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Ed7/3: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-01 23:07:40 UTC</tt>.<br>
: The original revision id was <tt>601174718</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">&lt;span style="font-size: 19.5px;"&gt;Division of a tenth (e. g. 7/3) into n equal parts&lt;/span&gt;


The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.


Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
== Applications ==
Division of 7/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.  


Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 5, 9, and 14 note MOS. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macroshrutis" might be a practically perfect term for it if it hasn't been named yet.</pre></div>
The structural utility of 7/3 (or another tenth) is apparent by being the absolute widest range most generally used in popular songs{{citation needed}} (and even the range of a {{w|Dastg%C4%81h-e_M%C4%81hur|dastgah}}{{citation needed}}).
<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;edX&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 19.5px;"&gt;Division of a tenth (e. g. 7/3) into n equal parts&lt;/span&gt;&lt;br /&gt;
== Chords and harmonies ==
&lt;br /&gt;
[[:Category:9-tone scales|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave|pseudo (false) octave]], with various degrees of accuracy.
&lt;br /&gt;
 
Division of e. g. the 7:3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of &lt;a class="wiki_link" href="/equivalence"&gt;equivalence&lt;/a&gt; has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs as well as a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.&lt;br /&gt;
Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].
&lt;br /&gt;
 
Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:6:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 5, 9, and 14 note MOS. While the notes are rather farther apart, the scheme is uncannily similar to meantone. &amp;quot;Macroshrutis&amp;quot; might be a practically perfect term for it if it hasn't been named yet.&lt;/body&gt;&lt;/html&gt;</pre></div>
== Individual pages for ed7/3's ==
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
| [[0ed7/3|0]]
| [[1ed7/3|1]]
| [[2ed7/3|2]]
| [[3ed7/3|3]]
| [[4ed7/3|4]]
| [[5ed7/3|5]]
| [[6ed7/3|6]]
| [[7ed7/3|7]]
| [[8ed7/3|8]]
| [[9ed7/3|9]]
|-
| [[10ed7/3|10]]
| [[11ed7/3|11]]
| [[12ed7/3|12]]
| [[13ed7/3|13]]
| [[14ed7/3|14]]
| [[15ed7/3|15]]
| [[16ed7/3|16]]
| [[17ed7/3|17]]
| [[18ed7/3|18]]
| [[19ed7/3|19]]
|-
| [[20ed7/3|20]]
| [[21ed7/3|21]]
| [[22ed7/3|22]]
| [[23ed7/3|23]]
| [[24ed7/3|24]]
| [[25ed7/3|25]]
| [[26ed7/3|26]]
| [[27ed7/3|27]]
| [[28ed7/3|28]]
| [[29ed7/3|29]]
|-
| [[30ed7/3|30]]
| [[31ed7/3|31]]
| [[32ed7/3|32]]
| [[33ed7/3|33]]
| [[34ed7/3|34]]
| [[35ed7/3|35]]
| [[36ed7/3|36]]
| [[37ed7/3|37]]
| [[38ed7/3|38]]
| [[39ed7/3|39]]
|-
| [[40ed7/3|40]]
| [[41ed7/3|41]]
| [[42ed7/3|42]]
| [[43ed7/3|43]]
| [[44ed7/3|44]]
| [[45ed7/3|45]]
| [[46ed7/3|46]]
| [[47ed7/3|47]]
| [[48ed7/3|48]]
| [[49ed7/3|49]]
|-
| [[50ed7/3|50]]
| [[51ed7/3|51]]
| [[52ed7/3|52]]
| [[53ed7/3|53]]
| [[54ed7/3|54]]
| [[55ed7/3|55]]
| [[56ed7/3|56]]
| [[57ed7/3|57]]
| [[58ed7/3|58]]
| [[59ed7/3|59]]
|-
| [[60ed7/3|60]]
| [[61ed7/3|61]]
| [[62ed7/3|62]]
| [[63ed7/3|63]]
| [[64ed7/3|64]]
| [[65ed7/3|65]]
| [[66ed7/3|66]]
| [[67ed7/3|67]]
| [[68ed7/3|68]]
| [[69ed7/3|69]]
|-
| [[70ed7/3|70]]
| [[71ed7/3|71]]
| [[72ed7/3|72]]
| [[73ed7/3|73]]
| [[74ed7/3|74]]
| [[75ed7/3|75]]
| [[76ed7/3|76]]
| [[77ed7/3|77]]
| [[78ed7/3|78]]
| [[79ed7/3|79]]
|-
| [[80ed7/3|80]]
| [[81ed7/3|81]]
| [[82ed7/3|82]]
| [[83ed7/3|83]]
| [[84ed7/3|84]]
| [[85ed7/3|85]]
| [[86ed7/3|86]]
| [[87ed7/3|87]]
| [[88ed7/3|88]]
| [[89ed7/3|89]]
|-
| [[90ed7/3|90]]
| [[91ed7/3|91]]
| [[92ed7/3|92]]
| [[93ed7/3|93]]
| [[94ed7/3|94]]
| [[95ed7/3|95]]
| [[96ed7/3|96]]
| [[97ed7/3|97]]
| [[98ed7/3|98]]
| [[99ed7/3|99]]
|}
 
[[Category:Ed7/3's| ]]
<!-- main article -->
[[Category:Lists of scales]]
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