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>2012-01-24 18:26:16 UTC</tt>.<br>~~

| de =

~~: The original revision id was <tt>295018996</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 ==

[[~~Chords~~]]

* Start here: [[Xen concepts for beginners]]

[[~~ScaleIndex|Scales~~]]

* [[Interval]]

[[~~Notation~~]]

* [[Ratio]]

** [[Ratio math]]

* [[Cent]]

* [[Chord]]

* [[Scale]]

* [[Mode]]

* [[Musical notation]]

* Terminology

** [[Glossary]]

** [[Acronyms]]

=Core ~~Concepts~~=

== Core concepts ==

[[Just intonation]]

* [[Just intonation]]

[[~~Regular Temperaments~~]]

* [[Harmonic series]]

[[Equal ~~Temperaments~~]]

** [[Chord of nature]]

[[~~Periods and Generators~~]]

* [[Equal division of the octave]]

[[~~EDO~~]]

** [[Equal-step tuning]] ([[edt]], [[edf]], …)

[[~~EDT~~]]

** [[Well temperament]]

[[~~MOSScales|~~MOS ~~Scales~~]]

* [[Regular temperaments]]

** [[Diatonic, chromatic, enharmonic, subchromatic]]

* [[MOS scale]]

** [[Periods and generators]]

* [[Hexany]]

* [[Delta-rational chord]]

=~~Javascript~~ tools=

== Online tools ==

~~[[Just Intonation -> EDO calculator]]~~

~~[[AnimatedSternBrocotTree~~|~~An animated Stern~~-~~Brocot tree, courtesy untwelve.org]]~~

~~[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]~~

~~=How it Works=~~

* [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.

[~~[Monzos]~~]

* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.

[[~~Vals~~]]

* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.

[[~~Mappings~~]]

[~~[Patent val]]~~

~~[[tempering out|Tempering Out]~~]

=~~Additional Stuff~~=

== Common scales ==

[[~~Benedetti height~~]]

* [[:Category: 5-tone scales]]

[[~~Tenney Height~~]]

* [[:Category: 6-tone scales]]

[[~~Graham complexity~~]]

* [[:Category: 7-tone scales]]

[[~~Modal UDP Notation~~]]

* [[:Category: 8-tone scales]]

[[~~Consonant class scale|Consonant Class Scale~~]]

* [[:Category: 9-tone scales]]

[[~~Maximum variety~~]]

* [[:Category: 10-tone scales]]

[[~~distributional evenness|Distributional Evenness~~]]

* [[:Category: 11-tone scales]]

[[~~Essential tempering commas~~]]

* [[:Category: 12-tone scales]]

=~~Advanced Theory~~=

== Regular temperament theory (RTT) ==

[[~~Mathematical Theory~~]]~~</pre></div>~~

* [[Monzo]]

~~<h4>Original HTML content:</h4>~~

* [[Val]]

<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"><html><head><title>General Theory</title></head><body>Here are some links to some of the key ideas underlying tuning:<br />

* [[Mapping]]

~~<br />~~

* [[Patent val]]

~~<h1 id="toc0"><a name="Basics"></a>Basics</h1>~~

* [[Tempering out]]

~~<a class="wiki_link" href="/Chords">Chords</a><br />~~

* [[Rank and codimension]]

~~<a class="wiki_link" href="/ScaleIndex">Scales</a><br />~~

* [[Keenan's explanation of vals]]

~~<a class="wiki_link" href="/Notation">Notation</a><br />~~

* [[Comma pump]]

~~<br />~~

* [[Comma basis]]

~~<h1 id="toc1"><a name="Core Concepts"></a>Core Concepts</h1>~~

* [[Saturation, torsion, and contorsion]]

~~<a class="wiki_link" href="/Just%20intonation">Just intonation</a><br />~~

* [[Dyadic chord]]

~~<a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a><br />~~

* [[Essential tempering comma]]

~~<a class="wiki_link" href="/Equal%20Temperaments">Equal Temperaments</a><br />~~

* [[Graham complexity]]

~~<a class="wiki_link" href="/Periods%20and%20Generators">Periods~~ and ~~Generators</a><br />~~

