28ed5: Difference between revisions
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Created page with "'''Division of the 5th harmonic into 28 equal parts''' (28ed5) is related to 12 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cent..." Tags: Mobile edit Mobile web edit |
fixed a table Tags: Mobile edit Mobile web edit |
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| Line 9: | Line 9: | ||
|- | |- | ||
| | 0 | | | 0 | ||
| | 0.0000 | | | 0.0000 | ||
| | exact [[1/1]] | | | exact [[1/1]] | ||
| | | | | | ||
| Line 31: | Line 31: | ||
| | 398.0448 | | | 398.0448 | ||
| | 34/27 | | | 34/27 | ||
| | pseudo-5/4 | | | pseudo-[[5/4]] | ||
|- | |- | ||
| | 5 | | | 5 | ||
| Line 46: | Line 46: | ||
| | 696.5784 | | | 696.5784 | ||
| | | | | | ||
| | meantone fifth <br>(pseudo-3/2) | | | meantone fifth <br>(pseudo-[[3/2]]) | ||
|- | |- | ||
| | 8 | | | 8 | ||
| Line 56: | Line 56: | ||
| | 895.6008 | | | 895.6008 | ||
| | 57/34 | | | 57/34 | ||
| | pseudo-5/3 | | | pseudo-[[5/3]] | ||
|- | |- | ||
| | 10 | | | 10 | ||
| Line 71: | Line 71: | ||
| | 1194.1344 | | | 1194.1344 | ||
| | 255/128 | | | 255/128 | ||
| | pseudo-2/1 | | | pseudo-[[Octave|2/1]] | ||
|- | |- | ||
| | 13 | | | 13 | ||
| Line 91: | Line 91: | ||
| | 1592.1793 | | | 1592.1793 | ||
| | 128/51 | | | 128/51 | ||
| | pseudo-5/2 | | | pseudo-[[5/2]] | ||
|- | |- | ||
| | 17 | | | 17 | ||
| Line 106: | Line 106: | ||
| | 1890.7129 | | | 1890.7129 | ||
| | 170/57 | | | 170/57 | ||
| | pseudo-3/1 | | | pseudo-[[3/1]] | ||
|- | |- | ||
| | 20 | | | 20 | ||
| Line 116: | Line 116: | ||
| | 2089.7353 | | | 2089.7353 | ||
| | | | | | ||
| | meantone major sixth plus an octave <br>(pseudo-10/3) | | | meantone major sixth plus an octave <br>(pseudo-[[10/3]]) | ||
|- | |- | ||
| | 22 | | | 22 | ||
| Line 131: | Line 131: | ||
| | 2388.2689 | | | 2388.2689 | ||
| | 135/34 | | | 135/34 | ||
| | pseudo-4/1 | | | pseudo-[[4/1]] | ||
|- | |- | ||
| | 25 | | | 25 | ||
Revision as of 09:03, 29 November 2018
Division of the 5th harmonic into 28 equal parts (28ed5) is related to 12 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size about 99.5112 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. This tuning also has the perfect fourth which is more accurate for 4/3 than that of 12edo, as well as 18/17, 19/16, and 24/17.
| degree | cents value | corresponding JI intervals |
comments |
| 0 | 0.0000 | exact 1/1 | |
| 1 | 99.5112 | 18/17 | |
| 2 | 199.0224 | 55/49 | |
| 3 | 298.5336 | 19/16 | |
| 4 | 398.0448 | 34/27 | pseudo-5/4 |
| 5 | 497.5560 | 4/3 | |
| 6 | 597.0672 | 24/17 | |
| 7 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 8 | 796.0896 | 19/12 | |
| 9 | 895.6008 | 57/34 | pseudo-5/3 |
| 10 | 995.1120 | 16/9 | |
| 11 | 1094.6232 | 32/17 | |
| 12 | 1194.1344 | 255/128 | pseudo-2/1 |
| 13 | 1293.6457 | 19/9 | |
| 14 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 15 | 1492.6681 | 45/19 | |
| 16 | 1592.1793 | 128/51 | pseudo-5/2 |
| 17 | 1691.6905 | 85/32 | |
| 18 | 1791.2017 | 45/16 | |
| 19 | 1890.7129 | 170/57 | pseudo-3/1 |
| 20 | 1990.2241 | 60/19 | |
| 21 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 22 | 2189.2465 | 85/24 | |
| 23 | 2288.7577 | 15/4 | |
| 24 | 2388.2689 | 135/34 | pseudo-4/1 |
| 25 | 2487.7801 | 80/19 | |
| 26 | 2587.2913 | 49/11 | |
| 27 | 2686.8025 | 85/18 | |
| 28 | 2786.3137 | exact 5/1 | just major third plus two octaves |