12edt
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2016-10-21 14:26:52 UTC.
- The original revision id was 596363030.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=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= ! 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]] [[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3|Tritave in 12]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]]
Original HTML content:
<html><head><title>12edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Division of the tritave (3/1) into 12 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->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 /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="A scala formatted description of the tuning"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Exactly analogous to meantone"></a><!-- ws:end:WikiTextHeadingRule:4 -->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 /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->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>