Maximal harmony epimorphic scales: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 405784046 - Original comment: **
 
ArrowHead294 (talk | contribs)
15,213 edits
m Clean up
 
(19 intermediate revisions by 4 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
If we look at all periodic scales [[Periodic_scale#Epimorphism|epimorphic]] with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of  a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the [[Graph-theoretic_properties_of_scales|graph of the scale]] is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-02-10 05:36:34 UTC</tt>.<br>
: The original revision id was <tt>405784046</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">If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of  a tie, the tie can sometimes be broken by means of larger chords (trias, tetrads etc.) Below we list a few examples.


=5-limit=
= 5-limit =
==Nine notes==
== Five notes ==
[[semilim2]]
 
[[semilim3]]
 
== Six notes, 6b val ==
[[dwarf6_5]]
 
[[cluster6e]]
 
[[x-wing1|x-wing1]]
 
[[x-wing2|x-wing2]]
 
== Seven notes ==
[[zarlino]]
 
[[mavchrome6]]
 
== Eight notes ==
[[semimaj1]]
 
[[semimaj2]]
 
== Nine notes ==
[[mavdie1]]
[[mavdie1]]
[[mavlim1]]
[[mavlim2]]


==Ten notes==
== Ten notes ==
[[blackchrome1]]
[[blackchrome1]]
[[blackchrome2]]</pre></div>
 
<h4>Original HTML content:</h4>
[[blackchrome2]]
<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;Maximal harmony epimorphic scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of  a tie, the tie can sometimes be broken by means of larger chords (trias, tetrads etc.) Below we list a few examples.&lt;br /&gt;
 
&lt;br /&gt;
= 7 odd limit =
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit&lt;/h1&gt;
== Seven notes ==
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x5-limit-Nine notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Nine notes&lt;/h2&gt;
[[maxsev1]]
&lt;a class="wiki_link" href="/mavdie1"&gt;mavdie1&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/mavlim1"&gt;mavlim1&lt;/a&gt;&lt;br /&gt;
[[maxsev2]]
&lt;a class="wiki_link" href="/mavlim2"&gt;mavlim2&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
= Seven limit marvel =
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x5-limit-Ten notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Ten notes&lt;/h2&gt;
== Seven notes ==
&lt;a class="wiki_link" href="/blackchrome1"&gt;blackchrome1&lt;/a&gt;&lt;br /&gt;
[[Gypsy_scale|Gypsy scale]]
&lt;a class="wiki_link" href="/blackchrome2"&gt;blackchrome2&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
= Eleven limit marvel =
== Seven notes ==
[[marvel11max7a]]
 
[[marvel11max7b]]
 
{{Navbox scale gallery}}
 
[[Category:Lists of scales]]

Latest revision as of 20:10, 11 February 2025

If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the graph of the scale is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

5-limit

Five notes

semilim2

semilim3

Six notes, 6b val

dwarf6_5

cluster6e

x-wing1

x-wing2

Seven notes

zarlino

mavchrome6

Eight notes

semimaj1

semimaj2

Nine notes

mavdie1

Ten notes

blackchrome1

blackchrome2

7 odd limit

Seven notes

maxsev1

maxsev2

Seven limit marvel

Seven notes

Gypsy scale

Eleven limit marvel

Seven notes

marvel11max7a

marvel11max7b


View • Talk • EditScale galleries
JI scales 12-tone JI • Combination product set • Constant structure • Harry Partch-related • Maximal harmony epimorphic • MOS transversal • Non-octave JI • Wakalix • Z-polygon transversal • Other JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS • 12-tone tempered • Chromatic pair • Clipper • Double mode • Essentially tempered • Fantasy detemper • Marvel woo • Meantone • Min ambiguity • MOS cradle • Negri-9 • Neutral third • Non-octave tempered • Scalesmith systematic • Ternary • Other tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo • 11 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 33 • 34 • 35 • 36 • 37 • 38 • 40 • 41 • 42 • 43 • 46 • 49 • 53 • 72 • 80
All other scale gallery pages are included in Category:Lists of scales
Retrieved from "https://en.xen.wiki/index.php?title=Maximal_harmony_epimorphic_scales&oldid=180358"