230edo
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Prime factorization
2 × 5 × 23
Step size
5.21739¢
Fifth
135\230 (704.348¢) (→27\46)
Semitones (A1:m2)
25:15 (130.4¢ : 78.26¢)
Dual sharp fifth
135\230 (704.348¢) (→27\46)
Dual flat fifth
134\230 (699.13¢) (→67\115)
Dual major 2nd
39\230 (203.478¢)
Consistency limit
3
Distinct consistency limit
3
| ← 229edo | 230edo | 231edo → |
230 equal divisions of the octave (abbreviated 230edo or 230ed2), also called 230-tone equal temperament (230tet) or 230 equal temperament (230et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 230 equal parts of about 5.22 ¢ each. Each step represents a frequency ratio of 21/230, or the 230th root of 2.
Theory
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +2.39 | -0.23 | +1.61 | -0.43 | +1.73 | -0.53 | +2.17 | -0.61 | -0.12 | -1.22 | -2.19 |
| relative (%) | +46 | -4 | +31 | -8 | +33 | -10 | +42 | -12 | -2 | -23 | -42 | |
| Steps (reduced) |
365 (135) |
534 (74) |
646 (186) |
729 (39) |
796 (106) |
851 (161) |
899 (209) |
940 (20) |
977 (57) |
1010 (90) |
1040 (120) | |
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 5.2 | superunison |
| 2 | 10.4 | superunison |
| 3 | 15.7 | superunison |
| 4 | 20.9 | superunison |
| 5 | 26.1 | superunison |
| 6 | 31.3 | superunison |
| 7 | 36.5 | superunison |
| 8 | 41.7 | subminor second |
| 9 | 47.0 | subminor second |
| 10 | 52.2 | subminor second |
| 11 | 57.4 | subminor second |
| 12 | 62.6 | subminor second |
| 13 | 67.8 | subminor second |
| 14 | 73.0 | subminor second |
| 15 | 78.3 | subminor second |
| 16 | 83.5 | minor second |
| 17 | 88.7 | minor second |
| 18 | 93.9 | minor second |
| 19 | 99.1 | minor second |
| 20 | 104.3 | minor second |
| 21 | 109.6 | minor second |
| 22 | 114.8 | minor second |
| 23 | 120.0 | supraminor second |
| 24 | 125.2 | supraminor second |
| 25 | 130.4 | supraminor second |
| 26 | 135.7 | supraminor second |
| 27 | 140.9 | neutral second |
| 28 | 146.1 | neutral second |
| 29 | 151.3 | neutral second |
| 30 | 156.5 | neutral second |
| 31 | 161.7 | submajor second |
| 32 | 167.0 | submajor second |
| 33 | 172.2 | submajor second |
| 34 | 177.4 | submajor second |
| 35 | 182.6 | major second |
| 36 | 187.8 | major second |
| 37 | 193.0 | major second |
| 38 | 198.3 | major second |
| 39 | 203.5 | major second |
| 40 | 208.7 | major second |
| 41 | 213.9 | major second |
| 42 | 219.1 | major second |
| 43 | 224.3 | supermajor second |
| 44 | 229.6 | supermajor second |
| 45 | 234.8 | supermajor second |
| 46 | 240.0 | ultramajor second |
| 47 | 245.2 | ultramajor second |
| 48 | 250.4 | ultramajor second |
| 49 | 255.7 | ultramajor second |
| 50 | 260.9 | subminor third |
| 51 | 266.1 | subminor third |
| 52 | 271.3 | subminor third |
| 53 | 276.5 | subminor third |
| 54 | 281.7 | minor third |
