User:BudjarnLambeth/101afdo - Revision history

BudjarnLambeth: Redirected page to 101afdo

2025-07-30T04:34:11Z

Redirected page to 101afdo

Show changes

BudjarnLambeth at 04:33, 30 July 2025

2025-07-30T04:33:42Z

Show changes

BudjarnLambeth: Replaced content with "See 101afdo."

2025-07-30T04:13:02Z

Replaced content with "See 101afdo."

Show changes

BudjarnLambeth at 04:12, 30 July 2025

2025-07-30T04:12:47Z

← Older revision		Revision as of 04:12, 30 July 2025
Line 1:		Line 1:
	{{Infobox AFDO\|steps=101}}		{{Infobox AFDO\|steps=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]], 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.		'''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.

	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)}}~~.		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]].

	== Lowest-error neji approximations ==		== Lowest-error neji approximations ==
Line 12:		Line 12:
	* [[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)</small>		* [[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)</small>

	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:<small>		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:<small>
	* [[5edo]] (101:116:133:153:176:202)		* [[5edo]] (101:116:133:153:176:202)
	* [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202)		* [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202)
Line 20:		Line 20:
	* [[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]] (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]] (<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.

	== Table of intervals ==		== Table of intervals ==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ Intervals of mode 101 of the harmonic series		\|+ Intervals of mode 101 of the harmonic series
	\|-		\|-
Line 537:		Line 539:

	== Scales ==		== Scales ==
			{{Idiosyncratic terms}}

	=== Non-neji ===		=== Non-neji ===
	Dante		Dante
Line 810:		Line 814:

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

			=== Explanation of idiosyncratic names ===
			[[Budjarn Lambeth]] named 101afdo the '''Dalmatian scale''' {{idiosyncratic}} but no one else do far 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. }}
	[[Category:Neji]]		[[Category:Neji]]
	[[Category:Primodality]]		[[Category:Primodality]]
	~~[[Category:AFDO]]~~
	[[Category:Harmonic series]]		[[Category:Harmonic series]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]

BudjarnLambeth: Created page with "{{Infobox AFDO|steps=101}} '''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, the Over-101 scale, or the '''Dalmatian scale''' {{idiosyncratic}}. This view is equivalent to 101a..."

2025-07-30T03:40:35Z

Created page with "{{Infobox AFDO|steps=101}} '''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, the Over-101 scale, or the '''Dalmatian scale''' {{idiosyncratic}}. This view is equivalent to 101a..."

New page

{{Infobox AFDO|steps=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]], 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.

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)}}.

== Lowest-error neji approximations ==
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:
* [[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 [[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)

== Table of intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of mode 101 of the harmonic series
|-
! Step
! Harmonic
! Just ratio
! [[Cent]]s 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 ==
=== 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

{{Todo|cleanup|comment=write these scales more compactly. }}
[[Category:Neji]]
[[Category:Primodality]]
[[Category:AFDO]]
[[Category:Harmonic series]]
[[Category:Just intonation scales]]
[[Category:Pages with mostly numerical content]]