Ed5/3: Difference between revisions

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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>~~

~~: This revision was~~ by ~~author~~ [[~~User:JosephRuhf~~|~~JosephRuhf~~]] ~~and made on <tt>2016-11-30 13:17:49 UTC<~~/~~tt>~~.~~<br>~~

== Properties ==

~~: The original revision id was <tt>601033080<~~/~~tt>~~.~~<br>~~

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.

~~: 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>~~

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.

~~<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~~"~~><span style=~~"~~font~~-~~size~~: 19.~~5px;">Division~~ of a ~~sixth~~ (e. g. 11/~~7 or 5~~/3~~) into n equal parts<~~/~~span><~~/~~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>~~

~~<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. 11~~/~~7 or 5~~/3~~) into n equal parts<~~/~~span><~~/~~body><~~/~~html>~~<~~/pre~~></~~div>~~

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.

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).

[[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]].

== 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]]

|}

[[Category:Ed5/3's| ]]

[[Category:Edonoi]]

[[Category:Lists of scales]]

{{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.}}

@@ Line 1: / Line 1: @@
-<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>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-30 13:17:49 UTC</tt>.<br>
+== Properties ==
-: The original revision id was <tt>601033080</tt>.<br>
+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.
-: 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>
+/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.
-<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 sixth (e. g. 11/7 or 5/3) into n equal parts&lt;/span&gt;</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>
-<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;edVI&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 19.5px;"&gt;Division of a sixth (e. g. 11/7 or 5/3) into n equal parts&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+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.
+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).
+[[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]].
+== 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]]
+|}
+[[Category:Ed5/3's| ]]
+<!-- main article -->
+[[Category:Edonoi]]
+[[Category:Lists of scales]]
+{{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.}}