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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:akjmicro|akjmicro]] and made on <tt>2012-07-29 01:54:52 UTC</tt>.<br>
| de =
: The original revision id was <tt>355237928</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=
If you are new to tuning theory looking for an overview, see [[Xen concepts for beginners]] and various others in our collection of [[guides]].
[[Ratios]]
[[cent|Cents]]
[[xenharmonic/Chords|Chords]]
[[xenharmonic/ScaleIndex|Scales]]
[[xenharmonic/Notation|Notation]]


=Core Concepts=
If you are looking for tools to start playing microtonal music, see [[List of music software]], but we would like to highlight these, which will aid your study of tuning theory:
[[xenharmonic/JI|JI]]
* [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.
[[xenharmonic/Regular Temperaments|Regular Temperaments]]
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
[[xenharmonic/Equal Temperaments|Equal Temperaments]]
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
[[xenharmonic/Periods and Generators|Periods and Generators]]
[[xenharmonic/EDO|EDO]]
[[xenharmonic/EDT|EDT]]
[[xenharmonic/MOSScales|MOS Scales]]
[[xenharmonic/EDL|EDL (Equal divisions of length)]]
[[xenharmonic/AID|Arithmetic irrational divisions]]
[[ADO|ADO (Arithmetic rational divisions)]]


=How it Works=  
== Basics ==
[[xenharmonic/Monzos|Monzos]]
* [[Interval]]
[[xenharmonic/Vals|Vals]]
* [[Ratio]]
[[xenharmonic/Mappings|Mappings]]
** [[Ratio math]]
[[xenharmonic/Patent val|Patent val]]
* [[Cent]]
[[xenharmonic/tempering out|Tempering Out]]
* [[Chord]]
[[xenharmonic/Rank and codimension|Rank and codimension]]
* [[Scale]]
* [[Mode]]
* [[Musical notation]]
* Terminology
** [[Glossary]]
** [[Acronyms]]


=Personal Explanations=  
== Core concepts ==
[[Mike's Lectures On Regular Temperament Theory]]
* [[Just intonation]]
[[xenharmonic/Keenan's explanation of vals|Keenan's explanation of vals]]
* [[Harmonic series]]
** [[Chord of nature]]
* [[Equal division of the octave]]
** [[Equal-step tuning]] ([[edt]], [[edf]], …)
** [[Well temperament]]
* [[Regular temperaments]]
** [[Diatonic, chromatic, enharmonic, subchromatic]]
* [[MOS scale]]
** [[Periods and generators]]
* [[Hexany]]
* [[Delta-rational chord]]


=Javascript tools=  
== Regular temperament theory (RTT) ==
[[xenharmonic/Interval calculator|Interval calculator--a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too]]
* [[Monzo]]
[[http://www.untwelve.org/javascript_demos/sb_tree.html?start=0,1,1,0|An animated Stern-Brocot tree, courtesy untwelve.org]]
* [[Val]]
[[http://www.untwelve.org/javascript_demos/MOSring.html|An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation]]
* [[Mapping]]
[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]
* [[Patent val]]
* [[Tempering out]]
* [[Rank and codimension]]
* [[Keenan's explanation of vals]]
* [[Comma pump]]
* [[Comma basis]]
* [[Saturation, torsion, and contorsion]]
* [[Dyadic chord]]
* [[Essential tempering comma]]
* [[Graham complexity]]


=Additional Stuff=  
== Advanced theory ==
[[xenharmonic/Benedetti height|Benedetti height]]
{{Main| Mathematical theory }}
[[xenharmonic/Kees height|Kees height]]
[[xenharmonic/Tenney Height|Tenney Height]]
[[xenharmonic/Epimericity|Epimericity]]
[[xenharmonic/Graham complexity|Graham complexity]]
[[xenharmonic/Generator complexity|Generator complexity]]
[[xenharmonic/Lumma stability|Lumma stability]]
[[xenharmonic/chord of nature|chord of nature]]
[[xenharmonic/Modal UDP Notation|Modal UDP Notation]]
[[Cluster temperament]]
[[xenharmonic/Consonant class scale|Consonant Class Scale]]
[[xenharmonic/Maximum variety|Maximum variety]]
[[xenharmonic/distributional evenness|Distributional Evenness]]
[[xenharmonic/Essential tempering commas|Essential tempering commas]]


=Advanced Theory=
[[Category:Theory]]
[[xenharmonic/Mathematical Theory|Mathematical Theory]]</pre></div>
[[Category:Todo:review]]
<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;
&lt;br /&gt;
&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/Epimericity"&gt;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 10:04, 18 September 2026

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

If you are new to tuning theory looking for an overview, see Xen concepts for beginners and various others in our collection of guides.

If you are looking for tools to start playing microtonal music, see List of music software, but we would like to highlight these, which will aid your study of tuning theory:

  • 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.

Basics

Core concepts

Regular temperament theory (RTT)

Advanced theory

Main article: Mathematical theory
Retrieved from "https://en.xen.wiki/index.php?title=General_theory&oldid=237376"