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{{Infobox AFDO|steps=101}}
{{Infobox AFDO|steps=101}}
'''[[Overtone scale|Mode 101 of the harmonic series]]''', also known as the '''Dalmatian scale''' {{idiosyncratic}}, is a 101-tone octave-repeating subset of the [[harmonic series]]. It is equivalent to '''[[AFDO|101afdo]]''' except that it has a fixed root and cannot be rotated.


It is a large [[Primodality|primodal]] scale which is suited for use as a [[Neji|NEJI]] tuning. It is the 26th [[Prime harmonic series|prime mode of the harmonic series]]. Its name is a reference to the animated TV series [[wikipedia:101_Dalmatian_Street|''101 Dalmatian Street (2019)'']].
'''101afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''101odo''' ([[otonal division]] of the octave), divides the octave into 101 parts of 1/101 each. It is a superset of [[100afdo]] and a subset of [[102afdo]]. As a scale it may be known as [[harmonic mode|mode 101 of the harmonic series]], the [[overtone scale #Over-n scales|Over-101]] scale, or the '''Dalmatian scale''' {{idiosyncratic}}. This view is equivalent to 101afdo except that it has a fixed root and cannot be rotated.


=== Optimal NEJI approximations ===
It is a large [[primodality|primodal]] scale which is suited for use as a [[neji]] tuning. It is the 26th [[prime harmonic series|prime mode of the harmonic series]]. Its name is a reference to the animated TV series {{w|101 Dalmatian Street|''101 Dalmatian Street'' (2019)}}.
The Dalmatian scale approximates four [[EDO|EDOs]], including two [[The Riemann zeta function and tuning|Zeta peak]] EDOs, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:


* [[19edo|19EDO]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
== Optimal NEJI approximations ==
* [[24edo|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)
The Dalmatian scale approximates four [[edo]]s, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:
* [[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)
* [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
* [[27edo|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)
* [[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)


It approximates ''seven'' EDOs, including ''three'' Zeta peak EDOs, with lower [[NEJI Tables/Average Error|average error]] than any smaller mode of the harmonic series:
It approximates ''seven'' edos, including ''three'' zeta peak edos, with lower [[NEJI Tables/Average Error|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)


* [[5edo|5EDO]] (101:116:133:153:176:202)
== Table of intervals ==
* [[12edo|12EDO]] (101:107:113:120:127:135:143:151:160:170:180:191:202)
* [[14edo|14EDO]] (101:106:112:117:123:129:136:143:150:158:166:174:183:192:202)
* [[22edo|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|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|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)
 
