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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The '''equal division of 5/3''' ('''ed5/3''') is a [[tuning]] obtained by dividing the [[5/3|just major sixth (5/3)]] into a number of [[equal]] steps. |
| 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-02 10:16:00 UTC</tt>.<br>
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| : The original revision id was <tt>601220128</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 sixth (e. g. 5/3 or 11/7) into n equal parts</span>
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| | == Properties == |
| | Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. |
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| Division of e. g. the 5:3 or the 11:7 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 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based [[Sensi|sensi]] temperament. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.
| | 5/3 is the most consonant interval in between 1/1 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature. |
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| Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(11) 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 four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.</pre></div>
| | [[Joseph Ruhf]] suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s|armotonic]]. |
| <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>edVI</title></head><body><span style="font-size: 19.5px;">Division of a sixth (e. g. 5/3 or 11/7) into n equal parts</span><br />
| | If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach. |
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| | ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: [[7ed5/3]] (7.30 cent error), [[9ed5/3]] (6.73 cent error), and [[16ed5/3]] (0.59 cent error). |
| Division of e. g. the 5:3 or the 11:7 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 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based <a class="wiki_link" href="/Sensi">sensi</a> temperament. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.<br />
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| | [[7ed5/3]], [[9ed5/3]], and [[16ed5/3]] are to the [[Ed5/3|division of 5/3]] what [[5edo]], [[7edo]], and [[12edo]] are to the [[EDO|division of 2/1]]. |
| Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(11) 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 four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. &quot;Microdiatonic&quot; might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.</body></html></pre></div>
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| | == Individual pages for ed5/3's == |
| | {| class="wikitable center-all" |
| | |+ style=white-space:nowrap | 0…49 |
| | | [[0ed5/3|0]] |
| | | [[1ed5/3|1]] |
| | | [[2ed5/3|2]] |
| | | [[3ed5/3|3]] |
| | | [[4ed5/3|4]] |
| | | [[5ed5/3|5]] |
| | | [[6ed5/3|6]] |
| | | [[7ed5/3|7]] |
| | | [[8ed5/3|8]] |
| | | [[9ed5/3|9]] |
| | |- |
| | | [[10ed5/3|10]] |
| | | [[11ed5/3|11]] |
| | | [[12ed5/3|12]] |
| | | [[13ed5/3|13]] |
| | | [[14ed5/3|14]] |
| | | [[15ed5/3|15]] |
| | | [[16ed5/3|16]] |
| | | [[17ed5/3|17]] |
| | | [[18ed5/3|18]] |
| | | [[19ed5/3|19]] |
| | |- |
| | | [[20ed5/3|20]] |
| | | [[21ed5/3|21]] |
| | | [[22ed5/3|22]] |
| | | [[23ed5/3|23]] |
| | | [[24ed5/3|24]] |
| | | [[25ed5/3|25]] |
| | | [[26ed5/3|26]] |
| | | [[27ed5/3|27]] |
| | | [[28ed5/3|28]] |
| | | [[29ed5/3|29]] |
| | |- |
| | | [[30ed5/3|30]] |
| | | [[31ed5/3|31]] |
| | | [[32ed5/3|32]] |
| | | [[33ed5/3|33]] |
| | | [[34ed5/3|34]] |
| | | [[35ed5/3|35]] |
| | | [[36ed5/3|36]] |
| | | [[37ed5/3|37]] |
| | | [[38ed5/3|38]] |
| | | [[39ed5/3|39]] |
| | |- |
| | | [[40ed5/3|40]] |
| | | [[41ed5/3|41]] |
| | | [[42ed5/3|42]] |
| | | [[43ed5/3|43]] |
| | | [[44ed5/3|44]] |
| | | [[45ed5/3|45]] |
| | | [[46ed5/3|46]] |
| | | [[47ed5/3|47]] |
| | | [[48ed5/3|48]] |
| | | [[49ed5/3|49]] |
| | |} |
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| | [[Category:Ed5/3's| ]] |
| | <!-- main article --> |
| | [[Category:Edonoi]] |
| | [[Category:Lists of scales]] |
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| | {{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 5/3 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.}} |