233edo: Difference between revisions
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'''233edo''' is the [[EDO|equal division of the octave]] into 233 parts of 5.1502 [[cent]]s each. It has a generally flat tendency, in the sense that if the octave is pure, 3, 5, 7, 11, 13, and 17 are all flat. 233edo is accurate for the 5th harmonic (only 0.0476 cents flat), but less for the third harmonic (1.5258 cents flat). It tempers out 78732/78125 and |-53 32 1> in the 5-limit; 2401/2400, 65625/65536, and 177147/175616 in the 7-limit (supporting [[Breedsmic temperaments|tertiaseptal]] and [[Breedsmic temperaments|catafourth]]). Using the patent val, it tempers out 243/242, 441/440, 35937/35840, and 78408/78125 in the 11-limit; 351/350, 1001/1000, 1575/1573, 4225/4224, and 6656/6655 in the 13-limit. | '''233edo''' is the [[EDO|equal division of the octave]] into 233 parts of 5.1502 [[cent]]s each. It has a generally flat tendency, in the sense that if the octave is pure, 3, 5, 7, 11, 13, and 17 are all flat. 233edo is accurate for the 5th harmonic (only 0.0476 cents flat), but less for the third harmonic (1.5258 cents flat). | ||
It tempers out 78732/78125 and |-53 32 1> in the 5-limit; 2401/2400, 65625/65536, and 177147/175616 in the 7-limit (supporting [[Breedsmic temperaments|tertiaseptal]] and [[Breedsmic temperaments|catafourth]]). Using the patent val, it tempers out 243/242, 441/440, 35937/35840, and 78408/78125 in the 11-limit; 351/350, 1001/1000, 1575/1573, 4225/4224, and 6656/6655 in the 13-limit. | |||
233edo is the 51st [[prime edo]]. | 233edo is the 51st [[prime edo]]. | ||
{{Harmonics in equal|233}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 03:34, 24 June 2023
| ← 232edo | 233edo | 234edo → |
233edo is the equal division of the octave into 233 parts of 5.1502 cents each. It has a generally flat tendency, in the sense that if the octave is pure, 3, 5, 7, 11, 13, and 17 are all flat. 233edo is accurate for the 5th harmonic (only 0.0476 cents flat), but less for the third harmonic (1.5258 cents flat).
It tempers out 78732/78125 and |-53 32 1> in the 5-limit; 2401/2400, 65625/65536, and 177147/175616 in the 7-limit (supporting tertiaseptal and catafourth). Using the patent val, it tempers out 243/242, 441/440, 35937/35840, and 78408/78125 in the 11-limit; 351/350, 1001/1000, 1575/1573, 4225/4224, and 6656/6655 in the 13-limit.
233edo is the 51st prime edo.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.53 | -0.05 | -0.59 | +2.10 | -0.24 | -1.04 | -1.57 | -1.95 | +1.20 | -2.11 | +0.05 |
| Relative (%) | -29.6 | -0.9 | -11.4 | +40.7 | -4.8 | -20.2 | -30.6 | -37.9 | +23.3 | -41.0 | +1.0 | |
| Steps (reduced) |
369 (136) |
541 (75) |
654 (188) |
739 (40) |
806 (107) |
862 (163) |
910 (211) |
952 (20) |
990 (58) |
1023 (91) |
1054 (122) | |