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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = General theory
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-07 12:16:28 UTC</tt>.<br>
| de =
: The original revision id was <tt>362853494</tt>.<br>
| es = Teoría Básica
: The revision comment was: <tt></tt><br>
| ja = 一般理論
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>
Here are some links to some of the key ideas underlying tuning:
<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">Here are some links to some of the key ideas underlying tuning:


=Basics=  
== Basics ==
[[Ratios]]
* Start here: [[Xen concepts for beginners]]
[[cent|Cents]]
* [[Interval]]
[[xenharmonic/Chords|Chords]]
* [[Ratio]]
[[xenharmonic/ScaleIndex|Scales]]
** [[Ratio math]]
[[xenharmonic/Notation|Notation]]
* [[Cent]]
* [[Chord]]
* [[Scale]]
* [[Mode]]
* [[Musical notation]]
* Terminology
** [[Glossary]]
** [[Acronyms]]


=Core Concepts=  
== Core concepts ==
[[xenharmonic/JI|JI]]
* [[Just intonation]]
[[xenharmonic/Regular Temperaments|Regular Temperaments]]
* [[Harmonic series]]
[[xenharmonic/Equal Temperaments|Equal Temperaments]]
** [[Chord of nature]]
[[xenharmonic/Periods and Generators|Periods and Generators]]
* [[Equal division of the octave]]
[[xenharmonic/EDO|EDO]]
** [[Equal-step tuning]] ([[edt]], [[edf]], …)
[[xenharmonic/EDT|EDT]]
** [[Well temperament]]
[[xenharmonic/MOSScales|MOS Scales]]
* [[Regular temperaments]]
[[xenharmonic/EDL|EDL (Equal divisions of length)]]
** [[Diatonic, chromatic, enharmonic, subchromatic]]
[[xenharmonic/AID|Arithmetic irrational divisions]]
* [[MOS scale]]
[[ADO|ADO (Arithmetic rational divisions)]]
** [[Periods and generators]]
* [[Hexany]]
* [[Delta-rational chord]]


=How it Works=  
== Online tools ==
[[xenharmonic/Monzos|Monzos]]
{{Main| List of music software #Browser-based }}
[[xenharmonic/Vals|Vals]]
[[xenharmonic/Mappings|Mappings]]
[[xenharmonic/Patent val|Patent val]]
[[xenharmonic/tempering out|Tempering Out]]
[[xenharmonic/Rank and codimension|Rank and codimension]]


=Personal Explanations=
* [https://scaleworkshop.plainsound.org/ Scale Workshop] – scale-creation site by [[Lumi Pakkanen]]. Allows playing via QWERTY computer keyboard. Can also export .scl and .kbm files.
[[Mike's Lectures On Regular Temperament Theory]]
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
[[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]]
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.


=Javascript tools=  
== Common scales ==
[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]
* [[:Category: 5-tone scales]]
[[http://www.untwelve.org/javascript_demos/sb_tree.html?start=0,1,1,0|An animated Stern-Brocot tree, courtesy untwelve.org]]
* [[:Category: 6-tone scales]]
[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]
* [[:Category: 7-tone scales]]
[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]
* [[:Category: 8-tone scales]]
* [[:Category: 9-tone scales]]
* [[:Category: 10-tone scales]]
* [[:Category: 11-tone scales]]
* [[:Category: 12-tone scales]]


=Additional Stuff=  
== Regular temperament theory (RTT) ==
[[xenharmonic/Benedetti height|Benedetti height]]
* [[Monzo]]
[[xenharmonic/Kees height|Kees height]]
* [[Val]]
[[xenharmonic/Tenney Height|Tenney Height]]
* [[Mapping]]
[[xenharmonic/ABC, High Quality Commas, and Epimericity|ABC, High Quality Commas, and Epimericity]]
* [[Patent val]]
[[xenharmonic/Graham complexity|Graham complexity]]
* [[Tempering out]]
[[xenharmonic/Generator complexity|Generator complexity]]
* [[Rank and codimension]]
[[xenharmonic/Lumma stability|Lumma stability]]
* [[Keenan's explanation of vals]]
[[xenharmonic/chord of nature|chord of nature]]
* [[Comma pump]]
[[xenharmonic/Modal UDP Notation|Modal UDP Notation]]
* [[Comma basis]]
[[Cluster temperament]]
* [[Saturation, torsion, and contorsion]]
[[xenharmonic/Consonant class scale|Consonant Class Scale]]
* [[Dyadic chord]]
[[xenharmonic/Maximum variety|Maximum variety]]
* [[Essential tempering comma]]
[[xenharmonic/distributional evenness|Distributional Evenness]]
* [[Graham complexity]]
[[xenharmonic/Essential tempering commas|Essential tempering commas]]


