234edo
Jump to navigation
Jump to search
| ← 233edo | 234edo | 235edo → |
234 equal divisions of the octave (abbreviated 234edo or 234ed2), also called 234-tone equal temperament (234tet) or 234 equal temperament (234et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 234 equal parts of about 5.13 ¢ each. Each step represents a frequency ratio of 21/234, or the 234th root of 2.
Theory
234edo is consistent to the 7-odd-limit, but the error of prime 5 is quite large. It is however fairly accurate in the 2.3.7.13 subgroup, with the same tuning as 468edo and tempering out the septiennealimma.
Besides that, the 7-limit patent val tempers out 5120/5103 and 16875/16807, supporting kwai. The alternative 234c val tempers out 10976/10935, 110592/109375 and 321489/320000, supporting bicommatic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.61 | -1.70 | +0.40 | +2.53 | +0.50 | -2.39 | -0.08 | +2.49 | +1.19 | -1.45 |
| Relative (%) | +0.0 | +11.9 | -33.1 | +7.9 | +49.3 | +9.7 | -46.6 | -1.5 | +48.7 | +23.2 | -28.2 | |
| Steps (reduced) |
234 (0) |
371 (137) |
543 (75) |
657 (189) |
810 (108) |
866 (164) |
956 (20) |
994 (58) |
1059 (123) |
1137 (201) |
1159 (223) | |
Subsets and supersets
Since 234 factors into primes as 2 × 32 × 13, 234edo has subset edos 2, 3, 6, 9, 13, 18, 26, 39, 78, and 117. 468edo, which doubles it, provides a possible correction for its approximation of 5 and 11.
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 5.1 | superunison |
| 2 | 10.3 | superunison |
| 3 | 15.4 | superunison |
| 4 | 20.5 | superunison |
| 5 | 25.6 | superunison |
| 6 | 30.8 | superunison |
| 7 | 35.9 | superunison |
| 8 | 41.0 | subminor second |
| 9 | 46.2 | subminor second |
| 10 | 51.3 | subminor second |
| 11 | 56.4 | subminor second |
| 12 | 61.5 | subminor second |
| 13 | 66.7 | subminor second |
| 14 | 71.8 | subminor second |
| 15 | 76.9 | subminor second |
| 16 | 82.1 | minor second |
| 17 | 87.2 | minor second |
| 18 | 92.3 | minor second |
| 19 | 97.4 | minor second |
| 20 | 102.6 | minor second |
| 21 | 107.7 | minor second |
| 22 | 112.8 | minor second |
| 23 | 117.9 | minor second |
| 24 | 123.1 | supraminor second |
| 25 | 128.2 | supraminor second |
| 26 | 133.3 | supraminor second |
| 27 | 138.5 | supraminor second |
| 28 | 143.6 | neutral second |
| 29 | 148.7 | neutral second |
| 30 | 153.8 | neutral second |
| 31 | 159.0 | neutral second |
| 32 | 164.1 | submajor second |
| 33 | 169.2 | submajor second |
| 34 | 174.4 | submajor second |
| 35 | 179.5 | submajor second |
| 36 | 184.6 | major second |
| 37 | 189.7 | major second |
| 38 | 194.9 | major second |
| 39 | 200.0 | major second |
| 40 | 205.1 | major second |
| 41 | 210.3 | major second |
| 42 | 215.4 | major second |
| 43 | 220.5 | supermajor second |
| 44 | 225.6 | supermajor second |
| 45 | 230.8 | supermajor second |
| 46 | 235.9 | supermajor second |
| 47 | 241.0 | ultramajor second |
| 48 | 246.2 | ultramajor second |
