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>2011-09-04 00:56:36 UTC</tt>.<br>
| de =
: The original revision id was <tt>250567876</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:


[[Vals]]
== Basics ==
* Start here: [[Xen concepts for beginners]]
* [[Interval]]
* [[Ratio]]
** [[Ratio math]]
* [[Cent]]
* [[Chord]]
* [[Scale]]
* [[Mode]]
* [[Musical notation]]
* Terminology
** [[Glossary]]
** [[Acronyms]]


(DON'T CLICK THESE JUST YET OR YOU WILL BE DESTROYED BY MATH)
== Core concepts ==
* [[Just intonation]]
* [[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]]


[[Periodic scale]]
== Online tools ==
[[MOSScales|MOS scales]]
{{Main| List of music software #Browser-based }}
[[MODMOS scales]]
 
[[Monzos and Interval Space]]
* [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.
[[Vals and Tuning Space]]
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
[[Smonzos and Svals]]
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
[[Wedgies and Multivals]]
 
[[TOP tuning]]
== Common scales ==
[[Tenney-Euclidean tuning]]
* [[:Category: 5-tone scales]]
[[Tenney-Euclidean temperament measures]]
* [[:Category: 6-tone scales]]
[[Tenney-Euclidean metrics]]
* [[:Category: 7-tone scales]]
[[Cangwu badness]]
* [[:Category: 8-tone scales]]
[[Fractional monzos]]
* [[:Category: 9-tone scales]]
[[Saturation]]
* [[:Category: 10-tone scales]]
[[Abstract regular temperament]]
* [[:Category: 11-tone scales]]
[[Target tunings]]
* [[:Category: 12-tone scales]]
[[Normal lists]]
 
[[Planar Temperament]]
== Regular temperament theory (RTT) ==
[[The Seven Limit Symmetrical Lattices]]
* [[Monzo]]
[[Modulatory space]]
* [[Val]]
[[Chordal space]]
* [[Mapping]]
[[Hahn distance]]
* [[Patent val]]
[[Transversal]]
* [[Tempering out]]
[[Transversal generators]]
* [[Rank and codimension]]
[[Minkowski blocks]]
* [[Keenan's explanation of vals]]
[[k*N subgroups]]</pre></div>
* [[Comma pump]]
<h4>Original HTML content:</h4>
* [[Comma basis]]
<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;
* [[Saturation, torsion, and contorsion]]
&lt;br /&gt;
* [[Dyadic chord]]
&lt;a class="wiki_link" href="/Vals"&gt;Vals&lt;/a&gt;&lt;br /&gt;
* [[Essential tempering comma]]
&lt;br /&gt;
* [[Graham complexity]]
(DON'T CLICK THESE JUST YET OR YOU WILL BE DESTROYED BY MATH)&lt;br /&gt;
 
&lt;br /&gt;
== Advanced theory ==
&lt;a class="wiki_link" href="/Periodic%20scale"&gt;Periodic scale&lt;/a&gt;&lt;br /&gt;
{{Main| Mathematical theory }}
&lt;a class="wiki_link" href="/MOSScales"&gt;MOS scales&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/MODMOS%20scales"&gt;MODMOS scales&lt;/a&gt;&lt;br /&gt;
[[Category:Theory]]
&lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;Monzos and Interval Space&lt;/a&gt;&lt;br /&gt;
[[Category:Todo:review]]
&lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Smonzos and Svals&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;Wedgies and Multivals&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Tenney-Euclidean%20tuning"&gt;Tenney-Euclidean tuning&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;Tenney-Euclidean temperament measures&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;Tenney-Euclidean metrics&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Cangwu%20badness"&gt;Cangwu badness&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Fractional monzos&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Saturation"&gt;Saturation&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Abstract%20regular%20temperament"&gt;Abstract regular temperament&lt;/a&gt;&lt;br /&gt;
&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;
&lt;a class="wiki_link" href="/Planar%20Temperament"&gt;Planar Temperament&lt;/a&gt;&lt;br /&gt;
&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;
&lt;a class="wiki_link" href="/Chordal%20space"&gt;Chordal space&lt;/a&gt;&lt;br /&gt;
&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 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"