Amity family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
=Amity=
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-26 18:43:13 UTC</tt>.<br>
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. [[99edo|99edo]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.
: The original revision id was <tt>339770078</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">[[toc|flat]]
 
=Amity=  
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. [[99edo]] is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.


In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.
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Map: [&lt;1 3 6|, &lt;0 -5 -13|]
Map: [&lt;1 3 6|, &lt;0 -5 -13|]
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
Badness: 0.0220
Badness: 0.0220


==7-limit==  
==7-limit==
Commas: 4375/4374, 5120/5103
Commas: 4375/4374, 5120/5103


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Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]
Map: [&lt;1 3 6 -2|, &lt;0 -5 -13 17|]
Wedgie: &lt;&lt;5 13 -17 9 -41 -76||
Wedgie: &lt;&lt;5 13 -17 9 -41 -76||
EDOs: 7, 39, 46, 53, 99, 251, 350
EDOs: 7, 39, 46, 53, 99, 251, 350
Badness: 0.0236
Badness: 0.0236


==11-limit==  
==11-limit==
Commas: 540/539, 4375/4374, 5120/5103
Commas: 540/539, 4375/4374, 5120/5103


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Map: [&lt;1 3 6 -2 21|, &lt;0 -5 -13 17 -62|]
Map: [&lt;1 3 6 -2 21|, &lt;0 -5 -13 17 -62|]
EDOs: 53, 99e, 152, 555de, 707de, 859bde
EDOs: 53, 99e, 152, 555de, 707de, 859bde
Badness: 0.0315
Badness: 0.0315


==Hitchcock==  
==Hitchcock==
Commas: 121/120, 176/175, 2200/2187
Commas: 121/120, 176/175, 2200/2187


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Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]
Map: [&lt;1 3 6 -2 6|, &lt;0 -5 -13 17 -9|]
EDOs: 7, 39, 46, 53, 99
EDOs: 7, 39, 46, 53, 99
Badness: 0.0352
Badness: 0.0352


==Hemiamity==  
==Hemiamity==
Commas: 4375/4374, 5120/5103, 3025/3024
Commas: 4375/4374, 5120/5103, 3025/3024


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Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]
Map: [&lt;2 1 -1 13 13|, &lt;0 5 13 -17 -14|]
EDOs: 14, 46, 106, 152, 350
EDOs: 14, 46, 106, 152, 350


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Map: [&lt;2 1 -1 3|, &lt;0 5 13 6|]
Map: [&lt;2 1 -1 3|, &lt;0 5 13 6|]
Wedgie: &lt;&lt;10 26 12 18 -9 -45||
Wedgie: &lt;&lt;10 26 12 18 -9 -45||
EDOs: 46, 60, 106d
EDOs: 46, 60, 106d
Badness: 0.0836
Badness: 0.0836


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Map: [&lt;2 1 -1 3 3|, &lt;0 5 13 6 9|]
Map: [&lt;2 1 -1 3 3|, &lt;0 5 13 6 9|]
EDOs: 14c, 46, 60e, 106de
EDOs: 14c, 46, 60e, 106de
Badness: 0.0355
Badness: 0.0355


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Map: [&lt;2 1 -1 3 3 0|, &lt;0 5 13 6 9 17|]
Map: [&lt;2 1 -1 3 3 0|, &lt;0 5 13 6 9 17|]
EDOs: 46, 106def, 152def
EDOs: 46, 106def, 152def
Badness: 0.0309
Badness: 0.0309


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Map: [&lt;1 8 19 15|, &lt;0 -10 -26 -19|]
Map: [&lt;1 8 19 15|, &lt;0 -10 -26 -19|]
Wedgie: &lt;&lt;10 26 19 18 2 -29||
Wedgie: &lt;&lt;10 26 19 18 2 -29||
EDOs: 14c, 39d, 53
EDOs: 14c, 39d, 53
Badness: 0.0740
Badness: 0.0740


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Map: [&lt;1 8 19 15 15|, &lt;0 -10 -26 -19 -18|]
Map: [&lt;1 8 19 15 15|, &lt;0 -10 -26 -19 -18|]
EDOs: 14c, 39d, 53
EDOs: 14c, 39d, 53
Badness: 0.0429
Badness: 0.0429


