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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>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-20 03:28:02 UTC</tt>.<br>
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| : The original revision id was <tt>602557176</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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"><span style="font-size: 19.5px;">Division of a tenth (e. g. 7/3) into n equal parts</span>
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| | 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. |
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| Division of e. g. the [[7_3|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 (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. 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. |
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| 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 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet.
| | 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}}). |
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| The branches of the Middletown family are named thus:
| | == Chords and harmonies == |
| | [[: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. |
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| 3&6: Tritetrachordal | | 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]]. |
| 4&5: Montrose (between 5/4edo and 4/3edo in particular, MOS generated by [pseudo] octaves belong to this branch) | |
| 2&7: Terra Rubra
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| The family of interlaced octatonic scale based temperaments in the "Middletown valley" is called Vesuvius (i. e. the volcano east of Naples).
| | == 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]] |
| | |} |
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| The temperaments neighboring Middletown proper are named thus:
| | [[Category:Ed7/3's| ]] |
| | | <!-- main article --> |
| 5&6: Rosablanca
| | [[Category:Lists of scales]] |
| 4&7: Saptimpun (10 1/2)
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| 5&7: 8bittone
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| [[8edX]]
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| [[9edX]]
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| [[15edX]]
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| [[16edX]]
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| [[17edX]]
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| [[19edX]]
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| Sort of unsurprisingly, though not so evidently, the golden tuning of edXs will turn out to divide a barely mistuned 5:2 of alomst exactly 45/34edo.</pre></div>
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| <h4>Original HTML content:</h4>
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| <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>edX</title></head><body><span style="font-size: 19.5px;">Division of a tenth (e. g. 7/3) into n equal parts</span><br />
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| <br />
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| Division of e. g. the <a class="wiki_link" href="/7_3">7:3</a> into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> 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 (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the &quot;Middletown valley&quot;, the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [wolf] fourth at most 560 cents wide). Incidentally <a class="wiki_link" href="/Pseudo-traditional%20harmonic%20functions%20of%20enneatonic%20scale%20degrees">enneatonic scales</a>, especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.<br />
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| <br />
| |
| 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 2 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. &quot;Macrobichromatic&quot; might be a practically perfect term for it if it hasn't been named yet.<br />
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| <br />
| |
| The branches of the Middletown family are named thus:<br />
| |
| <br />
| |
| 3&amp;6: Tritetrachordal<br />
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| 4&amp;5: Montrose (between 5/4edo and 4/3edo in particular, MOS generated by [pseudo] octaves belong to this branch)<br />
| |
| 2&amp;7: Terra Rubra<br />
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| <br />
| |
| The family of interlaced octatonic scale based temperaments in the &quot;Middletown valley&quot; is called Vesuvius (i. e. the volcano east of Naples).<br />
| |
| <br />
| |
| The temperaments neighboring Middletown proper are named thus:<br />
| |
| <br />
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| 5&amp;6: Rosablanca<br />
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| 4&amp;7: Saptimpun (10 1/2)<br />
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| 5&amp;7: 8bittone<br />
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| <br />
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| <a class="wiki_link" href="/8edX">8edX</a><br />
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| <a class="wiki_link" href="/9edX">9edX</a><br />
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| <a class="wiki_link" href="/15edX">15edX</a><br />
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| <a class="wiki_link" href="/16edX">16edX</a><br />
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| <a class="wiki_link" href="/17edX">17edX</a><br />
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| <a class="wiki_link" href="/19edX">19edX</a><br />
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| <br />
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| Sort of unsurprisingly, though not so evidently, the golden tuning of edXs will turn out to divide a barely mistuned 5:2 of alomst exactly 45/34edo.</body></html></pre></div>
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Todo: cleanup, explain edonoi
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.
|
The equal division of 7/3 (ed7/3) is a tuning obtained by dividing the septimal minor tenth (7/3) in a certain number of equal steps.
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 false octave, with various degrees of accuracy.
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 dastgah[citation needed]).
Chords and harmonies
Enneatonic scales, especially those equivalent at 7/3, can sensibly take tetrads 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 (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:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone.
Individual pages for ed7/3's
