Harmonics 101–202 - Revision history

Sintel at 00:41, 11 October 2026

2026-10-11T00:41:29Z

← Older revision		Revision as of 00:41, 11 October 2026
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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]]

Sintel: Sintel moved page 101afdo to Harmonics 101–202

2026-10-10T19:10:04Z

Sintel moved page 101afdo to Harmonics 101–202

← Older revision	Revision as of 19:10, 10 October 2026
(No difference)

BudjarnLambeth: /* Theory */

2025-09-27T10:09:11Z

Theory

← Older revision		Revision as of 10:09, 27 September 2025
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	== Theory ==		== Theory ==
	=== Lowest-error neji approximations ===		=== Lowest-error neji approximations ===
	101afdo approximates five [[edo]]s, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error\|maximum error]] than any smaller mode of the harmonic series:<small>		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>
	* [[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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	* [[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 <35, 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)

BudjarnLambeth at 09:13, 15 August 2025

2025-08-15T09:13:44Z

← Older revision		Revision as of 09:13, 15 August 2025
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	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]].

	== Lowest-error neji approximations ==		== Theory ==
	~~The Dalmatian scale~~ approximates five [[edo]]s, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error\|maximum error]] than any smaller mode of the harmonic series:<small>		=== Lowest-error neji approximations ===
			101afdo approximates five [[edo]]s, 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)

BudjarnLambeth: /* Lowest-error neji approximations */

2025-07-30T04:20:11Z

Lowest-error neji approximations

← Older revision		Revision as of 04:20, 30 July 2025
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	== Lowest-error neji approximations ==		== 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:<small>		The Dalmatian scale approximates five [[edo]]s, 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)
	* [[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)
	* [[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)		* [[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)

BudjarnLambeth: /* Explanation of idiosyncratic names */

2025-07-30T04:14:31Z

Explanation of idiosyncratic names

← Older revision		Revision as of 04:14, 30 July 2025
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	=== Explanation of idiosyncratic names ===		=== 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.		[[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.

	{{Todo\|cleanup\|comment=write these scales more compactly. }}		{{Todo\|cleanup\|comment=write these scales more compactly. }}

BudjarnLambeth: /* Explanation of idiosyncratic names */

2025-07-30T04:12:11Z

Explanation of idiosyncratic names

← Older revision		Revision as of 04:12, 30 July 2025
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	=== Explanation of idiosyncratic names ===		=== 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 ~~have been named~~ after characters from that series based on the 'mood' evoked by the scales resembling those characters' personalities.		[[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. }}

BudjarnLambeth: /* Table of intervals */

2025-07-30T04:11:41Z

Table of intervals

← Older revision		Revision as of 04:11, 30 July 2025
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	== 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
	\|-		\|-

BudjarnLambeth: Cleaned up; might do more, will look over the page again after

2025-07-30T04:11:09Z

Cleaned up; might do more, will look over the page again after

← Older revision		Revision as of 04:11, 30 July 2025
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	{{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 ==
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	* [[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)
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	* [[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 ==
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	== Scales ==		== Scales ==
			{{Idiosyncratic terms}}

	=== Non-neji ===		=== Non-neji ===
	Dante		Dante
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	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 have been named 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. }}

Fredg999: Categories

2025-07-30T03:57:00Z

← Older revision		Revision as of 03:57, 30 July 2025
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	[[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]]