Harmonics 101–202: Difference between revisions

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{{Infobox AFDO|steps=101}}
{{Infobox harmonics|101}}


'''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]] or the [[overtone scale #Over-n scales|Over-101]] scale. This view is equivalent to 101afdo except that it has a fixed root and cannot be rotated.
{{Harmonics intro|101}}


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]].
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]].
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== Theory ==
== Theory ==
=== Lowest-error neji approximations ===
=== Lowest-error neji approximations ===
101afdo approximates five [[edo]]s <35, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:<small>
This scale approximates five [[edo]]s <35, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:<small>
* [[8edo]] (101:110:120:131:143:156:170:185:202)
* [[8edo]] (101:110:120:131:143:156:170:185:202)
* [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
* [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
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* [[34edo]] (<small>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</small>)</small>
* [[34edo]] (<small>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</small>)</small>


Best-approximating this many edos in general, and this many zeta peak edos specifically, is more than average for an afdo of this size, but it's not that unusual. [[104afdo]], for example, best-approximates similar numbers of both.
Best-approximating this many edos in general, and this many zeta peak edos specifically, is more than average for a scale of this size, but it's not that unusual. harmonics 104–208, for example, best-approximates similar numbers of both.


== Table of intervals ==
== Table of intervals ==
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=== Explanation of idiosyncratic names ===
=== Explanation of idiosyncratic names ===
[[Budjarn Lambeth]] named 101afdo the '''Dalmatian scale''' {{idiosyncratic}} but no one else has been recorded using that name. That name is a reference to the animated TV series {{w|101 Dalmatian Street|''101 Dalmatian Street'' (2019)}}. He named some of its subsets after characters from that series based on the 'mood' evoked by the scales resembling those characters' personalities.
[[Budjarn Lambeth]] named this scale the '''Dalmatian scale''' {{idiosyncratic}} but no one else has been recorded using that name. That name is a reference to the animated TV series {{w|101 Dalmatian Street|''101 Dalmatian Street'' (2019)}}. He named some of its subsets after characters from that series based on the 'mood' evoked by the scales resembling those characters' personalities.


{{Todo|cleanup|comment=write these scales more compactly. }}
{{Todo|cleanup|comment=write these scales more compactly. }}
{{Navbox harmonics}}
[[Category:Neji]]
[[Category:Neji]]
[[Category:Primodality]]
[[Category:Primodality]]

Latest revision as of 00:41, 11 October 2026

Harmonics 101–202
Prime factorization 101 (prime)
Dual sharp fifth 152/101 (707.659c)
Dual flat fifth 151/101 (696.232c)

The harmonic segment 101::202 (also harmonics 101–202) consists of harmonics 101 through 202 (101:102:…:202) and spans one octave above the root. Used as a scale, it is also called mode 101 of the harmonic series.

It is a large primodal scale which is suited for use as a neji tuning. It is the 26th prime mode of the harmonic series.

Theory

Lowest-error neji approximations

This scale approximates five edos <35, including two zeta peak edos, with lower maximum error than any smaller mode of the harmonic series:

  • 8edo (101:110:120:131:143:156:170:185:202)
  • 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)

It approximates seven edos <35, 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)

Best-approximating this many edos in general, and this many zeta peak edos specifically, is more than average for a scale of this size, but it's not that unusual. harmonics 104–208, for example, best-approximates similar numbers of both.

Table of intervals

Intervals of mode 101 of the harmonic series
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 148/101 661.490
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 154/101 730.290
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 160/101 796.460
60 161st 161/101 807.246
61 162nd 162/101 817.966
62 163rd 163/101 828.620
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 173/101 931.700
73 174th 174/101 941.678
74 175th 175/101 951.600
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 1000.370
80 181st 181/101 1009.961
81 182nd 182/101 1019.500
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 1066.420
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 1200.000

