101edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

~~: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-09-19 01:05:21 UTC</tt>.<br>~~

~~: The original revision id was <tt>163685341</tt>.<br>~~

~~: The revision comment was: <tt></tt><br>~~

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

~~<h4>Original Wikitext content:</h4>~~

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=101 tone equal temperament=

~~17 17 8 17 17 17 8 : Pytagorean tuning (comparable~~ with ~~12edo)~~

== Theory ==

~~13 13 13~~ 5 ~~13 13 13 13~~ 5 ~~: Armodue tuning~~ (~~comparable with 39edo~~ and ~~62edo~~)</~~pre><~~/~~div>~~

101edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning.

~~<h4>Original HTML content:</h4>~~

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-~~html"><html><head><title>101edo&lt~~;/~~title><~~/~~head><body><!~~-- ~~ws:start:WikiTextHeadingRule:0:&lt;h1&gt;~~ --~~><h1 id~~=~~"toc0"><a name~~=~~"x101 tone~~ equal ~~temperament"></~~a~~><~~!-- ~~ws:end:WikiTextHeadingRule:0~~ --~~>101 tone equal temperament</h1>~~

=== Odd harmonics ===

~~<br />~~

17 17 8 17 17 17 8 : ~~Pytagorean tuning~~ (~~comparable with 12edo~~)~~<br~~ /~~&gt~~;

13 13 13 5 13 13 13 13 5 : ~~Armodue tuning~~ (~~comparable with 39edo and 62edo~~)~~&lt~~;/~~body><~~/~~html><~~/~~pre><~~/~~div>~~

=== Subsets and supersets ===

101edo is the 26th [[prime edo]], following [[97edo]] and before [[103edo]]. [[202edo]], which doubles it, provides a good correction to the 5th, 7th, and 11th harmonics.

== Intervals ==

== Scales ==

=== Mos scales ===

* 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}}

* Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101)

* Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)

* Superdiatonic 1/13-tone 13;5 relation: 13 13 13 5 13 13 13 13 5 ((13 26 39 44 57 70 83 96 101)\101)

* Sensi[11] 8L 3s: 10 10 7 10 10 10 7 10 10 10 7 ((10 20 27 37 47 57 64 74 84 94)\101){{clarify}}

* Anti-Ketradektriatoh 3L 11s: 7 7 7 8 7 7 7 7 8 7 7 7 7 8 ((7 14 22 29 36 43 50 58 65 72 79 86 93 101)\101)

== Instruments ==

* [[Lumatone mapping for 101edo]]

== Music ==

; [[Francium]]

* "Eggclent" from ''Eggs'' (2025) – [https://open.spotify.com/track/4S0BTeb9yDdMUuT1QJy26H Spotify] | [https://francium223.bandcamp.com/track/eggclent Bandcamp] | [https://www.youtube.com/watch?v=FAe4O71Mvj0 YouTube]

== External links ==

* [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}

[[Category:Armodue]]

[[Category:Grackle]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-09-19 01:05:21 UTC</tt>.<br>
-: The original revision id was <tt>163685341</tt>.<br>
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=101 tone equal temperament=
-17 8 17 17 17 8 : Pytagorean tuning (comparable with 12edo)
+== Theory ==
-13 13 5 13 13 13 13 5 : Armodue tuning (comparable with 39edo and 62edo)</pre></div>
+edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning.
-<h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;101edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x101 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;101 tone equal temperament&lt;/h1&gt;
+=== Odd harmonics ===
- &lt;br /&gt;
+{{Harmonics in equal|101}}
-17 8 17 17 17 8 : Pytagorean tuning (comparable with 12edo)&lt;br /&gt;
-13 13 5 13 13 13 13 5 : Armodue tuning (comparable with 39edo and 62edo)&lt;/body&gt;&lt;/html&gt;</pre></div>
+=== Subsets and supersets ===
+edo is the 26th [[prime edo]], following [[97edo]] and before [[103edo]]. [[202edo]], which doubles it, provides a good correction to the 5th, 7th, and 11th harmonics.
+== Intervals ==
+{{Interval table}}
+== Scales ==
+=== Mos scales ===
+* 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? -->
+* Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101)
+* Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)
+* Superdiatonic 1/13-tone 13;5 relation: 13 13 13 5 13 13 13 13 5 ((13 26 39 44 57 70 83 96 101)\101)
+* Sensi[11] 8L 3s: 10 10 7 10 10 10 7 10 10 10 7 ((10 20 27 37 47 57 64 74 84 94)\101){{clarify}} <!-- which val? -->
+* Anti-Ketradektriatoh 3L 11s: 7 7 7 8 7 7 7 7 8 7 7 7 7 8 ((7 14 22 29 36 43 50 58 65 72 79 86 93 101)\101)
+== Instruments ==
+* [[Lumatone mapping for 101edo]]
+== Music ==
+; [[Francium]]
+* "Eggclent" from ''Eggs'' (2025) – [https://open.spotify.com/track/4S0BTeb9yDdMUuT1QJy26H Spotify] | [https://francium223.bandcamp.com/track/eggclent Bandcamp] | [https://www.youtube.com/watch?v=FAe4O71Mvj0 YouTube]
+== External links ==
+* [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}
+[[Category:Armodue]]
+[[Category:Grackle]]