align:right;" | 153.1915 | ||
|162.383 | |||
|196.0851 (C4.15CA<sub>16</sub>) | |||
| style="text-align:center;" | minor 2nd | | style="text-align:center;" | minor 2nd | ||
| style="text-align:center;" | m2 | | style="text-align:center;" | m2 | ||
| Line 72: | Line 86: | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:right;" | 178.7234 | | style="text-align:right;" | 178.7234 | ||
|189.4468 | |||
|228.766 (E4.C416<sub>16</sub>) 261.4468 (105.7262<sub>16</sub>) 294.1277 (126.20AE<sub>16</sub>) 326.8085 (146.CEFB<sub>16</sub>) 359.4894 (167.7D47<sub>16</sub>) 392.1702 (188.2B93<sub>16</sub>) 424.8511 (1A8.D9DF<sub>16</sub>) 457.5319 (1C9.882C<sub>16</sub>) 490.2128 (1EA.3678<sub>16</sub>) 522.8936 (20A.E4C4<sub>16</sub>) 555.5745 (22B.931<sub>16</sub>) 588.2553 (24C.415D<sub>16</sub>) 620.9362 (26C.EFA9<sub>16</sub>) 653.617 (28D.9DF5<sub>16</sub>) 686.2979 (2AE.4C41<sub>16</sub>) 718.9787 (2CE.FA8E<sub>16</sub>) 751.6595 (2EF.A8DA<sub>16</sub>) 784.3404 (310.5726<sub>16</sub>) 817.0213 (331.0572<sub>16</sub>) 849.7021 (351.B3BF<sub>16</sub>) 882.383 (372.620B<sub>16</sub>) 915.0638 (393.1057<sub>16</sub>) 947.7447 (3B3.BEA3<sub>16</sub>) 980.4255 (3D4.6CF<sub>16</sub>) 1013.1064 (3F5.1B3C<sub>16</sub>) 1045.7872 (415.C988<sub>16</sub>) 1078.4681 (436.77D4<sub>16</sub>) 1111.1489 (457.2621<sub>16</sub>) 1143.8298 (477.D46D<sub>16</sub>) 1176.5106 (498.82B9<sub>16</sub>) 1209.1915 (4B9.3105<sub>16</sub>) 1241.8723 (4D9.DF52<sub>16</sub>) 1274.5532 (4FA.8D9E<sub>16</sub>) 1307.234 (51B.3BEA<sub>16</sub>) 1339.9149 (53B.EA36<sub>16</sub>) 1372.5957 (55C.9883<sub>16</sub>) 1405.2766 (57D.46CF<sub>16</sub>) 1437.95745 (59D.F51B<sub>16</sub>) 1470.6383 (5BE.A3678<sub>16</sub>) 1503.31915 (5DF.51B4<sub>16</sub>) | |||
| style="text-align:center;" | major 2nd | | style="text-align:center;" | major 2nd | ||
| style="text-align:center;" | M2 | | style="text-align:center;" | M2 | ||
| Line 78: | Line 94: | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:right;" | 204.2553 | | style="text-align:right;" | 204.2553 | ||
|216.5106 | |||
| | |||
| style="text-align:center;" | aug 2nd | | style="text-align:center;" | aug 2nd | ||
| style="text-align:center;" | A2 | | style="text-align:center;" | A2 | ||
| Line 84: | Line 102: | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:right;" | 229.7872 | | style="text-align:right;" | 229.7872 | ||
|243.5745 | |||
| | |||
| style="text-align:center;" | double-aug 2nd | | style="text-align:center;" | double-aug 2nd | ||
| style="text-align:center;" | AA2 | | style="text-align:center;" | AA2 | ||
| Line 89: | Line 109: | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:right;" | 255. | | style="text-align:right;" | 255.31915 | ||
|270.6383 | |||
| | |||
| style="text-align:center;" | triple-aug 2nd, triple-dim 3rd | | style="text-align:center;" | triple-aug 2nd, triple-dim 3rd | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>2, d<span style="font-size: 90%; vertical-align: super;">3</span>3 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>2, d<span style="font-size: 90%; vertical-align: super;">3</span>3 | ||
| Line 96: | Line 118: | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:right;" | 280.8511 | | style="text-align:right;" | 280.8511 | ||
|297.7021 | |||
| | |||
| style="text-align:center;" | double-dim 3rd | | style="text-align:center;" | double-dim 3rd | ||
| style="text-align:center;" | dd3 | | style="text-align:center;" | dd3 | ||
| Line 101: | Line 125: | ||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:right;" | 306. | | style="text-align:right;" | 306.383 | ||
|324.766 | |||
| | |||
