253edo: Difference between revisions
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''' | '''253edo''' is the [[EDO|equal division of the octave]] into 253 parts of 4.743083 [[cent]]s each. It is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[sesquiquartififths]] temperament. | ||
253 = 11 × 23, and has subset edos [[11edo]] and [[23edo]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|253}} | |||
43 43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]] | == Scales == | ||
* 63 32 63 63 32: [[3L_2s|Pentatonic]] | |||
* 43 43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]] | |||
* 41 41 24 41 41 41 24: [[Meantone|Meantonic tuning]] | |||
* 35 35 35 35 35 35 35 8: [[7L_1s|Porcupine tuning]] | |||
* 33 33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]] | |||
* 31 31 31 18 31 31 31 31 18: [[7L_2s|Superdiatonic tuning]] in the way of Mavila | |||
* 26 26 15 26 26 26 15 26 26 26 15: [[sensi11|Sensi tuning]] | |||
* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L_3s|Ketradektriatoh tuning]] | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category: | [[Category:Sesquiquartififths]] | ||
Revision as of 18:57, 13 March 2022
253edo is the equal division of the octave into 253 parts of 4.743083 cents each. It is consistent to the 17-odd-limit, approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit sesquiquartififths temperament.
253 = 11 × 23, and has subset edos 11edo and 23edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.02 | -2.12 | -1.24 | -1.12 | -1.00 | -0.61 | +1.30 | -2.19 | -0.33 | -1.95 |
| Relative (%) | +0.0 | +0.4 | -44.8 | -26.1 | -23.6 | -21.1 | -12.8 | +27.4 | -46.1 | -6.9 | -41.2 | |
| Steps (reduced) |
253 (0) |
401 (148) |
587 (81) |
710 (204) |
875 (116) |
936 (177) |
1034 (22) |
1075 (63) |
1144 (132) |
1229 (217) |
1253 (241) | |
Scales
- 63 32 63 63 32: Pentatonic
- 43 43 19 43 43 43 19: Pythagorean tuning
- 41 41 24 41 41 41 24: Meantonic tuning
- 35 35 35 35 35 35 35 8: Porcupine tuning
- 33 33 33 11 33 33 33 33 11: "The Hendecapliqued superdiatonic of the Icositriphony"
- 31 31 31 18 31 31 31 31 18: Superdiatonic tuning in the way of Mavila
- 26 26 15 26 26 26 15 26 26 26 15: Sensi tuning
- 20 20 20 11 20 20 20 20 11 20 20 20 20 11: Ketradektriatoh tuning