12edt: Difference between revisions

Line 1:

~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

=Division of the tritave (3/1) into 12 equal parts=

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 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.

~~: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 14:26:52 UTC</tt>.<br>~~

~~: The original revision id was <tt>596363030</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>~~

~~<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 the tritave (3/1) into 12 equal parts=

12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 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.

=A scala formatted description of the tuning=

~~=A scala formatted description of the tuning=~~

! C:\Cakewalk\scales\tritave-in-12.scl

~~! 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

=Exactly analogous to meantone=

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. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.

Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

=Compositions=

[http://www.seraph.it/XenoTunes3.html Instant Gamelan] [http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3 play] 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:edonoi]]

~~=Compositions=~~

[[Category:edt]]

~~[[http://www.seraph.it/XenoTunes3.html|Instant Gamelan]] [[http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3|play]] by [[Carlo Serafini]]~~

[[Category:equal]]

[[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3|Tritave in 12]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]]~~</pre></div>~~

[[Category:listen]]

~~<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>12edt</title></head><body><h1 id="toc0"><a name="Division of the tritave (3/1) into 12 equal ~~parts"></a>Division of the tritave (3/1) into 12 equal parts</h1>~~

12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for <a class="wiki_link" href="/Kleismic%20family#Hemikleismic">hemikleismic temperament</a>. 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.<br />

~~<br />~~

<h1 id="toc1"><a name="A scala formatted description of the tuning"></a>A scala formatted description of the tuning</h1>

~~<br />~~

~~! C:\Cakewalk\scales\tritave-in-12.scl<br />~~

~~!<br />~~

~~3/1 in 12<br />~~

~~12<br />~~

~~!<br />~~

~~158.49625<br />~~

~~316.99250<br />~~

~~475.48875<br />~~

~~633.98500<br />~~

~~792.48125<br />~~

~~950.97750<br />~~

~~1109.47375<br />~~

~~1267.97000<br />~~

~~1426.46625<br />~~

~~1584.96250<br />~~

~~1743.45875<br />~~

~~3/1<br />~~

~~<br />~~

<h1 id="toc2"><a name="Exactly analogous to meantone"></a>Exactly analogous to meantone</h1>

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. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.<br />

~~<br />~~

~~Another example of a macrodiatonic scale is <a class="wiki_link" href="/17ed5">hyperpyth</a> which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.<br />~~

~~<br />~~

~~<h1 id="toc3"><a name="Compositions"></a>Compositions</h1>~~

<a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow">Instant Gamelan</a> <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br />

<a class="wiki_link_ext" href="http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3" rel="nofollow">Tritave in 12</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a></body></html></pre></div>

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+=Division of the tritave (3/1) into 12 equal parts=
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 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.
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 14:26:52 UTC</tt>.<br>
-: The original revision id was <tt>596363030</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>
-<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 the tritave (3/1) into 12 equal parts=
-edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 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.
+=A scala formatted description of the tuning=
-=A scala formatted description of the tuning=
+! C:\Cakewalk\scales\tritave-in-12.scl
-! C:\Cakewalk\scales\tritave-in-12.scl
 !
 /1 in 12
 !
 .49625
 .99250
 .48875
 .98500
 .48125
 .97750
 .47375
 .97000
 .46625
 .96250
 .45875
 /1
 =Exactly analogous to meantone=
 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. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.
 Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.
+=Compositions=
+[http://www.seraph.it/XenoTunes3.html Instant Gamelan] [http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3 play] 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:edonoi]]
-=Compositions=
+[[Category:edt]]
-[[http://www.seraph.it/XenoTunes3.html|Instant Gamelan]] [[http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3|play]] by [[Carlo Serafini]]
+[[Category:equal]]
-[[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3|Tritave in 12]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]]</pre></div>
+[[Category:listen]]
-<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;
-edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for &lt;a class="wiki_link" href="/Kleismic%20family#Hemikleismic"&gt;hemikleismic temperament&lt;/a&gt;. 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.&lt;br /&gt;
-&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="A scala formatted description of the tuning"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;A scala formatted description of the tuning&lt;/h1&gt;
- &lt;br /&gt;
-! C:\Cakewalk\scales\tritave-in-12.scl&lt;br /&gt;
-!&lt;br /&gt;
-/1 in 12&lt;br /&gt;
-&lt;br /&gt;
-!&lt;br /&gt;
-.49625&lt;br /&gt;
-.99250&lt;br /&gt;
-.48875&lt;br /&gt;
-.98500&lt;br /&gt;
-.48125&lt;br /&gt;
-.97750&lt;br /&gt;
-.47375&lt;br /&gt;
-.97000&lt;br /&gt;
-.46625&lt;br /&gt;
-.96250&lt;br /&gt;
-.45875&lt;br /&gt;
-/1&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Exactly analogous to meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Exactly analogous to meantone&lt;/h1&gt;
- 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. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.&lt;br /&gt;
-&lt;br /&gt;
-Another example of a macrodiatonic scale is &lt;a class="wiki_link" href="/17ed5"&gt;hyperpyth&lt;/a&gt; which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.&lt;br /&gt;
-&lt;br /&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="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Compositions&lt;/h1&gt;
- &lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow"&gt;Instant Gamelan&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3" rel="nofollow"&gt;Tritave in 12&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>