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31edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-07-20 02:08:50 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 18:00:59 UTC</tt>.<br>
: The original revision id was <tt>615770067</tt>.<br>
: The original revision id was <tt>621460415</tt>.<br>
: The revision comment was: <tt></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>
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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Cb ||= B#
Cb ||= B#
Cv ||= C ||
Cv ||= C ||
All 31edo chords can be named using ups and downs:
0-7-18 = C Ebv G = C.vm = "C downminor"
0-8-18 = C Eb G = Cm = "C minor"
0-9-18 = C Ev G = C~ = "C mid"
0-10-18 = C E G = "C major" or "C"
0-11-18 = C E^ G = C.^= "C upmajor" or "C dot up"
0-12-18 = C Fv G = C(v4) = "C down-four"
etc.


Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
||~ quality ||~ color ||~ monzo format ||~ examples ||
||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
||= minor ||= fourthward white ||= {a, b}, b &lt; -1 ||= 16/9, 32/27 ||
||= " ||= green ||= {a, b, -1} ||= 6/5, 9/5 ||
||= mid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
||= " ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 16/11 ||
||= major ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 ||
||= " ||= fifthward white ||= {a, b}, b &gt; 1 ||= 9/8, 27/16 ||
||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
All 31edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
||= blue ||= 6:7:9 ||= 0-7-18 ||= C Ebv G ||= C.vm ||= C downminor ||
||= green ||= 10:12:15 ||= 0-8-18 ||= C Eb G ||= Cm ||= C minor ||
||= jade ||= 18:22:27 ||= 0-9-18 ||= C Ev G ||= C~ ||= C mid ||
||= yellow ||= 4:5:6 ||= 0-10-18 ||= C E G ||= C ||= C major or C ||
||= red ||= 14:18:27 ||= 0-11-18 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].


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&lt;/table&gt;
&lt;/table&gt;


All 31edo chords can be named using ups and downs:&lt;br /&gt;
0-7-18 = C Ebv G = C.vm = &amp;quot;C downminor&amp;quot;&lt;br /&gt;
0-8-18 = C Eb G = Cm = &amp;quot;C minor&amp;quot;&lt;br /&gt;
0-9-18 = C Ev G = C~ = &amp;quot;C mid&amp;quot;&lt;br /&gt;
0-10-18 = C E G = &amp;quot;C major&amp;quot; or &amp;quot;C&amp;quot;&lt;br /&gt;
0-11-18 = C E^ G = C.^= &amp;quot;C upmajor&amp;quot; or &amp;quot;C dot up&amp;quot;&lt;br /&gt;
0-12-18 = C Fv G = C(v4) = &amp;quot;C down-four&amp;quot;&lt;br /&gt;
etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Combining ups and downs notation with &lt;a class="wiki_link" href="/Kite%27s%20color%20notation"&gt;color notation&lt;/a&gt;, qualities can be loosely associated with colors:&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;quality&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;color&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;monzo format&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;examples&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downminor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/6, 7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fourthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;lt; -1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/9, 32/27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5, 9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;mid&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/9, 11/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;amber&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/11, 16/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;major&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4, 5/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fifthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;gt; 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8, 27/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upmajor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7, 12/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
All 31edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;color of the 3rd&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;JI chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes as edosteps&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes of C chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;written name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;spoken name&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6:7:9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-7-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ebv G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.vm&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downminor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10:12:15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-8-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Eb G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cm&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18:22:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-9-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ev G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C~&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C mid&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4:5:6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-10-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C E G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C major or C&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14:18:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-11-18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C E^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C upmajor or C dot up&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:85:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:85 --&gt;Practical Theory / Books&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:85:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:85 --&gt;Practical Theory / Books&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:8485:&amp;lt;a href=&amp;quot;http://www.ronsword.com/books.html&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/TSG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 116px; width: 87px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/TSG_sm.jpg" alt="external image TSG_sm.jpg" title="external image TSG_sm.jpg" style="height: 116px; width: 87px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8485 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank"&gt;Sword, Ronald. &amp;quot;Tricesimoprimal Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: March 2009.&lt;/a&gt; - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:8663:&amp;lt;a href=&amp;quot;http://www.ronsword.com/books.html&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/TSG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 116px; width: 87px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"&gt;&lt;img src="http://ronsword.com/images/TSG_sm.jpg" alt="external image TSG_sm.jpg" title="external image TSG_sm.jpg" style="height: 116px; width: 87px;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8663 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank"&gt;Sword, Ronald. &amp;quot;Tricesimoprimal Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: March 2009.&lt;/a&gt; - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:87:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Other Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:87 --&gt;Other Articles&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:87:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Other Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:87 --&gt;Other Articles&lt;/h1&gt;
  &lt;ul&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow"&gt;de Beer, Anton, ''The Development of 31-tone Music&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow"&gt;Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Fokker, A.D., &amp;quot;New Music with 31 Notes&amp;quot; translated by Leigh Gerdine&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow"&gt;Rapoport, Paul, ''About 31-tone Equal Temperament&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow"&gt;Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia article&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow"&gt;de Beer, Anton, ''The Development of 31-tone Music&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow"&gt;Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Fokker, A.D., &amp;quot;New Music with 31 Notes&amp;quot; translated by Leigh Gerdine&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow"&gt;Rapoport, Paul, ''About 31-tone Equal Temperament&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow"&gt;Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia article&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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