~~<a class="wiki_link" href="/EDO">EDO</a><br />~~

== Advanced theory ==

~~<a class="wiki_link" href="/EDT">EDT</a><br />~~

~~<a class="wiki_link" href="/MOSScales">MOS Scales</a><br />~~

~~<br />~~

[[Category:Theory]]

~~<h1 id="toc2"><a name="Javascript tools"></a>Javascript tools</h1>~~

[[Category:Todo:review]]

~~<a class="wiki_link" href="/Just%20Intonation%20-%3E%20EDO%20calculator">Just Intonation -&gt; EDO calculator</a><br />~~

~~<a class="wiki_link" href="/AnimatedSternBrocotTree">An animated Stern-Brocot tree~~, ~~courtesy untwelve.org</a><br />~~

~~<a class="wiki_link_ext" href="http://www.toverlamp.org/static/wickisynth/wickisynth.html" rel="nofollow">An excellent Firefox browser tuning demo synthesizer~~, ~~'Wicksynth'</a><br />~~

~~<br />~~

~~<h1 id="toc3"><a name="How it Works"></a>How it Works</h1>~~

~~<a class="wiki_link" href="/Monzos">Monzos</a><br />~~

~~<a class="wiki_link" href="/Vals">Vals</a><br />~~

~~<a class="wiki_link" href="/Mappings">Mappings</a><br />~~

~~<a class="wiki_link" href="/Patent%20val">Patent val</a><br />~~

~~<a class="wiki_link" href="/~~tempering~~%20out">Tempering Out</a><br />~~

~~<br />~~

~~<h1 id="toc4"><a name="Additional Stuff"></a>Additional Stuff</h1>~~

~~<a class="wiki_link" href="/Benedetti%20height">Benedetti height</a><br />~~

~~<a class="wiki_link" href="/Tenney%20Height">Tenney Height</a><br />~~

~~<a class="wiki_link" href="/Graham%20complexity">~~Graham complexity~~</a><br />~~

~~<a class="wiki_link" href="/Modal%20UDP%20Notation">Modal UDP Notation</a><br />~~

~~<a class~~=~~"wiki_link" href~~=~~"/Consonant%20class%20scale">Consonant Class Scale</a><br />~~

~~<a class~~=~~"wiki_link" href~~=~~"/Maximum%20variety">Maximum variety</a><br />~~

~~<a class="wiki_link" href="/distributional%20evenness">Distributional Evenness</a><br />~~

~~<a class="wiki_link" href="/Essential%20tempering%20commas">Essential tempering commas</a><br />~~