| style="text-align:center;" | dim 3rd | | style="text-align:center;" | dim 3rd | ||
| style="text-align:center;" | d3 | | style="text-align:center;" | d3 | ||
| Line 108: | Line 134: | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:right;" | 331.9149 | | style="text-align:right;" | 331.9149 | ||
|351.8298 | |||
| | |||
| style="text-align:center;" | minor 3rd | | style="text-align:center;" | minor 3rd | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
| Line 114: | Line 142: | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:right;" | 357.4468 | | style="text-align:right;" | 357.4468 | ||
|378.8936 | |||
| | |||
| style="text-align:center;" | major 3rd | | style="text-align:center;" | major 3rd | ||
| style="text-align:center;" | M3 | | style="text-align:center;" | M3 | ||
| Line 120: | Line 150: | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:right;" | 382.9787 | | style="text-align:right;" | 382.9787 | ||
|405.95745 | |||
| | |||
| style="text-align:center;" | aug 3rd | | style="text-align:center;" | aug 3rd | ||
| style="text-align:center;" | A3 | | style="text-align:center;" | A3 | ||
| Line 126: | Line 158: | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:right;" | 408.5106 | | style="text-align:right;" | 408.5106 | ||
|433.0213 | |||
| | |||
| style="text-align:center;" | double-aug 3rd | | style="text-align:center;" | double-aug 3rd | ||
| style="text-align:center;" | AA3 | | style="text-align:center;" | AA3 | ||
| Line 131: | Line 165: | ||
|- | |- | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| style="text-align:right;" | 434. | | style="text-align:right;" | 434.04255 | ||
|460.0851 | |||
| | |||
| style="text-align:center;" | triple-aug 3rd, triple-dim 4th | | style="text-align:center;" | triple-aug 3rd, triple-dim 4th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>3, d<span style="font-size: 90%; vertical-align: super;">3</span>4 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>3, d<span style="font-size: 90%; vertical-align: super;">3</span>4 | ||
| Line 138: | Line 174: | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| style="text-align:right;" | 459.5745 | | style="text-align:right;" | 459.5745 | ||
|487.1489 | |||
| | |||
| style="text-align:center;" | double-dim 4th | | style="text-align:center;" | double-dim 4th | ||
| style="text-align:center;" | dd4 | | style="text-align:center;" | dd4 | ||
| Line 144: | Line 182: | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:right;" | 485.1064 | | style="text-align:right;" | 485.1064 | ||
|514.2128 | |||
| | |||
| style="text-align:center;" | dim 4th | | style="text-align:center;" | dim 4th | ||
| style="text-align:center;" | d4 | | style="text-align:center;" | d4 | ||
| Line 150: | Line 190: | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| style="text-align:right;" | 510.6383 | | style="text-align:right;" | 510.6383 | ||
|541.2766 | |||
| | |||
| style="text-align:center;" | perfect 4th | | style="text-align:center;" | perfect 4th | ||
| style="text-align:center;" | P4 | | style="text-align:center;" | P4 | ||
| Line 156: | Line 198: | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| style="text-align:right;" | 536.1702 | | style="text-align:right;" | 536.1702 | ||
|568.3404 | |||
| | |||
| style="text-align:center;" | aug 4th | | style="text-align:center;" | aug 4th | ||
| style="text-align:center;" | A4 | | style="text-align:center;" | A4 | ||
| Line 162: | Line 206: | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| style="text-align:right;" | 561.7021 | | style="text-align:right;" | 561.7021 | ||
|595.4043 | |||
| | |||
| style="text-align:center;" | double-aug 4th | | style="text-align:center;" | double-aug 4th | ||
