101afdo

Revision as of 07:53, 16 April 2023 by BudjarnLambeth (talk | contribs) (Added a table of intervals)

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.

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