=== Table of intervals ===
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+ Intervals of mode 101 of the harmonic series
|+ Intervals of mode 101 of the harmonic series
|-
|-
!Step
! Step
!Harmonic
! Harmonic
!Just ratio
! Just ratio
![[Cent|Cents]] value
! [[Cent]]s value
|-
|-
|1
| 1
|102nd
| 102nd
|102/101
| 102/101
|17.057
| 17.057
|-
|-
|2
| 2
|103rd
| 103rd
|103/101
| 103/101
|33.947
| 33.947
|-
|-
|3
| 3
|104th
| 104th
|104/101
| 104/101
|50.674
| 50.674
|-
|-
|4
| 4
|105th
| 105th
|105/101
| 105/101
|67.241
| 67.241
|-
|-
|5
| 5
|106th
| 106th
|106/101
| 106/101
|83.651
| 83.651
|-
|-
|6
| 6
|107th
| 107th
|107/101
| 107/101
|99.907
| 99.907
|-
|-
|7
| 7
|108th
| 108th
|108/101
| 108/101
|116.011
| 116.011
|-
|-
|8
| 8
|109th
| 109th
|109/101
| 109/101
|131.967
| 131.967
|-
|-
|9
| 9
|110th
| 110th
|110/101
| 110/101
|147.778
| 147.778
|-
|-
|10
| 10
|111th
| 111th
|111/101
| 111/101
|163.445
| 163.445
|-
|-
|11
| 11
|112th
| 112th
|112/101
| 112/101
|178.972
| 178.972
|-
|-
|12
| 12
|113th
| 113th
|113/101
| 113/101
|194.361
| 194.361
|-
|-
|13
| 13
|114th
| 114th
|114/101
| 114/101
|209.614
| 209.614
|-
|-
|14
| 14
|115th
| 115th
|115/101
| 115/101
|224.734
| 224.734
|-
|-
|15
| 15
|116th
| 116th
|116/101
| 116/101
|239.723
| 239.723
|-
|-
|16
| 16
|117th
| 117th
|117/101
| 117/101
|254.584
| 254.584
|-
|-
|17
| 17
|118th
| 118th
|118/101
| 118/101
|269.318
| 269.318
|-
|-
|18
| 18
|119th
| 119th
|119/101
| 119/101
|283.928
| 283.928
|-
|-
|19
| 19
|120th
| 120th
|120/101
| 120/101
|298.415
| 298.415
|-
|-
|20
| 20
|121st
| 121st
|121/101
| 121/101
|312.782
| 312.782
|-
|-
|21
| 21
|122nd
| 122nd
|122/101
| 122/101
|327.031
| 327.031
|-
|-
|22
| 22
|123rd
| 123rd
|123/101
| 123/101
|341.164
| 341.164
|-
|-
|23
| 23
|124th
| 124th
|124/101
| 124/101
|355.182
| 355.182
|-
|-
|24
| 24
|125th
| 125th
|125/101
| 125/101
|369.087
| 369.087
|-
|-
|25
| 25
|126th
| 126th
|126/101
| 126/101
|382.882
| 382.882
|-
|-
|26
| 26
|127th
| 127th
|127/101
| 127/101
|396.568
| 396.568
|-
|-
|27
| 27
|128th
| 128th
|128/101
| 128/101
|410.146
| 410.146
|-
|-
|28
| 28
|129th
| 129th
|129/101
| 129/101
|423.619
| 423.619
|-
|-
|29
| 29
|130th
| 130th
|130/101
| 130/101
|436.988
| 436.988
|-
|-
|30
| 30
|131st
| 131st
|131/101
| 131/101
|450.254
| 450.254
|-
|-
|31
| 31
|132nd
| 132nd
|132/101
| 132/101
|463.419
| 463.419
|-
|-
|32
| 32
|133rd
| 133rd
|133/101
| 133/101
|476.485
| 476.485
|-
|-
|33
| 33
|134th
| 134th
|134/101
| 134/101
|489.453
| 489.453
|-
|-
|34
| 34
|135th
| 135th
|135/101
| 135/101
|502.325
| 502.325
|-
|-
|35
| 35
|136th
| 136th
|136/101
| 136/101
|515.102
| 515.102
|-
|-
|36
| 36
|137th
| 137th
|137/101
| 137/101
|527.785
| 527.785
|-
|-
|37
| 37
|138th
| 138th
|138/101
| 138/101
|540.376
| 540.376
|-
|-
|38
| 38
|139th
| 139th
|139/101
| 139/101
|552.876
| 552.876
|-
|-
|39
| 39
|140th
| 140th
|140/101
| 140/101
|565.286
| 565.286
|-
|-
|40
| 40
|141st
| 141st
|141/101
| 141/101
|577.608
| 577.608
|-
|-
|41
| 41
|142nd
| 142nd
|142/101
| 142/101
|589.843
| 589.843
|-
|-
|42
| 42
|143rd
| 143rd
|143/101
| 143/101
|601.992
| 601.992
|-
|-
|43
| 43
|144th
| 144th
|144/101
| 144/101
|614.056
| 614.056
|-
|-
|44
| 44
|145th
| 145th
|145/101
| 145/101
|626.037
| 626.037
|-
|-
|45
| 45
|146th
| 146th
|146/101
| 146/101
|637.936
| 637.936
|-
|-
|46
| 46
|147th
| 147th
|147/101
| 147/101
|649.753
| 649.753
|-
|-
|47
| 47
|148th
| 148th
|148/101
| 148/101
|661.490
| 661.490
|-
|-
|48
| 48
|149th
| 149th
|149/101
| 149/101
|673.148
| 673.148
|-
|-
|49
| 49
|150th
| 150th
|150/101
| 150/101
|684.729
| 684.729
|-
|-
|50
| 50
|151st
| 151st
|151/101
| 151/101
|696.232
| 696.232
|-
|-
|51
| 51
|152nd
| 152nd
|152/101
| 152/101
|707.659
| 707.659
|-
|-
|52
| 52
|153rd
| 153rd
|153/101
| 153/101
|719.012
| 719.012
|-
|-
|53
| 53
|154th
| 154th
|154/101
| 154/101
|730.290
| 730.290
|-
|-
|54
| 54
|155th
| 155th
|155/101
| 155/101
|741.496
| 741.496
|-
|-
|55
| 55
|156th
| 156th
|156/101
| 156/101