| style="text-align:center;" | AA4 | | style="text-align:center;" | AA4 | ||
| Line 168: | Line 214: | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| style="text-align:right;" | 587.2340 | | style="text-align:right;" | 587.2340 | ||
|622.4681 | |||
| | |||
| style="text-align:center;" | triple-aug 4th | | style="text-align:center;" | triple-aug 4th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4 | ||
| Line 174: | Line 222: | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| style="text-align:right;" | 612.7660 | | style="text-align:right;" | 612.7660 | ||
|649.5319 | |||
| | |||
| style="text-align:center;" | triple-dim 5th | | style="text-align:center;" | triple-dim 5th | ||
| style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5 | | style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5 | ||
| Line 180: | Line 230: | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| style="text-align:right;" | 638.2979 | | style="text-align:right;" | 638.2979 | ||
|676.5957 | |||
| | |||
| style="text-align:center;" | double-dim 5th | | style="text-align:center;" | double-dim 5th | ||
| style="text-align:center;" | dd5 | | style="text-align:center;" | dd5 | ||
| Line 186: | Line 238: | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| style="text-align:right;" | 663.8298 | | style="text-align:right;" | 663.8298 | ||
|703.6596 | |||
| | |||
| style="text-align:center;" | dim 5th | | style="text-align:center;" | dim 5th | ||
| style="text-align:center;" | d5 | | style="text-align:center;" | d5 | ||
| Line 192: | Line 246: | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| style="text-align:right;" | 689.3617 | | style="text-align:right;" | 689.3617 | ||
|730.7234 | |||
| | |||
| style="text-align:center;" | perfect 5th | | style="text-align:center;" | perfect 5th | ||
| style="text-align:center;" | P5 | | style="text-align:center;" | P5 | ||
| Line 198: | Line 254: | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| style="text-align:right;" | 714.8936 | | style="text-align:right;" | 714.8936 | ||
|757.7872 | |||
| | |||
| style="text-align:center;" | aug 5th | | style="text-align:center;" | aug 5th | ||
| style="text-align:center;" | A5 | | style="text-align:center;" | A5 | ||
| Line 204: | Line 262: | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| style="text-align:right;" | 740.4255 | | style="text-align:right;" | 740.4255 | ||
|784.8511 | |||
| | |||
| style="text-align:center;" | double-aug 5th | | style="text-align:center;" | double-aug 5th | ||
| style="text-align:center;" | AA5 | | style="text-align:center;" | AA5 | ||
| Line 209: | Line 269: | ||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| style="text-align:right;" | 765. | | style="text-align:right;" | 765.95745 | ||
|811.9149 | |||
| | |||
| style="text-align:center;" | triple-aug 5th, triple-dim 6th | | style="text-align:center;" | triple-aug 5th, triple-dim 6th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6 | ||
| Line 216: | Line 278: | ||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| style="text-align:right;" | 791.4894 | | style="text-align:right;" | 791.4894 | ||
|838.9787 | |||
| | |||
| style="text-align:center;" | double-dim 6th | | style="text-align:center;" | double-dim 6th | ||
| style="text-align:center;" | dd6 | | style="text-align:center;" | dd6 | ||
| Line 222: | Line 286: | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
| style="text-align:right;" | 817.0213 | | style="text-align:right;" | 817.0213 | ||
|866.04255 | |||
| | |||
| style="text-align:center;" | dim 6th | | style="text-align:center;" | dim 6th | ||