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Map: [&lt;1 8 19 15 15 30|, &lt;0 -10 -26 -19 -18 -41|]
Map: [&lt;1 8 19 15 15 30|, &lt;0 -10 -26 -19 -18 -41|]
EDOs: 53
EDOs: 53
Badness: 0.0298
Badness: 0.0298
</pre></div>
<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;Amity family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:22:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;a href="#Amity"&gt;Amity&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Bamity"&gt;Bamity&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Hamity"&gt;Hamity&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;
&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Amity&lt;/h1&gt;
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;amp;53 temperament, or by its wedgie, &amp;lt;&amp;lt;5 13 -17 9 -41 -76||. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.&lt;br /&gt;
&lt;br /&gt;
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.&lt;br /&gt;
&lt;br /&gt;
Comma: 1600000/1594323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.519&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6|, &amp;lt;0 -5 -13|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873&lt;br /&gt;
Badness: 0.0220&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
Commas: 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.432&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2|, &amp;lt;0 -5 -13 17|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 13 -17 9 -41 -76||&lt;br /&gt;
EDOs: 7, 39, 46, 53, 99, 251, 350&lt;br /&gt;
Badness: 0.0236&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/200 = 339.464&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 21|, &amp;lt;0 -5 -13 17 -62|]&lt;br /&gt;
EDOs: 53, 99e, 152, 555de, 707de, 859bde&lt;br /&gt;
Badness: 0.0315&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hitchcock&lt;/h2&gt;
Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 339.340&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 6 -2 6|, &amp;lt;0 -5 -13 17 -9|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 99&lt;br /&gt;
Badness: 0.0352&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemiamity&lt;/h2&gt;
Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~ 243/200 = 339.493&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 -1 13 13|, &amp;lt;0 5 13 -17 -14|]&lt;br /&gt;
EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Bamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Bamity&lt;/h1&gt;
Commas: 245/243, 64827/64000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/6 = 260.402&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 -1 3|, &amp;lt;0 5 13 6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 26 12 18 -9 -45||&lt;br /&gt;
EDOs: 46, 60, 106d&lt;br /&gt;
Badness: 0.0836&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Bamity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
Commas: 121/120, 245/243, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/6 = 260.393&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 -1 3 3|, &amp;lt;0 5 13 6 9|]&lt;br /&gt;
EDOs: 14c, 46, 60e, 106de&lt;br /&gt;
Badness: 0.0355&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Bamity-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
Commas: 91/90, 121/120, 245/243, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/6 = 260.618&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 -1 3 3 0|, &amp;lt;0 5 13 6 9 17|]&lt;br /&gt;
EDOs: 46, 106def, 152def&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Hamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Hamity&lt;/h1&gt;
Commas: 2430/2401, 4000/3969 &lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 430.219&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 8 19 15|, &amp;lt;0 -10 -26 -19|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 26 19 18 2 -29||&lt;br /&gt;
EDOs: 14c, 39d, 53&lt;br /&gt;
Badness: 0.0740&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hamity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
Commas: 99/98, 121/120, 4000/3969&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 430.192&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 8 19 15 15|, &amp;lt;0 -10 -26 -19 -18|]&lt;br /&gt;
EDOs: 14c, 39d, 53&lt;br /&gt;
Badness: 0.0429&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Hamity-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
Commas: 99/98, 121/120, 275/273, 572/567&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 430.216&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 8 19 15 15 30|, &amp;lt;0 -10 -26 -19 -18 -41|]&lt;br /&gt;
EDOs: 53&lt;br /&gt;
Badness: 0.0298&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Amity

The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. 99edo is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.

In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.

Comma: 1600000/1594323

POTE generator: ~243/200 = 339.519

Map: [<1 3 6|, <0 -5 -13|]

EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873

Badness: 0.0220

7-limit

Commas: 4375/4374, 5120/5103

POTE generator: ~243/200 = 339.432

Map: [<1 3 6 -2|, <0 -5 -13 17|]

Wedgie: <<5 13 -17 9 -41 -76||

EDOs: 7, 39, 46, 53, 99, 251, 350

Badness: 0.0236

11-limit

Commas: 540/539, 4375/4374, 5120/5103

POTE generator: ~243/200 = 339.464

Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]

EDOs: 53, 99e, 152, 555de, 707de, 859bde

Badness: 0.0315

Hitchcock

Commas: 121/120, 176/175, 2200/2187

POTE generator: ~11/9 = 339.340

Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]

EDOs: 7, 39, 46, 53, 99

Badness: 0.0352

Hemiamity

Commas: 4375/4374, 5120/5103, 3025/3024

POTE generator: ~ 243/200 = 339.493

Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]

EDOs: 14, 46, 106, 152, 350

Bamity

Commas: 245/243, 64827/64000

POTE generator: ~7/6 = 260.402

Map: [<2 1 -1 3|, <0 5 13 6|]

Wedgie: <<10 26 12 18 -9 -45||

EDOs: 46, 60, 106d

Badness: 0.0836

11-limit

Commas: 121/120, 245/243, 441/440

POTE generator: ~7/6 = 260.393

Map: [<2 1 -1 3 3|, <0 5 13 6 9|]

EDOs: 14c, 46, 60e, 106de

Badness: 0.0355

13-limit

Commas: 91/90, 121/120, 245/243, 441/440

POTE generator: ~7/6 = 260.618

Map: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|]

EDOs: 46, 106def, 152def

Badness: 0.0309

Hamity

Commas: 2430/2401, 4000/3969

POTE generator: ~9/7 = 430.219

Map: [<1 8 19 15|, <0 -10 -26 -19|]

Wedgie: <<10 26 19 18 2 -29||

EDOs: 14c, 39d, 53

Badness: 0.0740

11-limit

Commas: 99/98, 121/120, 4000/3969

POTE generator: ~9/7 = 430.192

Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]

EDOs: 14c, 39d, 53

Badness: 0.0429

13-limit

Commas: 99/98, 121/120, 275/273, 572/567

POTE generator: ~9/7 = 430.216

Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]

EDOs: 53

Badness: 0.0298

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