| 49 | 251.3 | ultramajor second |
| 50 | 256.4 | ultramajor second |
| 51 | 261.5 | subminor third |
| 52 | 266.7 | subminor third |
| 53 | 271.8 | subminor third |
| 54 | 276.9 | subminor third |
| 55 | 282.1 | minor third |
| 56 | 287.2 | minor third |
| 57 | 292.3 | minor third |
| 58 | 297.4 | minor third |
| 59 | 302.6 | minor third |
| 60 | 307.7 | minor third |
| 61 | 312.8 | minor third |
| 62 | 317.9 | minor third |
| 63 | 323.1 | supraminor third |
| 64 | 328.2 | supraminor third |
| 65 | 333.3 | supraminor third |
| 66 | 338.5 | supraminor third |
| 67 | 343.6 | neutral third |
| 68 | 348.7 | neutral third |
| 69 | 353.8 | neutral third |
| 70 | 359.0 | neutral third |
| 71 | 364.1 | submajor third |
| 72 | 369.2 | submajor third |
| 73 | 374.4 | submajor third |
| 74 | 379.5 | submajor third |
| 75 | 384.6 | major third |
| 76 | 389.7 | major third |
| 77 | 394.9 | major third |
| 78 | 400.0 | major third |
| 79 | 405.1 | major third |
| 80 | 410.3 | major third |
| 81 | 415.4 | major third |
| 82 | 420.5 | supermajor third |
| 83 | 425.6 | supermajor third |
| 84 | 430.8 | supermajor third |
| 85 | 435.9 | supermajor third |
| 86 | 441.0 | ultramajor third |
| 87 | 446.2 | ultramajor third |
| 88 | 451.3 | ultramajor third |
| 89 | 456.4 | ultramajor third |
| 90 | 461.5 | subfourth |
| 91 | 466.7 | subfourth |
| 92 | 471.8 | subfourth |
| 93 | 476.9 | subfourth |
| 94 | 482.1 | perfect fourth |
| 95 | 487.2 | perfect fourth |
| 96 | 492.3 | perfect fourth |
| 97 | 497.4 | perfect fourth |
| 98 | 502.6 | perfect fourth |
| 99 | 507.7 | perfect fourth |
| 100 | 512.8 | perfect fourth |
| 101 | 517.9 | superfourth |
| 102 | 523.1 | superfourth |
| 103 | 528.2 | superfourth |
| 104 | 533.3 | superfourth |
| 105 | 538.5 | superfourth |
| 106 | 543.6 | superfourth |
| 107 | 548.7 | superfourth |
| 108 | 553.8 | superfourth |
| 109 | 559.0 | superfourth |
| 110 | 564.1 | low tritone |
| 111 | 569.2 | low tritone |
| 112 | 574.4 | low tritone |
| 113 | 579.5 | low tritone |
| 114 | 584.6 | low tritone |
| 115 | 589.7 | low tritone |
| 116 | 594.9 | low tritone |
| 117 | 600.0 | high tritone |
| 118 | 605.1 | high tritone |
| 119 | 610.3 | high tritone |
| 120 | 615.4 | high tritone |
| 121 | 620.5 | high tritone |
| 122 | 625.6 | high tritone |
| 123 | 630.8 | high tritone |
| 124 | 635.9 | high tritone |
| 125 | 641.0 | subfifth |
| 126 | 646.2 | subfifth |
| 127 | 651.3 | subfifth |
| 128 | 656.4 | subfifth |
| 129 | 661.5 | subfifth |
| 130 | 666.7 | subfifth |
| 131 | 671.8 | subfifth |
| 132 | 676.9 | subfifth |
| 133 | 682.1 | subfifth |
| 134 | 687.2 | perfect fifth |
| 135 | 692.3 | perfect fifth |
| 136 | 697.4 | perfect fifth |
| 137 | 702.6 | perfect fifth |
| 138 | 707.7 | perfect fifth |
| 139 | 712.8 | perfect fifth |
| 140 | 717.9 | perfect fifth |
| 141 | 723.1 | superfifth |
| 142 | 728.2 | superfifth |
| 143 | 733.3 | superfifth |
| 144 | 738.5 | superfifth |
| 145 | 743.6 | ultrafifth |
