101afdo
The Dalmatian scale (also known as mode 101 of the harmonic series, or 101AFDO) is a large primodal scale which is excellent for use as a NEJI tuning. It is the 26th prime mode of the harmonic series.
Optimal NEJI approximations
The Dalmatian scale approximates four EDOs, including two Zeta peak EDOs, with lower maximum error than any smaller mode of the harmonic series:
- 19EDO (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
- 24EDO (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
- 25EDO (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
- 27EDO (101:104:106:109:112:115:118:121:124:127:131:134:137:141:145:148:152:156:160:164:169:173:178:182:187:192:197:202)
Even more impressively, the Dalmatian scale approximates seven EDOs, including three Zeta peak EDOs, with lower average error than any smaller mode of the harmonic series:
- 5EDO (101:116:133:153:176:202)
- 12EDO (101:107:113:120:127:135:143:151:160:170:180:191:202)
- 14EDO (101:106:112:117:123:129:136:143:150:158:166:174:183:192:202)
- 22EDO (101:104:108:111:115:118:122:126:130:134:138:143:147:152:157:162:167:173:178:184:190:196:202)
- 24EDO (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
- 25EDO (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
- 34EDO (101:103:105:107:110:112:114:116:119:121:124:126:129:132:134:137:140:143:146:149:152:155:158:161:165:168:172:175:179:182:186:190:194:198:202)
Table of intervals
| Step | Harmonic | Just ratio | Cents value |
| 1 | 102nd | 102/101 | 17.057 |
| 2 | 103rd | 103/101 | 33.947 |
| 3 | 104th | 104/101 | 50.674 |
| 4 | 105th | 105/101 | 67.241 |
| 5 | 106th | 106/101 | 83.651 |
| 6 | 107th | 107/101 | 99.907 |
| 7 | 108th | 108/101 | 116.011 |
| 8 | 109th | 109/101 | 131.967 |
| 9 | 110th | 110/101 | 147.778 |
| 10 | 111th | 111/101 | 163.445 |
| 11 | 112th | 112/101 | 178.972 |
| 12 | 113th | 113/101 | 194.361 |
| 13 | 114th | 114/101 | 209.614 |
| 14 | 115th | 115/101 | 224.734 |
| 15 | 116th | 116/101 | 239.723 |
| 16 | 117th | 117/101 | 254.584 |
| 17 | 118th | 118/101 | 269.318 |
| 18 | 119th | 119/101 | 283.928 |
| 19 | 120th | 120/101 | 298.415 |
| 20 | 121st | 121/101 | 312.782 |
| 21 | 122nd | 122/101 | 327.031 |
| 22 | 123rd | 123/101 | 341.164 |
| 23 | 124th | 124/101 | 355.182 |
| 24 | 125th | 125/101 | 369.087 |
| 25 | 126th | 126/101 | 382.882 |
| 26 | 127th | 127/101 | 396.568 |
| 27 | 128th | 128/101 | 410.146 |
| 28 | 129th | 129/101 | 423.619 |
| 29 | 130th | 130/101 | 436.988 |
| 30 | 131st | 131/101 | 450.254 |
| 31 | 132nd | 132/101 | 463.419 |
| 32 | 133rd | 133/101 | 476.485 |
| 33 | 134th | 134/101 | 489.453 |
| 34 | 135th | 135/101 | 502.325 |
| 35 | 136th | 136/101 | 515.102 |
| 36 | 137th | 137/101 | 527.785 |
| 37 | 138th | 138/101 | 540.376 |
| 38 | 139th | 139/101 | 552.876 |
| 39 | 140th | 140/101 | 565.286 |
| 40 | 141st | 141/101 | 577.608 |
| 41 | 142nd | 142/101 | 589.843 |
| 42 | 143rd | 143/101 | 601.992 |
| 43 | 144th | 144/101 | 614.056 |
| 44 | 145th | 145/101 | 626.037 |
| 45 | 146th | 146/101 | 637.936 |
| 46 | 147th | 147/101 | 649.753 |
| 47 | 148th | 148/101 | 661.49 |
| 48 | 149th | 149/101 | 673.148 |
| 49 | 150th | 150/101 | 684.729 |
| 50 | 151st | 151/101 | 696.232 |
| 51 | 152nd | 152/101 | 707.659 |
| 52 | 153rd | 153/101 | 719.012 |
| 53 | 154th | 154/101 | 730.29 |
| 54 | 155th | 155/101 | 741.496 |
| 55 | 156th | 156/101 | 752.629 |
| 56 | 157th | 157/101 | 763.691 |
| 57 | 158th | 158/101 | 774.683 |
| 58 | 159th | 159/101 | 785.606 |
| 59 | 160th | 160/101 | 796.46 |
| 60 | 161st | 161/101 | 807.246 |
| 61 | 162nd | 162/101 | 817.966 |
| 62 | 163rd | 163/101 | 828.62 |
| 63 | 164th | 164/101 | 839.209 |
| 64 | 165th | 165/101 | 849.733 |
| 65 | 166th | 166/101 | 860.194 |
| 66 | 167th | 167/101 | 870.591 |
| 67 | 168th | 168/101 | 880.927 |
| 68 | 169th | 169/101 | 891.202 |
| 69 | 170th | 170/101 | 901.415 |
| 70 | 171st | 171/101 | 911.569 |
| 71 | 172nd | 172/101 | 921.664 |
| 72 | 173rd | 173/101 | 931.7 |
| 73 | 174th | 174/101 | 941.678 |
| 74 | 175th | 175/101 | 951.6 |
| 75 | 176th | 176/101 | 961.464 |
| 76 | 177th | 177/101 | 971.273 |
| 77 | 178th | 178/101 | 981.026 |
| 78 | 179th | 179/101 | 990.725 |
| 79 | 180th | 180/101 | 1000.37 |
| 80 | 181st | 181/101 | 1009.961 |
| 81 | 182nd | 182/101 | 1019.5 |
| 82 | 183rd | 183/101 | 1028.986 |
| 83 | 184th | 184/101 | 1038.421 |
| 84 | 185th | 185/101 | 1047.804 |
| 85 | 186th | 186/101 | 1057.137 |
| 86 | 187th | 187/101 | 1066.42 |
| 87 | 188th | 188/101 | 1075.653 |
| 88 | 189th | 189/101 | 1084.837 |
| 89 | 190th | 190/101 | 1093.973 |
| 90 | 191st | 191/101 | 1103.061 |
| 91 | 192nd | 192/101 | 1112.101 |
| 92 | 193rd | 193/101 | 1121.095 |
| 93 | 194th | 194/101 | 1130.042 |
| 94 | 195th | 195/101 | 1138.943 |
| 95 | 196th | 196/101 | 1147.798 |
| 96 | 197th | 197/101 | 1156.608 |
| 97 | 198th | 198/101 | 1165.374 |
| 98 | 199th | 199/101 | 1174.096 |
| 99 | 200th | 200/101 | 1182.774 |
| 100 | 201st | 201/101 | 1191.408 |
| 101 | 202nd | 202/101 | 1200 |