| 55 | 287.0 | minor third |
| 56 | 292.2 | minor third |
| 57 | 297.4 | minor third |
| 58 | 302.6 | minor third |
| 59 | 307.8 | minor third |
| 60 | 313.0 | minor third |
| 61 | 318.3 | minor third |
| 62 | 323.5 | supraminor third |
| 63 | 328.7 | supraminor third |
| 64 | 333.9 | supraminor third |
| 65 | 339.1 | supraminor third |
| 66 | 344.3 | neutral third |
| 67 | 349.6 | neutral third |
| 68 | 354.8 | neutral third |
| 69 | 360.0 | submajor third |
| 70 | 365.2 | submajor third |
| 71 | 370.4 | submajor third |
| 72 | 375.7 | submajor third |
| 73 | 380.9 | major third |
| 74 | 386.1 | major third |
| 75 | 391.3 | major third |
| 76 | 396.5 | major third |
| 77 | 401.7 | major third |
| 78 | 407.0 | major third |
| 79 | 412.2 | major third |
| 80 | 417.4 | major third |
| 81 | 422.6 | supermajor third |
| 82 | 427.8 | supermajor third |
| 83 | 433.0 | supermajor third |
| 84 | 438.3 | supermajor third |
| 85 | 443.5 | ultramajor third |
| 86 | 448.7 | ultramajor third |
| 87 | 453.9 | ultramajor third |
| 88 | 459.1 | ultramajor third |
| 89 | 464.3 | subfourth |
| 90 | 469.6 | subfourth |
| 91 | 474.8 | subfourth |
| 92 | 480.0 | perfect fourth |
| 93 | 485.2 | perfect fourth |
| 94 | 490.4 | perfect fourth |
| 95 | 495.7 | perfect fourth |
| 96 | 500.9 | perfect fourth |
| 97 | 506.1 | perfect fourth |
| 98 | 511.3 | perfect fourth |
| 99 | 516.5 | perfect fourth |
| 100 | 521.7 | superfourth |
| 101 | 527.0 | superfourth |
| 102 | 532.2 | superfourth |
| 103 | 537.4 | superfourth |
| 104 | 542.6 | superfourth |
| 105 | 547.8 | superfourth |
| 106 | 553.0 | superfourth |
| 107 | 558.3 | superfourth |
| 108 | 563.5 | low tritone |
| 109 | 568.7 | low tritone |
| 110 | 573.9 | low tritone |
| 111 | 579.1 | low tritone |
| 112 | 584.3 | low tritone |
| 113 | 589.6 | low tritone |
| 114 | 594.8 | low tritone |
| 115 | 600.0 | high tritone |
| 116 | 605.2 | high tritone |
| 117 | 610.4 | high tritone |
| 118 | 615.7 | high tritone |
| 119 | 620.9 | high tritone |
| 120 | 626.1 | high tritone |
| 121 | 631.3 | high tritone |
| 122 | 636.5 | high tritone |
| 123 | 641.7 | subfifth |
| 124 | 647.0 | subfifth |
| 125 | 652.2 | subfifth |
| 126 | 657.4 | subfifth |
| 127 | 662.6 | subfifth |
| 128 | 667.8 | subfifth |
| 129 | 673.0 | subfifth |
| 130 | 678.3 | subfifth |
| 131 | 683.5 | perfect fifth |
| 132 | 688.7 | perfect fifth |
| 133 | 693.9 | perfect fifth |
| 134 | 699.1 | perfect fifth |
| 135 | 704.3 | perfect fifth |
| 136 | 709.6 | perfect fifth |
| 137 | 714.8 | perfect fifth |
| 138 | 720.0 | superfifth |
| 139 | 725.2 | superfifth |
| 140 | 730.4 | superfifth |
| 141 | 735.7 | superfifth |
| 142 | 740.9 | ultrafifth |
| 143 | 746.1 | ultrafifth |
| 144 | 751.3 | ultrafifth |
| 145 | 756.5 | ultrafifth |
| 146 | 761.7 | subminor sixth |
| 147 | 767.0 | subminor sixth |