| 146 | 748.7 | ultrafifth |
| 147 | 753.8 | ultrafifth |
| 148 | 759.0 | ultrafifth |
| 149 | 764.1 | subminor sixth |
| 150 | 769.2 | subminor sixth |
| 151 | 774.4 | subminor sixth |
| 152 | 779.5 | subminor sixth |
| 153 | 784.6 | minor sixth |
| 154 | 789.7 | minor sixth |
| 155 | 794.9 | minor sixth |
| 156 | 800.0 | minor sixth |
| 157 | 805.1 | minor sixth |
| 158 | 810.3 | minor sixth |
| 159 | 815.4 | minor sixth |
| 160 | 820.5 | supraminor sixth |
| 161 | 825.6 | supraminor sixth |
| 162 | 830.8 | supraminor sixth |
| 163 | 835.9 | supraminor sixth |
| 164 | 841.0 | neutral sixth |
| 165 | 846.2 | neutral sixth |
| 166 | 851.3 | neutral sixth |
| 167 | 856.4 | neutral sixth |
| 168 | 861.5 | submajor sixth |
| 169 | 866.7 | submajor sixth |
| 170 | 871.8 | submajor sixth |
| 171 | 876.9 | submajor sixth |
| 172 | 882.1 | major sixth |
| 173 | 887.2 | major sixth |
| 174 | 892.3 | major sixth |
| 175 | 897.4 | major sixth |
| 176 | 902.6 | major sixth |
| 177 | 907.7 | major sixth |
| 178 | 912.8 | major sixth |
| 179 | 917.9 | major sixth |
| 180 | 923.1 | supermajor sixth |
| 181 | 928.2 | supermajor sixth |
| 182 | 933.3 | supermajor sixth |
| 183 | 938.5 | supermajor sixth |
| 184 | 943.6 | ultramajor sixth |
| 185 | 948.7 | ultramajor sixth |
| 186 | 953.8 | ultramajor sixth |
| 187 | 959.0 | ultramajor sixth |
| 188 | 964.1 | subminor seventh |
| 189 | 969.2 | subminor seventh |
| 190 | 974.4 | subminor seventh |
| 191 | 979.5 | subminor seventh |
| 192 | 984.6 | minor seventh |
| 193 | 989.7 | minor seventh |
| 194 | 994.9 | minor seventh |
| 195 | 1000.0 | minor seventh |
| 196 | 1005.1 | minor seventh |
| 197 | 1010.3 | minor seventh |
| 198 | 1015.4 | minor seventh |
| 199 | 1020.5 | supraminor seventh |
| 200 | 1025.6 | supraminor seventh |
| 201 | 1030.8 | supraminor seventh |
| 202 | 1035.9 | supraminor seventh |
| 203 | 1041.0 | neutral seventh |
| 204 | 1046.2 | neutral seventh |
| 205 | 1051.3 | neutral seventh |
| 206 | 1056.4 | neutral seventh |
| 207 | 1061.5 | submajor seventh |
| 208 | 1066.7 | submajor seventh |
| 209 | 1071.8 | submajor seventh |
| 210 | 1076.9 | submajor seventh |
| 211 | 1082.1 | major seventh |
| 212 | 1087.2 | major seventh |
| 213 | 1092.3 | major seventh |
| 214 | 1097.4 | major seventh |
| 215 | 1102.6 | major seventh |
| 216 | 1107.7 | major seventh |
| 217 | 1112.8 | major seventh |
| 218 | 1117.9 | major seventh |
| 219 | 1123.1 | supermajor seventh |
| 220 | 1128.2 | supermajor seventh |
| 221 | 1133.3 | supermajor seventh |
| 222 | 1138.5 | supermajor seventh |
| 223 | 1143.6 | ultramajor seventh |
| 224 | 1148.7 | ultramajor seventh |
| 225 | 1153.8 | ultramajor seventh |
| 226 | 1159.0 | ultramajor seventh |
| 227 | 1164.1 | suboctave |
| 228 | 1169.2 | suboctave |
| 229 | 1174.4 | suboctave |
| 230 | 1179.5 | suboctave |
| 231 | 1184.6 | suboctave |
| 232 | 1189.7 | suboctave |
| 233 | 1194.9 | suboctave |
| 234 | 1200.0 | perfect octave |