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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-03 23:48:38 UTC</tt>.<br>
| de =
: The original revision id was <tt>250563410</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:


(DON'T CLICK THESE JUST YET OR YOU WILL BE DESTROYED BY MATH)
If you are new to tuning theory looking for an overview, see [[Xen concepts for beginners]] and various others in our collection of [[guides]].


[[Periodic scale]]
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:
[[MOSScales|MOS scales]]
* [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.
[[MODMOS scales]]
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
[[Monzos and Interval Space]]
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
[[Vals and Tuning Space]]
 
[[Smonzos and Svals]]
== Basics ==
[[Wedgies and Multivals]]
* [[Interval]]
[[TOP tuning]]
* [[Ratio]]
[[Tenney-Euclidean tuning]]
** [[Ratio math]]
[[Tenney-Euclidean temperament measures]]
* [[Cent]]
[[Tenney-Euclidean metrics]]
* [[Chord]]
[[Cangwu badness]]
* [[Scale]]
[[Fractional monzos]]
* [[Mode]]
[[Saturation]]
* [[Musical notation]]
[[Abstract regular temperament]]
* Terminology
[[Target tunings]]
** [[Glossary]]
[[Normal lists]]
** [[Acronyms]]
[[Planar Temperament]]
 
[[The Seven Limit Symmetrical Lattices]]
== Core concepts ==
[[Modulatory space]]
* [[Just intonation]]
[[Chordal space]]
* [[Harmonic series]]
[[Hahn distance]]
** [[Chord of nature]]
[[Transversal]]
* [[Equal division of the octave]]
[[Transversal generators]]
** [[Equal-step tuning]] ([[edt]], [[edf]], …)
[[Minkowski blocks]]
** [[Well temperament]]
[[k*N subgroups]]</pre></div>
* [[Regular temperaments]]
<h4>Original HTML content:</h4>
** [[Diatonic, chromatic, enharmonic, subchromatic]]
<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;
* [[MOS scale]]
&lt;br /&gt;
** [[Periods and generators]]
(DON'T CLICK THESE JUST YET OR YOU WILL BE DESTROYED BY MATH)&lt;br /&gt;
* [[Hexany]]
&lt;br /&gt;
* [[Delta-rational chord]]
&lt;a class="wiki_link" href="/Periodic%20scale"&gt;Periodic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/MOSScales"&gt;MOS scales&lt;/a&gt;&lt;br /&gt;
== Regular temperament theory (RTT) ==
&lt;a class="wiki_link" href="/MODMOS%20scales"&gt;MODMOS scales&lt;/a&gt;&lt;br /&gt;
* [[Monzo]]
&lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;Monzos and Interval Space&lt;/a&gt;&lt;br /&gt;
* [[Val]]
&lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;&lt;br /&gt;
* [[Mapping]]
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Smonzos and Svals&lt;/a&gt;&lt;br /&gt;
* [[Patent val]]
&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;Wedgies and Multivals&lt;/a&gt;&lt;br /&gt;
* [[Tempering out]]
&lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt;&lt;br /&gt;
* [[Rank and codimension]]
&lt;a class="wiki_link" href="/Tenney-Euclidean%20tuning"&gt;Tenney-Euclidean tuning&lt;/a&gt;&lt;br /&gt;
* [[Keenan's explanation of vals]]
&lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;Tenney-Euclidean temperament measures&lt;/a&gt;&lt;br /&gt;
* [[Comma pump]]
&lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;Tenney-Euclidean metrics&lt;/a&gt;&lt;br /&gt;
* [[Comma basis]]
&lt;a class="wiki_link" href="/Cangwu%20badness"&gt;Cangwu badness&lt;/a&gt;&lt;br /&gt;
* [[Saturation, torsion, and contorsion]]
&lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;&lt;br /&gt;
* [[Dyadic chord]]
&lt;a class="wiki_link" href="/Saturation"&gt;Saturation&lt;/a&gt;&lt;br /&gt;
* [[Essential tempering comma]]
&lt;a class="wiki_link" href="/Abstract%20regular%20temperament"&gt;Abstract regular temperament&lt;/a&gt;&lt;br /&gt;
* [[Graham complexity]]
&lt;a class="wiki_link" href="/Target%20tunings"&gt;Target tunings&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Normal%20lists"&gt;Normal lists&lt;/a&gt;&lt;br /&gt;
== Advanced theory ==
&lt;a class="wiki_link" href="/Planar%20Temperament"&gt;Planar Temperament&lt;/a&gt;&lt;br /&gt;
{{Main| Mathematical theory }}
&lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;The Seven Limit Symmetrical Lattices&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Modulatory%20space"&gt;Modulatory space&lt;/a&gt;&lt;br /&gt;
[[Category:Theory]]
&lt;a class="wiki_link" href="/Chordal%20space"&gt;Chordal space&lt;/a&gt;&lt;br /&gt;
[[Category:Todo:review]]
&lt;a class="wiki_link" href="/Hahn%20distance"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Transversal"&gt;Transversal&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Transversal%20generators"&gt;Transversal generators&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Minkowski%20blocks"&gt;Minkowski blocks&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;k*N subgroups&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"