| style="text-align:center;" | d6 | | style="text-align:center;" | d6 | ||
| Line 228: | Line 294: | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
| style="text-align:right;" | 842.5532 | | style="text-align:right;" | 842.5532 | ||
|893.1064 | |||
| | |||
| style="text-align:center;" | minor 6th | | style="text-align:center;" | minor 6th | ||
| style="text-align:center;" | m6 | | style="text-align:center;" | m6 | ||
| Line 234: | Line 302: | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
| style="text-align:right;" | 868.0851 | | style="text-align:right;" | 868.0851 | ||
|920.1702 | |||
| | |||
| style="text-align:center;" | major 6th | | style="text-align:center;" | major 6th | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
| Line 239: | Line 309: | ||
|- | |- | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
| style="text-align:right;" | 893. | | style="text-align:right;" | 893.617 | ||
|947.234 | |||
| | |||
| style="text-align:center;" | aug 6th | | style="text-align:center;" | aug 6th | ||
| style="text-align:center;" | A6 | | style="text-align:center;" | A6 | ||
| Line 246: | Line 318: | ||
| style="text-align:center;" | 36 | | style="text-align:center;" | 36 | ||
| style="text-align:right;" | 919.1489 | | style="text-align:right;" | 919.1489 | ||
|974.2979 | |||
| | |||
| style="text-align:center;" | double-aug 6th | | style="text-align:center;" | double-aug 6th | ||
| style="text-align:center;" | AA6 | | style="text-align:center;" | AA6 | ||
| Line 251: | Line 325: | ||
|- | |- | ||
| style="text-align:center;" | 37 | | style="text-align:center;" | 37 | ||
| style="text-align:right;" | 944. | | style="text-align:right;" | 944.68085 | ||
|1001.3617 | |||
| | |||
| style="text-align:center;" | triple-aug 6th, triple-dim 7th | | style="text-align:center;" | triple-aug 6th, triple-dim 7th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>6, d<span style="font-size: 90%; vertical-align: super;">3</span>7 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>6, d<span style="font-size: 90%; vertical-align: super;">3</span>7 | ||
| Line 258: | Line 334: | ||
| style="text-align:center;" | 38 | | style="text-align:center;" | 38 | ||
| style="text-align:right;" | 970.2128 | | style="text-align:right;" | 970.2128 | ||
|1028.4255 | |||
| | |||
| style="text-align:center;" | double-dim 7th | | style="text-align:center;" | double-dim 7th | ||
| style="text-align:center;" | dd7 | | style="text-align:center;" | dd7 | ||
| Line 264: | Line 342: | ||
| style="text-align:center;" | 39 | | style="text-align:center;" | 39 | ||
| style="text-align:right;" | 995.7447 | | style="text-align:right;" | 995.7447 | ||
|1055.4894 | |||
| | |||
| style="text-align:center;" | dim 7th | | style="text-align:center;" | dim 7th | ||
| style="text-align:center;" | d7 | | style="text-align:center;" | d7 | ||
| Line 270: | Line 350: | ||
| style="text-align:center;" | 40 | | style="text-align:center;" | 40 | ||
| style="text-align:right;" | 1021.2766 | | style="text-align:right;" | 1021.2766 | ||
|1082.5532 | |||
| | |||
| style="text-align:center;" | minor 7th | | style="text-align:center;" | minor 7th | ||
| style="text-align:center;" | m7 | | style="text-align:center;" | m7 | ||
| Line 276: | Line 358: | ||
| style="text-align:center;" | 41 | | style="text-align:center;" | 41 | ||
| style="text-align:right;" | 1046.8085 | | style="text-align:right;" | 1046.8085 | ||
|1109.617 | |||
| | |||
| style="text-align:center;" | major 7th | | style="text-align:center;" | major 7th | ||
| style="text-align:center;" | M7 | | style="text-align:center;" | M7 | ||
| Line 282: | Line 366: | ||
| style="text-align:center;" | 42 | | style="text-align:center;" | 42 | ||
