101afdo

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101afdo

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Prime factorization	101 (prime)
Dual sharp fifth	152/101 (707.659c)
Dual flat fifth	151/101 (696.231c)

101afdo (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 mode 101 of the harmonic series or the Over-101 scale. This view is equivalent to 101afdo except that it has a fixed root and cannot be rotated.

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

101afdo approximates five edos, 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, 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 an afdo of this size, but it's not that unusual. 104afdo, 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 101afdo 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.