Xenharmonic Wiki

101edo: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 164489577 - Original comment: **
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
Link to lumatone mapping
 
(59 intermediate revisions by 21 users not shown)
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:genewardsmith|genewardsmith]] and made on <tt>2010-09-22 04:36:45 UTC</tt>.<br>
: The original revision id was <tt>164489577</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=
//101edo// divides the octave into 101 parts of 11.881 cents each. It can be used to tune the [[Schismatic family|grackle temperament]].


5-limit commas: 32805/32768, &lt;5 13 -11|
== Theory ==
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.


7-limit commas: 126/125, 32805/32768, 2430/2401
=== Odd harmonics ===
{{Harmonics in equal|101}}


=== 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.


17 17 8 17 17 17 8: 5L2s MOS (superpythagoren)
== Intervals ==
{{Interval table}}


13 13 13 5 13 13 13 13 5: 7L2s MOS (Armodue)</pre></div>
== Scales ==
<h4>Original HTML content:</h4>
=== Mos scales ===
<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;
* 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? -->
&lt;em&gt;101edo&lt;/em&gt; divides the octave into 101 parts of 11.881 cents each. It can be used to tune the &lt;a class="wiki_link" href="/Schismatic%20family"&gt;grackle temperament&lt;/a&gt;.&lt;br /&gt;
* Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101)
&lt;br /&gt;
* Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)
5-limit commas: 32805/32768, &amp;lt;5 13 -11|&lt;br /&gt;
* 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)
&lt;br /&gt;
* 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? -->
7-limit commas: 126/125, 32805/32768, 2430/2401&lt;br /&gt;
* 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)
&lt;br /&gt;
 
&lt;br /&gt;
== Instruments ==
17 17 8 17 17 17 8: 5L2s MOS (superpythagoren)&lt;br /&gt;
* [[Lumatone mapping for 101edo]]
&lt;br /&gt;
 
13 13 13 5 13 13 13 13 5: 7L2s MOS (Armodue)&lt;/body&gt;&lt;/html&gt;</pre></div>
== 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]]
Retrieved from "https://en.xen.wiki/w/101edo"