| style="text-align:right;" | 1072.3404 | | style="text-align:right;" | 1072.3404 | ||
|1136.68085 | |||
| | |||
| style="text-align:center;" | aug 7th | | style="text-align:center;" | aug 7th | ||
| style="text-align:center;" | A7 | | style="text-align:center;" | A7 | ||
| Line 288: | Line 374: | ||
| style="text-align:center;" | 43 | | style="text-align:center;" | 43 | ||
| style="text-align:right;" | 1097.8723 | | style="text-align:right;" | 1097.8723 | ||
|1163.7447 | |||
| | |||
| style="text-align:center;" | double-aug 7th | | style="text-align:center;" | double-aug 7th | ||
| style="text-align:center;" | AA7 | | style="text-align:center;" | AA7 | ||
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| style="text-align:center;" | 44 | | style="text-align:center;" | 44 | ||
| style="text-align:right;" | 1123.4043 | | style="text-align:right;" | 1123.4043 | ||
|1190.8085 | |||
| | |||
| style="text-align:center;" | triple-aug 7th, triple-dim 8ve | | style="text-align:center;" | triple-aug 7th, triple-dim 8ve | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>7, d<span style="font-size: 90%; vertical-align: super;">3</span>8 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>7, d<span style="font-size: 90%; vertical-align: super;">3</span>8 | ||
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| style="text-align:center;" | 45 | | style="text-align:center;" | 45 | ||
| style="text-align:right;" | 1148.9362 | | style="text-align:right;" | 1148.9362 | ||
|1217.8723 | |||
| | |||
| style="text-align:center;" | double-dim 8ve | | style="text-align:center;" | double-dim 8ve | ||
| style="text-align:center;" | dd8 | | style="text-align:center;" | dd8 | ||
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| style="text-align:center;" | 46 | | style="text-align:center;" | 46 | ||
| style="text-align:right;" | 1174.4681 | | style="text-align:right;" | 1174.4681 | ||
|1244.9362 | |||
| | |||
| style="text-align:center;" | dim 8ve | | style="text-align:center;" | dim 8ve | ||
| style="text-align:center;" | d8 | | style="text-align:center;" | d8 | ||
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|- | |- | ||
| style="text-align:center;" | 47 | | style="text-align:center;" | 47 | ||
| style="text-align:right;" | 1200 | | style="text-align:right;" | 1200 | ||
|1272 | |||
|1536 (600<sub>16</sub>) | |||
| style="text-align:center;" | perfect 8ve | | style="text-align:center;" | perfect 8ve | ||
| style="text-align:center;" | P8 | | style="text-align:center;" | P8 | ||
Revision as of 17:53, 3 April 2019
47 tone Equal Temperament
47-EDO divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit 2*47 subgroup of the 23-limit, on which it tempers out the same commas as 94edo. It provides a good tuning for baldy and silver temperaments and relatives.
47edo is the 15th prime edo, following 43edo and preceding 53edo.
47edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as flat (see 42edo for the opposite extreme).
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale:
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#3 - F#5 - A#3 - C# or as Eb4 - Gbb - Ab4 - Db6. This is an aug-three double-dim-seven chord, written D#3(A3)dd7 or Eb4(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#3(#3)b37 or Eb4(#3)b37.
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.
Intervals of 47edo
| Degree | Size (Cents) | pions | 7mus | relative notation | absolute notation | |
|---|---|---|---|---|---|---|
| 0 | 0.0000 | perfect unison | P1 | D | ||
| 1 | 25.5319 | 27.0638 | 32.68085 (20.AE4C16) | aug 1sn | A1 | D# |
| 2 | 51.0638 | 54.1277 | 65.3617 (41.5C98816) | double-aug 1sn | AA1 | Dx |
