1/5-comma meantone: 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 = 1/5-comma meantone

~~: This revision was by author [[User:genewardsmith~~|~~genewardsmith]] and made on <tt>2011-09~~-~~30 12:15:16 UTC</tt>.<br>~~

| de = Fünftelkomma-mitteltönig

~~: The original revision id was <tt>260032358</tt>.<br>~~

}}

~~: The revision comment was: <tt></tt><br>~~

'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely.

~~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>~~

<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 1/5-comma [[meantone]] temperament, each perfect fifth is tempered by a fifth of a [[~~Syntonic Comma|~~syntonic comma]] from its just value of [[~~3_2|~~3/2]]. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.

1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)~~</pre></div>~~

The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224|septimal kleisma (225/224)]].

~~<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~~"~~><html><head><title>1~~-~~5 Syntonic Comma Meantone</title></head><body>In~~ 1/5-~~comma <a class="wiki_link" href="~~/~~meantone">meantone<~~/a> temperament, each perfect fifth is tempered by a fifth of a <a class="wiki_link" href="/Syntonic%20Comma">syntonic comma</a> from its just value of <a class="wiki_link" href="/3_2">3/2~~</a>. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines~~ 1/5~~-comma; it is the regular tuning which tempers out 81~~/~~80 and tunes~~ 2 ~~and 16/15 purely~~.~~<br />~~

1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)

~~<br />~~

~~1/5~~-~~comma meantone is practically identical to the closed system of <a class~~=~~"wiki_link" href~~="/~~43edo">43edo<~~/~~a>~~ (~~although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.~~)~~</body></html></pre></div>~~

== Tuning profile ==

[[Projection map]]:

{| class="right-all"

|-

| [⟨ || 1 || 4/5 || -4/5 || -5 || ]

|-

| ⟨ || 0 || 1/5 || 4/5 || 2 || ]

|-

| ⟨ || 0 || 1/5 || 4/5 || 2 || ]

|-

| ⟨ || 0 || 0 || 0 || 0 || ]]

|}

[[Tuning map]]: {{val| 1200 1897.6537 2790.6150 3376.5374 }}

[[Error map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}

== Music ==

; [[septimal lemon]]

* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025)

[[Category:Meantone]]

[[Category:Historical]]

@@ 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 = 1/5-comma meantone
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-30 12:15:16 UTC</tt>.<br>
+| de = Fünftelkomma-mitteltönig
-: The original revision id was <tt>260032358</tt>.<br>
+}}
-: The revision comment was: <tt></tt><br>
+'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely.
-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>
-<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 1/5-comma [[meantone]] temperament, each perfect fifth is tempered by a fifth of a [[Syntonic Comma|syntonic comma]] from its just value of [[3_2|3/2]]. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.
-/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)</pre></div>
+The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224|septimal kleisma (225/224)]].
-<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;1-5 Syntonic Comma Meantone&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In 1/5-comma &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; temperament, each perfect fifth is tempered by a fifth 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 major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.&lt;br /&gt;
+/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)
-&lt;br /&gt;
-/5-comma meantone is practically identical to the closed system of &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)&lt;/body&gt;&lt;/html&gt;</pre></div>
+== Tuning profile ==
+[[Projection map]]:
+{| class="right-all"
+|-
+| [⟨ || 1 || 4/5 || -4/5 || -5 || ]
+|-
+| ⟨ || 0 || 1/5 || 4/5 || 2 || ]
+|-
+| ⟨ || 0 || 1/5 || 4/5 || 2 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]]
+|}
+[[Tuning map]]: {{val| 1200 1897.6537 2790.6150 3376.5374 }}
+[[Error map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }}
+== Music ==
+; [[septimal lemon]]
+* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025)
+[[Category:Meantone]]
+[[Category:Historical]]