Xenharmonic Wiki

12edt: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>xenwolf
**Imported revision 239486187 - Original comment: **
Dummy index (talk | contribs)
autopatrolled, emailconfirmed
606 edits
→Theory: fix link
 
(28 intermediate revisions by 17 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-30 09:07:12 UTC</tt>.<br>
 
: The original revision id was <tt>239486187</tt>.<br>
12edt corresponds to 7.571&nbsp;edo, and can be used as a generator chain for [[Kleismic_family#Hemikleismic|hemikleismic temperament]]. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.  
: 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>
== Prime harmonics ==
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|12|3|1|intervals=prime}}
<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 the tritave (3/1) into 12 equal parts=  
 
==Compositions==  
== Theory ==
[[http://www.seraph.it/XenoTunes3.html|Instant Gamelan]] by [[Carlo Serafini]]</pre></div>
In octave land, 12edo handles the 2.3.5 subgroup and [[11edo]] handles the 2.7.11 subgroup—ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen–Pierce) and 12edt handles the 2.3.5.13.17.19—and, it is a multiple of 4edt which is the simplest BP equal temperament.
<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;12edt&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 the tritave (3/1) into 12 equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of the tritave (3/1) into 12 equal parts&lt;/h1&gt;
=== Macrodiatonic and macromeantone ===
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Division of the tritave (3/1) into 12 equal parts-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Compositions&lt;/h2&gt;
12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic]] {{mos scalesig|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).
&lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow"&gt;Instant Gamelan&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.
 
== Interval table ==
{{Interval table}}
 
== Scala file ==
<pre>
! C:\Cakewalk\scales\tritave-in-12.scl
!
3/1 in 12
12
!
158.49625
316.99250
475.48875
633.98500
792.48125
950.97750
1109.47375
1267.97000
1426.46625
1584.96250
1743.45875
3/1
</pre>
 
== Compositions ==
[https://archive.org/details/InstantGamelan Instant Gamelan] by [[Carlo_Serafini|Carlo Serafini]]
 
[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3 Tritave in 12] by [http://www.chrisvaisvil.com Chris Vaisvil]     
[[Category:listen]]
[[category:macrotonal]]
Retrieved from "https://en.xen.wiki/w/12edt"