| 3 | 76.5957 | 81.1915 | 98.04255 (62.0AE516) | triple-aug 1sn, triple-dim 2nd | A31, d32 | D#3, Eb4 |
| 4 | 102.1277 | 108.2553 | 130.7234 (82.B93116) | double-dim 2nd | dd2 | Eb3 |
| 5 | 127.6596 | 135.31915 | 163.4043 (A3.677D16) | dim 2nd | d2 | Ebb |
| 6 | 153.1915 | 162.383 | 196.0851 (C4.15CA16) | minor 2nd | m2 | Eb |
| 7 | 178.7234 | 189.4468 | 228.766 (E4.C41616) 261.4468 (105.726216) 294.1277 (126.20AE16) 326.8085 (146.CEFB16) 359.4894 (167.7D4716) 392.1702 (188.2B9316) 424.8511 (1A8.D9DF16) 457.5319 (1C9.882C16) 490.2128 (1EA.367816) 522.8936 (20A.E4C416) 555.5745 (22B.93116) 588.2553 (24C.415D16) 620.9362 (26C.EFA916) 653.617 (28D.9DF516) 686.2979 (2AE.4C4116) 718.9787 (2CE.FA8E16) 751.6595 (2EF.A8DA16) 784.3404 (310.572616) 817.0213 (331.057216) 849.7021 (351.B3BF16) 882.383 (372.620B16) 915.0638 (393.105716) 947.7447 (3B3.BEA316) 980.4255 (3D4.6CF16) 1013.1064 (3F5.1B3C16) 1045.7872 (415.C98816) 1078.4681 (436.77D416) 1111.1489 (457.262116) 1143.8298 (477.D46D16) 1176.5106 (498.82B916) 1209.1915 (4B9.310516) 1241.8723 (4D9.DF5216) 1274.5532 (4FA.8D9E16) 1307.234 (51B.3BEA16) 1339.9149 (53B.EA3616) 1372.5957 (55C.988316) 1405.2766 (57D.46CF16) 1437.95745 (59D.F51B16) 1470.6383 (5BE.A367816) 1503.31915 (5DF.51B416) | major 2nd | M2 | E |
| 8 | 204.2553 | 216.5106 | aug 2nd | A2 | E# | |
| 9 | 229.7872 | 243.5745 | double-aug 2nd | AA2 | Ex | |
| 10 | 255.31915 | 270.6383 | triple-aug 2nd, triple-dim 3rd | A32, d33 | E#3, Fb3 | |
| 11 | 280.8511 | 297.7021 | double-dim 3rd | dd3 | Fbb | |
| 12 | 306.383 | 324.766 | dim 3rd | d3 | Fb | |
| 13 | 331.9149 | 351.8298 | minor 3rd | m3 | F | |
| 14 | 357.4468 | 378.8936 | major 3rd | M3 | F# | |
| 15 | 382.9787 | 405.95745 | aug 3rd | A3 | Fx | |
| 16 | 408.5106 | 433.0213 | double-aug 3rd | AA3 | F#3 | |
| 17 | 434.04255 | 460.0851 | triple-aug 3rd, triple-dim 4th | A33, d34 | F#4, Gb3 | |
| 18 | 459.5745 | 487.1489 | double-dim 4th | dd4 | Gbb | |
| 19 | 485.1064 | 514.2128 | dim 4th | d4 | Gb | |
| 20 | 510.6383 | 541.2766 | perfect 4th | P4 | G | |
| 21 | 536.1702 | 568.3404 | aug 4th | A4 | G# | |
| 22 | 561.7021 | 595.4043 | double-aug 4th | AA4 | Gx | |
| 23 | 587.2340 | 622.4681 | triple-aug 4th | A34 | G#3 | |
| 24 | 612.7660 | 649.5319 | triple-dim 5th | d35 | Ab3 | |
| 25 | 638.2979 | 676.5957 | double-dim 5th | dd5 | Abb | |
| 26 | 663.8298 | 703.6596 | dim 5th | d5 | Ab | |
| 27 | 689.3617 | 730.7234 | perfect 5th | P5 | A | |
| 28 | 714.8936 | 757.7872 | aug 5th | A5 | A# | |
| 29 | 740.4255 | 784.8511 | double-aug 5th | AA5 | Ax | |
| 30 | 765.95745 | 811.9149 | triple-aug 5th, triple-dim 6th | A35, d36 | A#3, Bb4 | |
| 31 | 791.4894 | 838.9787 | double-dim 6th | dd6 | Bb3 | |
| 32 | 817.0213 | 866.04255 | dim 6th | d6 | Bbb | |
| 33 | 842.5532 | 893.1064 | minor 6th | m6 | Bb | |
| 34 | 868.0851 | 920.1702 | major 6th | M6 | B | |
| 35 | 893.617 | 947.234 | aug 6th | A6 | B# | |
| 36 | 919.1489 | 974.2979 | double-aug 6th | AA6 | Bx | |
| 37 | 944.68085 | 1001.3617 | triple-aug 6th, triple-dim 7th | A36, d37 | B#3, Cb3 | |
| 38 | 970.2128 | 1028.4255 | double-dim 7th | dd7 | Cbb | |
| 39 | 995.7447 | 1055.4894 | dim 7th | d7 | Cb | |
| 40 | 1021.2766 | 1082.5532 | minor 7th | m7 | C | |
| 41 | 1046.8085 | 1109.617 | major 7th | M7 | C# | |
| 42 | 1072.3404 | 1136.68085 | aug 7th | A7 | Cx | |
| 43 | 1097.8723 | 1163.7447 | double-aug 7th | AA7 | C#3 | |
| 44 | 1123.4043 | 1190.8085 | triple-aug 7th, triple-dim 8ve | A37, d38 | C#4, Db3 | |
| 45 | 1148.9362 | 1217.8723 | double-dim 8ve | dd8 | Dbb | |
| 46 | 1174.4681 | 1244.9362 | dim 8ve | d8 | Db | |
| 47 | 1200 | 1272 | 1536 (60016) | perfect 8ve | P8 | D |