~~<br />~~

~~<h1 id="toc5"><a name="Advanced~~ Theory~~"></a>Advanced Theory</h1>~~

~~<a class="wiki_link" href="/Mathematical%20Theory">Mathematical Theory</a></body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<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>2012-01-24 18:26:16 UTC</tt>.<br>
+| de =
-: The original revision id was <tt>295018996</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 ==
-[[Chords]]
+* Start here: [[Xen concepts for beginners]]
-[[ScaleIndex|Scales]]
+* [[Interval]]
-[[Notation]]
+* [[Ratio]]
+** [[Ratio math]]
+* [[Cent]]
+* [[Chord]]
+* [[Scale]]
+* [[Mode]]
+* [[Musical notation]]
+* Terminology
+** [[Glossary]]
+** [[Acronyms]]
-=Core Concepts=
+== Core concepts ==
-[[Just intonation]]
+* [[Just intonation]]
-[[Regular Temperaments]]
+* [[Harmonic series]]
-[[Equal Temperaments]]
+** [[Chord of nature]]
-[[Periods and Generators]]
+* [[Equal division of the octave]]
-[[EDO]]
+** [[Equal-step tuning]] ([[edt]], [[edf]], …)
-[[EDT]]
+** [[Well temperament]]
-[[MOSScales|MOS Scales]]
+* [[Regular temperaments]]
+** [[Diatonic, chromatic, enharmonic, subchromatic]]
+* [[MOS scale]]
+** [[Periods and generators]]
+* [[Hexany]]
+* [[Delta-rational chord]]
-=Javascript tools=
+== Online tools ==
-[[Just Intonation -&gt; EDO calculator]]
+{{Main| List of music software #Browser-based }}
-[[AnimatedSternBrocotTree|An animated Stern-Brocot tree, courtesy untwelve.org]]
-[[http://www.toverlamp.org/static/wickisynth/wickisynth.html|An excellent Firefox browser tuning demo synthesizer, 'Wicksynth']]
-=How it Works=
+* [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.
-[[Monzos]]
+* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
-[[Vals]]
+* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.
-[[Mappings]]
-[[Patent val]]
-[[tempering out|Tempering Out]]
-=Additional Stuff=
+== Common scales ==
-[[Benedetti height]]
+* [[:Category: 5-tone scales]]
-[[Tenney Height]]
+* [[:Category: 6-tone scales]]
-[[Graham complexity]]
+* [[:Category: 7-tone scales]]
-[[Modal UDP Notation]]
+* [[:Category: 8-tone scales]]
-[[Consonant class scale|Consonant Class Scale]]
+* [[:Category: 9-tone scales]]
-[[Maximum variety]]
+* [[:Category: 10-tone scales]]
-[[distributional evenness|Distributional Evenness]]
+* [[:Category: 11-tone scales]]
-[[Essential tempering commas]]
+* [[:Category: 12-tone scales]]
-=Advanced Theory=
+== Regular temperament theory (RTT) ==
-[[Mathematical Theory]]</pre></div>
+* [[Monzo]]
-<h4>Original HTML content:</h4>
+* [[Val]]
-<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;
+* [[Mapping]]
-&lt;br /&gt;
+* [[Patent val]]
-&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;
+* [[Tempering out]]
- &lt;a class="wiki_link" href="/Chords"&gt;Chords&lt;/a&gt;&lt;br /&gt;
+* [[Rank and codimension]]
-&lt;a class="wiki_link" href="/ScaleIndex"&gt;Scales&lt;/a&gt;&lt;br /&gt;
+* [[Keenan's explanation of vals]]
-&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
+* [[Comma pump]]
-&lt;br /&gt;
+* [[Comma basis]]
-&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;
+* [[Saturation, torsion, and contorsion]]
- &lt;a class="wiki_link" href="/Just%20intonation"&gt;Just intonation&lt;/a&gt;&lt;br /&gt;
+* [[Dyadic chord]]
-&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt;&lt;br /&gt;
+* [[Essential tempering comma]]
-&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal Temperaments&lt;/a&gt;&lt;br /&gt;
+* [[Graham complexity]]
-&lt;a class="wiki_link" href="/Periods%20and%20Generators"&gt;Periods and Generators&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;&lt;br /&gt;
+== Advanced theory ==
-&lt;a class="wiki_link" href="/EDT"&gt;EDT&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;br /&gt;
+[[Category:Theory]]
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Javascript tools"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Javascript tools&lt;/h1&gt;
+[[Category:Todo:review]]
-&lt;a class="wiki_link" href="/Just%20Intonation%20-%3E%20EDO%20calculator"&gt;Just Intonation -&amp;gt; EDO calculator&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/AnimatedSternBrocotTree"&gt;An animated Stern-Brocot tree, courtesy untwelve.org&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:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="How it Works"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;How it Works&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Monzos"&gt;Monzos&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Vals"&gt;Vals&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Mappings"&gt;Mappings&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Patent%20val"&gt;Patent val&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/tempering%20out"&gt;Tempering Out&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="Additional Stuff"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Additional Stuff&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Benedetti%20height"&gt;Benedetti height&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Tenney%20Height"&gt;Tenney Height&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;Modal UDP Notation&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Consonant%20class%20scale"&gt;Consonant Class Scale&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Maximum%20variety"&gt;Maximum variety&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/distributional%20evenness"&gt;Distributional Evenness&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Essential%20tempering%20commas"&gt;Essential tempering commas&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="Advanced Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Advanced Theory&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Mathematical%20Theory"&gt;Mathematical Theory&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>