1/3-comma meantone: Difference between revisions

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**Imported revision 295493550 - Original comment: **
clarify in “practically identical”
 
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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>
| de = Drittelkomma-mitteltönig
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-01-26 07:23:31 UTC</tt>.<br>
| en = 1/3 syntonic comma meantone
: The original revision id was <tt>295493550</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<h4>Original Wikitext content:</h4>
'''1/3-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]). In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[Eigenmonzo|eigenmonzo (unchanged interval)]] of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (''c''. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter).
<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">In 1/3-comma [[meantone]] temperament, each perfect fifth is tempered by a third of a [[Syntonic Comma|syntonic comma]] from its just value of [[3_2|3/2]]. This results in minor thirds being exactly [[6_5|6/5]] (and major sixths being exactly [[5_3|5/3]]).
In other words, 1/3-comma meantone is the specific tuning of meantone temperament with an [[Fractional monzos|eigenmonzo]] of 6/5.


The fifth is 694.786 cents in size, and the major third 379.145 cents, which is about 7 cents flatter than in [[Quarter-comma meantone|1/4-comma meantone]].
== Tuning profile ==
[[Projection map]]:


1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference).
{| class="right-all"
=External links=
|-
[[http://www.lehrklaenge.de/html/mitteltonige_stimmung_iii.html|Die mitteltönige Stimmung mit reinen kleinen Terzen]] (explanation of 1/3 comma meantone, in german)</pre></div>
| [⟨ || 1 || 4/3 || 4/3 || 1/3 || ]
<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;1-3 Syntonic Comma Meantone&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In 1/3-comma &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; temperament, each perfect fifth is tempered by a third of a &lt;a class="wiki_link" href="/Syntonic%20Comma"&gt;syntonic comma&lt;/a&gt; from its just value of &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;. This results in minor thirds being exactly &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; (and major sixths being exactly &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;).&lt;br /&gt;
| ⟨ || 0 || -1/3 || -4/3 || -10/3 || ]
In other words, 1/3-comma meantone is the specific tuning of meantone temperament with an &lt;a class="wiki_link" href="/Fractional%20monzos"&gt;eigenmonzo&lt;/a&gt; of 6/5.&lt;br /&gt;
|-
&lt;br /&gt;
| ⟨ || 0 || 1/3 || 4/3 || 10/3 || ]
The fifth is 694.786 cents in size, and the major third 379.145 cents, which is about 7 cents flatter than in &lt;a class="wiki_link" href="/Quarter-comma%20meantone"&gt;1/4-comma meantone&lt;/a&gt;.&lt;br /&gt;
|-
&lt;br /&gt;
| ⟨ || 0 || 0 || 0 || 0 || ]]
1/3-comma meantone is practically identical to the closed system of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; (although technically there is a slight difference).&lt;br /&gt;
|}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;External links&lt;/h1&gt;
 
&lt;a class="wiki_link_ext" href="http://www.lehrklaenge.de/html/mitteltonige_stimmung_iii.html" rel="nofollow"&gt;Die mitteltönige Stimmung mit reinen kleinen Terzen&lt;/a&gt; (explanation of 1/3 comma meantone, in german)&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }}
 
[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }}
 
== External links ==
* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Lehrklaenge.de | ''Die mitteltönige Stimmung mit reinen kleinen Terzen''] (explanation of 1/3 comma meantone, German)
* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on [[Tonalsoft Encyclopedia]]
 
[[Category:Meantone]]
[[Category:Historical]]

Latest revision as of 18:43, 23 January 2026

1/3-comma meantone is the tuning of meantone temperament in which each perfect fifth is tempered by a third of a syntonic comma from its just value of 3/2. This results in minor thirds being exactly 6/5 (and major sixths being exactly 5/3). In other words, 1/3-comma meantone is the specific tuning of meantone temperament with an eigenmonzo (unchanged interval) of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (c. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of 19edo (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter).

Tuning profile

Projection map:

[⟨ 1 4/3 4/3 1/3 ]
⟨ 0 -1/3 -4/3 -10/3 ]
⟨ 0 1/3 4/3 10/3 ]
⟨ 0 0 0 0 ]]

Tuning map: ⟨1200 1894.7862 2779.1450 3347.8624]

Error map: ⟨0 -7.1688 -7.1688 -20.9635]

External links

Retrieved from "https://en.xen.wiki/index.php?title=1/3-comma_meantone&oldid=222253"