101afdo: Difference between revisions

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~~{{delete|bizarre}}~~

'''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 ==

== Theory ==

~~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:

=== 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:

* [[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)

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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)

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)

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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)

* [[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 ==

{| class="wikitable mw-collapsible"

{| class="wikitable mw-collapsible mw-collapsed"

|+ Intervals of mode 101 of the harmonic series

|-

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== Scales ==

=== Non-neji ===

Dante

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

=== 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.

[[Category:Neji]]

[[Category:Primodality]]

~~[[Category:AFDO]]~~

[[Category:Harmonic series]]

[[Category:Just intonation scales]]

[[Category:Pages with mostly numerical content]]

@@ Line 1: / Line 1: @@
 {{Infobox AFDO|steps=101}}
-{{delete|bizarre}}
-'''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 ==
+== Theory ==
-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>
+=== Lowest-error neji approximations ===
+afdo 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)
 * [[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)
@@ Line 13: / Line 14: @@
 * [[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)
 * [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202)
@@ Line 21: / Line 22: @@
 * [[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>
+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 ==
-{| class="wikitable mw-collapsible"
+{| class="wikitable mw-collapsible mw-collapsed"
 |+ Intervals of mode 101 of the harmonic series
 |-
@@ Line 538: / Line 541: @@
 == Scales ==
+{{Idiosyncratic terms}}
 === Non-neji ===
 Dante
@@ Line 811: / Line 816: @@
 :113:127:143:160:180:202
+=== 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.
 {{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]]