19edt: 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 = 19ed3

~~: This revision was by author [[User:JosephRuhf~~|~~JosephRuhf]] and made on <tt>2015-06-30 15:05:35 UTC</tt>.<br>~~

| de = Bernhard Stopper

~~: The original revision id was <tt>554760793</tt>.<br>~~

}}

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

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly~~ as ~~Wikispaces rendered it.<br>~~

{{ED intro}} It is also known as '''Stopper tuning'''.

~~<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">=Division of 3/1 into 19 equal parts=

~~= =~~

~~[[http://www.piano-stopper.de/html/onlypure_tuning.html|Bernhard~~ Stopper'~~s OnlyPure tuning]]~~

~~Note: 19 equal divisions of the tritave~~ is not a xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo|12-tone scale]]. ~~Or if you insist that~~ it is, it is the tritave ~~twin~~ of godzilla temperament (with a generator of 400.4 cents)</~~pre~~></~~div~~>

== Theory ==

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

19edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].

~~<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>19ED3</title></head><body><h1 id~~=~~"toc0"><a name~~=~~"Division of~~ 3/1 ~~into~~ 19 ~~equal parts"></a>Division of~~ 3/1 ~~into 19~~ equal ~~parts</h1>~~

~~<h1 id~~=~~"toc1"><!~~-~~- ws:end:WikiTextHeadingRule:2 --> <~~/~~h1>~~

This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig|5L 4s<3/1>|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig|8L 3s<3/1>|link=1}} scale.

~~<a class~~=~~"wiki_link_ext" href~~=~~"http~~://~~www.~~piano-stopper.de/~~html/onlypure_tuning.html" rel~~=~~"nofollow"~~&~~gt;Bernhard Stopper's~~ OnlyPure tuning~~</a><br />~~

~~<br />~~

=== Harmonics ===

~~Note~~: ~~19 equal divisions of the tritave is not a xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal <a class="wiki_link" href="/~~12edo~~">12-tone scale</a>. Or if you insist that it is, it is the tritave twin of godzilla temperament (with a generator of 400.4 cents)</body></html></pre></div>~~

{{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 19edt (continued)}}

=== Subsets and supersets ===

19edt is the 8th [[prime equal division|prime edt]], following [[17edt]] and before [[23edt]].

== Intervals ==

== See also ==

* [[7edf]] – relative edf

* [[12edo]] – relative edo

* [[28ed5]] – relative ed5

* [[31ed6]] – relative ed6

* [[34ed7]] – relative ed7

* [[40ed10]] – relative ed10

* [[43ed12]] – relative ed12

* [[76ed80]] – close to the zeta-optimized tuning for 12edo

* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]

== External links ==

* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}

[[Category:12edo]]

[[Category:Macrotonal]]

@@ 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 = 19ed3
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-06-30 15:05:35 UTC</tt>.<br>
+| de = Bernhard Stopper
-: The original revision id was <tt>554760793</tt>.<br>
+}}
-: The revision comment was: <tt></tt><br>
+{{Infobox ET}}
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+{{ED intro}} It is also known as '''Stopper tuning'''.
-<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">=Division of 3/1 into 19 equal parts=
-= =
-[[http://www.piano-stopper.de/html/onlypure_tuning.html|Bernhard Stopper's OnlyPure tuning]]
-Note: 19 equal divisions of the tritave is not a xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo|12-tone scale]]. Or if you insist that it is, it is the tritave twin of godzilla temperament (with a generator of 400.4 cents)</pre></div>
+== Theory ==
-<h4>Original HTML content:</h4>
+edt is not a truly [[xenharmonic]] tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal [[12edo|12-tone scale]]. Although it is really just the normal 12edo framed in a pure-3 tuning, it can still be used as a temperament with no twos like other tritave-equivalent tunings, although limited in [[accuracy]], with [[5/3]] approximated as 9 steps and [[7/3]] approximated by 15 steps. It completely misses the next tritave-reduced prime harmonic, [[11/9]].
-<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;19ED3&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of 3/1 into 19 equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of 3/1 into 19 equal parts&lt;/h1&gt;
- &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h1&gt;
+This approach can create very non-standard chords and scales such as the approximation of the 5:7:9 chord as 0–600–1000 cents. These could be considered xenharmonic in a sense, since they have little connection to standard 12-tone practice in spite of using the 12-tone interval set. The "default" approach to it is as a "macro-[[godzilla]]" temperament (with a generator of 400.4 cents and a 3:1 ratio {{mos scalesig|5L 4s<3/1>|link=1}} scale, and it is an interesting coincidence how [[17edt]] and 19edt tonality have the same "default" scheme with two tones more or less). Beyond this, it also contains the tritave twin of [[meantone]] temperament (with a generator of 700.7 or 1201.2 cents), producing a basic {{mos scalesig|8L 3s<3/1>|link=1}} scale.
- &lt;a class="wiki_link_ext" href="http://www.piano-stopper.de/html/onlypure_tuning.html" rel="nofollow"&gt;Bernhard Stopper's OnlyPure tuning&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+=== Harmonics ===
-Note: 19 equal divisions of the tritave is not a xenharmonic tuning; it is a slightly stretched version (with an octave of 1201.2 cents) of the normal &lt;a class="wiki_link" href="/12edo"&gt;12-tone scale&lt;/a&gt;. Or if you insist that it is, it is the tritave twin of godzilla temperament (with a generator of 400.4 cents)&lt;/body&gt;&lt;/html&gt;</pre></div>
+{{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer}}
+{{Harmonics in equal|steps=19|num=3|denom=1|intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 19edt (continued)}}
+=== Subsets and supersets ===
+edt is the 8th [[prime equal division|prime edt]], following [[17edt]] and before [[23edt]].
+== Intervals ==
+{{Interval table}}
+== See also ==
+* [[7edf]] – relative edf
+* [[12edo]] – relative edo
+* [[28ed5]] – relative ed5
+* [[31ed6]] – relative ed6
+* [[34ed7]] – relative ed7
+* [[40ed10]] – relative ed10
+* [[43ed12]] – relative ed12
+* [[76ed80]] – close to the zeta-optimized tuning for 12edo
+* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
+== External links ==
+* [[Bernhard Stopper]]'s [https://piano-stopper.de/?page_id=107&lang=en OnlyPure tuning]{{dead link}}
+[[Category:12edo]]
+[[Category:Macrotonal]]