General theory: Difference between revisions

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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>2011-09-19 15:17:08 UTC</tt>.<br>
| de =
: The original revision id was <tt>255774560</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">Tuning theory can become heavily mathematical, and as such can be difficult to understand. Here are some links for the rest of us:


=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]].
[[Chords]]
[[ScaleIndex|Scales]]
[[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:
[[Just intonation]]
* [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.
[[Periods and Generators]]
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
[[Regular Temperaments]]
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
[[EDO]]
[[EDT]]


=How it Works=  
== Basics ==
[[Monzos]]
* [[Interval]]
[[Vals]]
* [[Ratio]]
[[Mappings]]
** [[Ratio math]]
[[Patent val]]</pre></div>
* [[Cent]]
<h4>Original HTML content:</h4>
* [[Chord]]
<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;Tuning theory can become heavily mathematical, and as such can be difficult to understand. Here are some links for the rest of us:&lt;br /&gt;
* [[Scale]]
&lt;br /&gt;
* [[Mode]]
&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;
* [[Musical notation]]
&lt;a class="wiki_link" href="/Chords"&gt;Chords&lt;/a&gt;&lt;br /&gt;
* Terminology
&lt;a class="wiki_link" href="/ScaleIndex"&gt;Scales&lt;/a&gt;&lt;br /&gt;
** [[Glossary]]
&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
** [[Acronyms]]
&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;
== Core concepts ==
&lt;a class="wiki_link" href="/Just%20intonation"&gt;Just intonation&lt;/a&gt;&lt;br /&gt;
* [[Just intonation]]
&lt;a class="wiki_link" href="/Periods%20and%20Generators"&gt;Periods and Generators&lt;/a&gt;&lt;br /&gt;
* [[Harmonic series]]
&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt;&lt;br /&gt;
** [[Chord of nature]]
&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;&lt;br /&gt;
* [[Equal division of the octave]]
&lt;a class="wiki_link" href="/EDT"&gt;EDT&lt;/a&gt;&lt;br /&gt;
** [[Equal-step tuning]] ([[edt]], [[edf]], …)
&lt;br /&gt;
** [[Well temperament]]
&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;
* [[Regular temperaments]]
&lt;a class="wiki_link" href="/Monzos"&gt;Monzos&lt;/a&gt;&lt;br /&gt;
** [[Diatonic, chromatic, enharmonic, subchromatic]]
&lt;a class="wiki_link" href="/Vals"&gt;Vals&lt;/a&gt;&lt;br /&gt;
* [[MOS scale]]
&lt;a class="wiki_link" href="/Mappings"&gt;Mappings&lt;/a&gt;&lt;br /&gt;
** [[Periods and generators]]
&lt;a class="wiki_link" href="/Patent%20val"&gt;Patent val&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[Hexany]]
* [[Delta-rational chord]]
 
== Regular temperament theory (RTT) ==
* [[Monzo]]
* [[Val]]
* [[Mapping]]
* [[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]]
 
== Advanced theory ==
{{Main| Mathematical theory }}
 
[[Category:Theory]]
[[Category:Todo:review]]

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"