Harmonics 101–202: Difference between revisions

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~~'''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]].

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== Theory ==

=== 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:

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:

* [[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)

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* [[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.

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 ==

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=== 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.

[[Category:Neji]]

[[Category:Primodality]]

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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]].
@@ Line 7: / Line 7: @@
 == Theory ==
 === Lowest-error neji approximations ===
-afdo 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)
 * [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
@@ Line 23: / Line 23: @@
 * [[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 ==
@@ Line 818: / Line 818: @@
 === 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. }}
+{{Navbox harmonics}}
 [[Category:Neji]]
 [[Category:Primodality]]