=Advanced Theory=  
== Advanced theory ==
[[xenharmonic/Mathematical Theory|Mathematical Theory]]</pre></div>
{{Main| Mathematical theory }}
<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;General Theory&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Here are some links to some of the key ideas underlying tuning:&lt;br /&gt;
[[Category:Theory]]
&lt;br /&gt;
[[Category:Todo:review]]
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Basics&lt;/h1&gt;
&lt;a class="wiki_link" href="/Ratios"&gt;Ratios&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/cent"&gt;Cents&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chords"&gt;Chords&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/ScaleIndex"&gt;Scales&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Core Concepts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Core Concepts&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/JI"&gt;JI&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Equal%20Temperaments"&gt;Equal Temperaments&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Periods%20and%20Generators"&gt;Periods and Generators&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDO"&gt;EDO&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDT"&gt;EDT&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS Scales&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/EDL"&gt;EDL (Equal divisions of length)&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/AID"&gt;Arithmetic irrational divisions&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/ADO"&gt;ADO (Arithmetic rational divisions)&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="How it Works"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;How it Works&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Monzos"&gt;Monzos&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vals"&gt;Vals&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mappings"&gt;Mappings&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val"&gt;Patent val&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;Tempering Out&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rank%20and%20codimension"&gt;Rank and codimension&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Personal Explanations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Personal Explanations&lt;/h1&gt;
&lt;a class="wiki_link" href="/Mike%27s%20Lectures%20On%20Regular%20Temperament%20Theory"&gt;Mike's Lectures On Regular Temperament Theory&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keenan%27s%20explanation%20of%20vals"&gt;Keenan's explanation of vals&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Javascript tools"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Javascript tools&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Interval%20calculator"&gt;Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/sb_tree.html?start=0,1,1,0" rel="nofollow"&gt;An animated Stern-Brocot tree, courtesy untwelve.org&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.untwelve.org/javascript_demos/MOSring.html" rel="nofollow"&gt;An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow"&gt;An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Additional Stuff"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Additional Stuff&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Benedetti%20height"&gt;Benedetti height&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kees%20height"&gt;Kees height&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tenney%20Height"&gt;Tenney Height&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/ABC%2C%20High%20Quality%20Commas%2C%20and%20Epimericity"&gt;ABC, High Quality Commas, and Epimericity&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Generator%20complexity"&gt;Generator complexity&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Lumma%20stability"&gt;Lumma stability&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/chord%20of%20nature"&gt;chord of nature&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20Notation"&gt;Modal UDP Notation&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Cluster%20temperament"&gt;Cluster temperament&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Consonant%20class%20scale"&gt;Consonant Class Scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Maximum%20variety"&gt;Maximum variety&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/distributional%20evenness"&gt;Distributional Evenness&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Essential%20tempering%20commas"&gt;Essential tempering commas&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Advanced Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Advanced Theory&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mathematical%20Theory"&gt;Mathematical Theory&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 04:54, 2 December 2025

Here are some links to some of the key ideas underlying tuning:

Basics

Core concepts

Online tools

Main article: List of music software § Browser-based
  • Scale Workshop – scale-creation site by Lumi Pakkanen. Allows playing via QWERTY computer keyboard. Can also export .scl and .kbm files.
  • Xenpaper – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
  • xen-calc – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.

Common scales

Regular temperament theory (RTT)

Advanced theory

Main article: Mathematical theory
Retrieved from "https://en.xen.wiki/index.php?title=General_theory&oldid=218410"