|752.629
| 752.629
|-
|-
|56
| 56
|157th
| 157th
|157/101
| 157/101
|763.691
| 763.691
|-
|-
|57
| 57
|158th
| 158th
|158/101
| 158/101
|774.683
| 774.683
|-
|-
|58
| 58
|159th
| 159th
|159/101
| 159/101
|785.606
| 785.606
|-
|-
|59
| 59
|160th
| 160th
|160/101
| 160/101
|796.460
| 796.460
|-
|-
|60
| 60
|161st
| 161st
|161/101
| 161/101
|807.246
| 807.246
|-
|-
|61
| 61
|162nd
| 162nd
|162/101
| 162/101
|817.966
| 817.966
|-
|-
|62
| 62
|163rd
| 163rd
|163/101
| 163/101
|828.620
| 828.620
|-
|-
|63
| 63
|164th
| 164th
|164/101
| 164/101
|839.209
| 839.209
|-
|-
|64
| 64
|165th
| 165th
|165/101
| 165/101
|849.733
| 849.733
|-
|-
|65
| 65
|166th
| 166th
|166/101
| 166/101
|860.194
| 860.194
|-
|-
|66
| 66
|167th
| 167th
|167/101
| 167/101
|870.591
| 870.591
|-
|-
|67
| 67
|168th
| 168th
|168/101
| 168/101
|880.927
| 880.927
|-
|-
|68
| 68
|169th
| 169th
|169/101
| 169/101
|891.202
| 891.202
|-
|-
|69
| 69
|170th
| 170th
|170/101
| 170/101
|901.415
| 901.415
|-
|-
|70
| 70
|171st
| 171st
|171/101
| 171/101
|911.569
| 911.569
|-
|-
|71
| 71
|172nd
| 172nd
|172/101
| 172/101
|921.664
| 921.664
|-
|-
|72
| 72
|173rd
| 173rd
|173/101
| 173/101
|931.700
| 931.700
|-
|-
|73
| 73
|174th
| 174th
|174/101
| 174/101
|941.678
| 941.678
|-
|-
|74
| 74
|175th
| 175th
|175/101
| 175/101
|951.600
| 951.600
|-
|-
|75
| 75
|176th
| 176th
|176/101
| 176/101
|961.464
| 961.464
|-
|-
|76
| 76
|177th
| 177th
|177/101
| 177/101
|971.273
| 971.273
|-
|-
|77
| 77
|178th
| 178th
|178/101
| 178/101
|981.026
| 981.026
|-
|-
|78
| 78
|179th
| 179th
|179/101
| 179/101
|990.725
| 990.725
|-
|-
|79
| 79
|180th
| 180th
|180/101
| 180/101
|1000.370
| 1000.370
|-
|-
|80
| 80
|181st
| 181st
|181/101
| 181/101
|1009.961
| 1009.961
|-
|-
|81
| 81
|182nd
| 182nd
|182/101
| 182/101
|1019.500
| 1019.500
|-
|-
|82
| 82
|183rd
| 183rd
|183/101
| 183/101
|1028.986
| 1028.986
|-
|-
|83
| 83
|184th
| 184th
|184/101
| 184/101
|1038.421
| 1038.421
|-
|-
|84
| 84
|185th
| 185th
|185/101
| 185/101
|1047.804
| 1047.804
|-
|-
|85
| 85
|186th
| 186th
|186/101
| 186/101
|1057.137
| 1057.137
|-
|-
|86
| 86
|187th
| 187th
|187/101
| 187/101
|1066.420
| 1066.420
|-
|-
|87
| 87
|188th
| 188th
|188/101
| 188/101
|1075.653
| 1075.653
|-
|-
|88
| 88
|189th
| 189th
|189/101
| 189/101
|1084.837
| 1084.837
|-
|-
|89
| 89
|190th
| 190th
|190/101
| 190/101
|1093.973
| 1093.973
|-
|-
|90
| 90
|191st
| 191st
|191/101
| 191/101
|1103.061
| 1103.061
|-
|-
|91
| 91
|192nd
| 192nd
|192/101
| 192/101
|1112.101
| 1112.101
|-
|-
|92
| 92
|193rd
| 193rd
|193/101
| 193/101
|1121.095
| 1121.095
|-
|-
|93
| 93
|194th
| 194th
|194/101
| 194/101
|1130.042
| 1130.042
|-
|-
|94
| 94
|195th
| 195th
|195/101
| 195/101
|1138.943
| 1138.943
|-
|-
|95
| 95
|196th
| 196th
|196/101
| 196/101
|1147.798
| 1147.798
|-
|-
|96
| 96
|197th
| 197th
|197/101
| 197/101
|1156.608
| 1156.608
|-
|-
|97
| 97
|198th
| 198th
|198/101
| 198/101
|1165.374
| 1165.374
|-
|-
|98
| 98
|199th
| 199th
|199/101
| 199/101
|1174.096
| 1174.096
|-
|-
|99
| 99
|200th
| 200th
|200/101
| 200/101
|1182.774
| 1182.774
|-
|-
|100
| 100
|201st
| 201st
|201/101
| 201/101
|1191.408
| 1191.408
|-
|-
|101
| 101
|202nd
| 202nd
|202/101
| 202/101
|1200.000
| 1200.000
|}
|}


=== Subsets ===
== Scales ==
 
=== Non-neji ===
==== Non-NEJI ====
Dante
Dante


Line 687: Line 685:




==== NEJI 5EDO ====
=== Neji 5edo ===
Equipentatonic
Equipentatonic


Line 701: Line 699:




==== NEJI 6EDO ====
=== Neji 6edo ===


Liquorice
Liquorice
Line 718: Line 716:




==== NEJI 12EDO ====
=== Neji 12edo ===
Blues Aeolian Hexatonic
Blues Aeolian Hexatonic


Line 1,354: Line 1,352:
202/101
202/101


==== NEJI 14EDO ====
{{Todo|cleanup|comment=write these scales more compactly. }}
 
==== NEJI 19EDO ====
 
==== NEJI 22EDO ====
 
==== NEJI 24EDO ====
 
==== NEJI 25EDO ====
 
==== NEJI 27EDO ====
 
==== NEJI 34EDO ====
[[Category:Neji]]
[[Category:Neji]]
[[Category:Primodality]]
[[Category:Primodality]]
Retrieved from "https://en.xen.wiki/w/101afdo"