101afdo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
m Added a table of intervals
Line 19: Line 19:
* [[25edo|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)
* [[25edo|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|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)
* [[34edo|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 ===
{| class="wikitable"
|Step
|Harmonic
|Just ratio
|[[Cent|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
|}
[[Category:Neji]]
[[Category:Neji]]
[[Category:Primodality]]
[[Category:Primodality]]

Revision as of 07:53, 16 April 2023

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
Retrieved from "https://en.xen.wiki/index.php?title=101afdo&oldid=107886"