Scales

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Non-neji

Dante

101:114:120:152:189:202


Da Vinci

101:113:126:151:178:202


Dawkins

101:118:135:152:185:202


Deepak

101:126:135:152:160:202


Deja Vu

101:121:151:162:182:202


Delgado

101:107:126:152:177:202


Dolly

101:127:134:152:177:202


Dylan

101:135:151:161:180:202


Fergus

101:121:135:140:151:175:181:202


Hansel

101:113:126:135:151:169:189:202


Neji 5edo

Equipentatonic

101:116:133:153:176:202


Neji 6edo

Liquorice

101:113:127:143:160:180:202


Neji 12edo

Blues Aeolian Hexatonic

101:120:135:143:151:160:202


Blues Aeolian Pentatonic I

101:120:135:151:160:202


Blues Aeolian Pentatonic II

101:120:151:160:180:202


Blues Bright Double Harmonic

101:107:127:135:151:160:180:191:202


Blues Dark Double Harmonic

101:113:120:135:143:151:160:191:202


Blues Dorian Hexatonic

101:120:135:151:170:180:202


Blues Dorian Pentatonic

101:120:151:170:180:202


Blues Dorian Septatonic

101:120:135:143:151:170:180:202


Blues Harmonic Hexatonic

101:113:120:135:151:191:202


Blues Harmonic Septatonic

101:120:135:143:151:160:191:202


Blues Leading

101:120:135:143:151:180:191:202


Blues Minor

101:120:135:143:151:180:202


Blues Minor Maj7

101:120:135:143:151:191:202


Blues Pentachordal

101:113:120:135:143:151:202


Dominant Pentatonic

101:113:127:151:180:202


Dorian

101:113:120:135:151:170:180:202


Double Harmonic

1101:07:127:135:151:160:191:202


Hirajoshi

101:113:120:151:160:202


Ionian Pentatonic

101:127:135:151:191:202


Javanese Pentachordal

101:107:120:143:151:202


Kokin-Joshi

101:113:120:151:170:202


Locrian

101:107:120:135:143:160:180:202


Lydian

101:113:127:143:151:170:191:202


Major

101:113:127:135:151:170:191:202


Major Pentatonic

101:113:127:151:170:202


Minor

101:113:120:135:151:160:180:202


Minor Harmonic

101:113:120:135:151:160:191:202


Minor Harmonic Pentatonic

101:113:120:151:191:202


Minor Hexatonic

101:113:120:135:151:180:202


Minor Melodic

101:113:120:135:151:170:191:202


Minor Pentatonic

101:120:135:151:180:202


Mixolydian

101:113:127:135:151:170:180:202


Mixolydian Harmonic

101:127:135:151:160:180:202


Mixolydian Pentatonic

101:127:135:151:180:202


Phrygian

101:107:120:135:151:160:180:202


Phrygian Dominant

101:107:127:135:151:160:180:202


Phrygian Dominant Hexatonic

101:107:127:135:151:180:202


Phrygian Dominant Pentatonic

101:127:135:151:160:202


Phrygian Pentatonic

101:107:120:151:160:202


Picardy Hexatonic

101:113:127:135:151:160:202


Picardy Pentatonic

101:113:127:151:160:202


Liquorice (Whole Tone)

101:113:127:143:160:180:202

Explanation of idiosyncratic names

Budjarn Lambeth named this scale the Dalmatian scale [idiosyncratic term] but no one else has been recorded using that name. That name is a reference to the animated TV series 101 Dalmatian Street (2019). He named some of its subsets after characters from that series based on the 'mood' evoked by the scales resembling those characters' personalities.

View • Talk • EditOvertone scales 
Small modes 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24
Larger modes 30 • 32 • 36 • 48 • 60 • 128
Families /2: 2 • 4 • 8 • 16 • 32 • 128
/3: 3 • 6 • 9 • 12 • 15 • 18 • 21 • 24
/5: 5 • 10 • 15 • 20 • 25 • 30 • 35 • 60 • 80
/7: 7 • 14 • 21 • 28 • 35 • 56
/11: 11 • 22 • 33
/13: 13 • 26
Related Harmonic series • Subharmonic series • Carlos harmonic scale • Ringer scale • Primodality
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