| 148 | 772.2 | subminor sixth |
| 149 | 777.4 | subminor sixth |
| 150 | 782.6 | minor sixth |
| 151 | 787.8 | minor sixth |
| 152 | 793.0 | minor sixth |
| 153 | 798.3 | minor sixth |
| 154 | 803.5 | minor sixth |
| 155 | 808.7 | minor sixth |
| 156 | 813.9 | minor sixth |
| 157 | 819.1 | minor sixth |
| 158 | 824.3 | supraminor sixth |
| 159 | 829.6 | supraminor sixth |
| 160 | 834.8 | supraminor sixth |
| 161 | 840.0 | neutral sixth |
| 162 | 845.2 | neutral sixth |
| 163 | 850.4 | neutral sixth |
| 164 | 855.7 | neutral sixth |
| 165 | 860.9 | submajor sixth |
| 166 | 866.1 | submajor sixth |
| 167 | 871.3 | submajor sixth |
| 168 | 876.5 | submajor sixth |
| 169 | 881.7 | major sixth |
| 170 | 887.0 | major sixth |
| 171 | 892.2 | major sixth |
| 172 | 897.4 | major sixth |
| 173 | 902.6 | major sixth |
| 174 | 907.8 | major sixth |
| 175 | 913.0 | major sixth |
| 176 | 918.3 | major sixth |
| 177 | 923.5 | supermajor sixth |
| 178 | 928.7 | supermajor sixth |
| 179 | 933.9 | supermajor sixth |
| 180 | 939.1 | supermajor sixth |
| 181 | 944.3 | ultramajor sixth |
| 182 | 949.6 | ultramajor sixth |
| 183 | 954.8 | ultramajor sixth |
| 184 | 960.0 | subminor seventh |
| 185 | 965.2 | subminor seventh |
| 186 | 970.4 | subminor seventh |
| 187 | 975.7 | subminor seventh |
| 188 | 980.9 | minor seventh |
| 189 | 986.1 | minor seventh |
| 190 | 991.3 | minor seventh |
| 191 | 996.5 | minor seventh |
| 192 | 1001.7 | minor seventh |
| 193 | 1007.0 | minor seventh |
| 194 | 1012.2 | minor seventh |
| 195 | 1017.4 | minor seventh |
| 196 | 1022.6 | supraminor seventh |
| 197 | 1027.8 | supraminor seventh |
| 198 | 1033.0 | supraminor seventh |
| 199 | 1038.3 | supraminor seventh |
| 200 | 1043.5 | neutral seventh |
| 201 | 1048.7 | neutral seventh |
| 202 | 1053.9 | neutral seventh |
| 203 | 1059.1 | neutral seventh |
| 204 | 1064.3 | submajor seventh |
| 205 | 1069.6 | submajor seventh |
| 206 | 1074.8 | submajor seventh |
| 207 | 1080.0 | major seventh |
| 208 | 1085.2 | major seventh |
| 209 | 1090.4 | major seventh |
| 210 | 1095.7 | major seventh |
| 211 | 1100.9 | major seventh |
| 212 | 1106.1 | major seventh |
| 213 | 1111.3 | major seventh |
| 214 | 1116.5 | major seventh |
| 215 | 1121.7 | supermajor seventh |
| 216 | 1127.0 | supermajor seventh |
| 217 | 1132.2 | supermajor seventh |
| 218 | 1137.4 | supermajor seventh |
| 219 | 1142.6 | ultramajor seventh |
| 220 | 1147.8 | ultramajor seventh |
| 221 | 1153.0 | ultramajor seventh |
| 222 | 1158.3 | ultramajor seventh |
| 223 | 1163.5 | suboctave |
| 224 | 1168.7 | suboctave |
| 225 | 1173.9 | suboctave |
| 226 | 1179.1 | suboctave |
| 227 | 1184.3 | suboctave |
| 228 | 1189.6 | suboctave |
| 229 | 1194.8 | suboctave |
| 230 | 1200.0 | perfect octave |
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