233edo
Theory
233et has a generally flat tendency, in the sense that if the octave is pure, prime harmonics 3 through 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).
The equal temperament 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.
Odd harmonics
| 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) | |
Subsets and supersets
233edo is the 51st prime edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-369 233⟩ | [⟨233 369]] | 0.4813 | 0.4815 | 9.35 |- | 2.3.5 | 78732/78125, [-53 32 1⟩ | [⟨233 369 541]] | 0.3277 | 0.4492 | 8.72 |- | 2.3.5.7 | 2401/2400, 65625/65536, 78732/78125 | [⟨233 369 541 654]] | 0.2979 | 0.3924 | 7.62 |- | 2.3.5.7.11 | 243/242, 441/440, 540/539, 2401/2400 | [⟨233 369 541 654 806]] | 0.2525 | 0.3625 | 7.04 |- | 2.3.5.7.11.13 | 243/242, 351/350, 441/440, 540/539, 1001/1000 | [⟨233 369 541 654 806 862]] | 0.2574 | 0.3311 | 6.43 |- | 2.3.5.7.11.13.17 | 351/350, 441/440, 540/539, 561/560, 936/935, 1156/1155 | [⟨233 369 541 654 806 862 952]] | 0.2888 | 0.3161 | 6.14 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 15\233 | 77.25 | 256/245 | Tertiaseptal |- | 1 | 22\233 | 113.30 | 16/15 | Misneb |- | 1 | 55\233 | 283.26 | 189/160 | Neominor |- | 1 | 77\233 | 396.57 | 98304/78125 | Squarschmidt |- | 1 | 86\233 | 442.92 | 9/7 | Sensi |- | 1 | 95\233 | 489.27 | 250/189 | Catafourth Template:Rank-2 end Template:Orf