3L 7s: Difference between revisions

Revision as of 11:20, 7 June 2012

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=3L+7s "Fair Mosh" (Modi Sephirotorum)= 
= = 
Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0).

This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephirotorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.

If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and so on. This ends at s=0 which gives multiples of [[3edo]].

Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details [[http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf]]
(I know it should be "tractatus", changing it is just a bother)

There are MODMOS as well, but I haven't explored them yet. There's enough undiscovered harmonic resource already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: [[3L 4s|4s+3L "mish"]] in the form of modes of ssLsLsL "led".

(ascending)
s s s L s s L s s L - Mode Keter
s s L s s L s s L s - Chesed
s L s s L s s L s s - Netzach
L s s L s s L s s s - Malkuth
s s L s s L s s s L - Binah
s L s s L s s s L s - Tiferet
L s s L s s s L s s - Yesod
s s L s s s L s s L - Chokmah
s L s s s L s s L s - Gevurah
L s s s L s s L s s - Hod

--
|| 3/10 ||   ||   ||   ||   ||   || 360 || 120 || 120 ||   ||
||   ||   ||   ||   ||   || 19/63 || 361.905 || 133.333 || 114.286 ||   ||
||   ||   ||   ||   || 16/53 ||   || 362.264 || 135.849 || 113.208 ||   ||
||   ||   ||   || 13/43 ||   ||   || 362.791 || 139.535 || 111.63 ||   ||
||   ||   || 10/33 ||   ||   ||   || 363.636 || 145.455 || 109.091 ||   ||
||   ||   ||   || 17/56 ||   ||   || 364.286 || 150 || 107.143 ||   ||
||   || 7/23 ||   ||   ||   ||   || 365.217 || 156.522 || 104.348 ||   ||
||   ||   || 11/36 ||   ||   ||   || 366.667 || 166.667 || 100 ||   ||
||   ||   ||   || 15/49 ||   ||   || 367.347 || 171.429 || 97.959 ||   ||
|| 4/13 ||   ||   ||   ||   ||   || 369.231 || 184.615 || 92.308 || Boundary of propriety
(smaller generators are proper) ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   || 9/29 ||   ||   ||   || 372.414 || 206.897 || 82.759 ||   ||
||   ||   ||   || 14/45 ||   ||   || 373.333 || 213.333 || 80 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   || 5/16 ||   ||   ||   ||   || 375 || 225 || 75 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   || 6/19 ||   ||   ||   || 378.947 || 252.632 || 63.158 ||   ||
||   ||   ||   ||   ||   || 19/60 || 380 || 260 || 60 || Magic is in here ||
||   ||   ||   ||   || 13/41 ||   || 380.488 || 263.415 || 58.537 ||   ||
||   ||   ||   ||   ||   || 20/63 || 380.952 || 266.667 || 57.143 ||   ||
||   ||   ||   || 7/22 ||   ||   || 381.818 || 272.727 || 54.545 ||   ||
||   ||   ||   ||   ||   || 15/47 || 382.979 || 331.915 || 51.064 ||   ||
||   ||   ||   ||   || 8/25 ||   || 384 || 336 || 48 ||   ||
||   ||   ||   ||   ||   || 9/28 || 385.714 || 342.857 || 42.857 ||   ||
|| 1/3 ||   ||   ||   ||   ||   || 400 || 400 || 0 ||   ||

L=1 s=1 [[10edo]]
L=2 s=1 [[13edo]]

(L=3 s=1 [[16edo]])
L=3 s=2 [[23edo]]

(L=4 s=1 [[19edo]])
L=4 s=3 [[33edo]]

(L=5 s=1 [[22edo]])
(L=5 s=2 [[29edo]])
L=5 s=3 [[36edo]]
L=5 s=4 [[43edo]]

(L=6 s=1 [[25edo|25edo)]]
L=6 s=5 [[53edo]]

L=7 s=6 [[63edo]]
L=7 s=5 [[56edo]]
L=7 s=4 [[49edo]]
etc.

Original HTML content:

<html><head><title>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L+7s &quot;Fair Mosh&quot; (Modi Sephirotorum)"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L+7s &quot;Fair Mosh&quot; (Modi Sephirotorum)</h1>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
 Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0).<br />
<br />
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephirotorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.<br />
<br />
If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall <a class="wiki_link" href="/13edo">13edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, and so on. This ends at s=0 which gives multiples of <a class="wiki_link" href="/3edo">3edo</a>.<br />
<br />
Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details <a class="wiki_link_ext" href="http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf" rel="nofollow">http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf</a><br />
(I know it should be &quot;tractatus&quot;, changing it is just a bother)<br />
<br />
There are MODMOS as well, but I haven't explored them yet. There's enough undiscovered harmonic resource already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: <a class="wiki_link" href="/3L%204s">4s+3L &quot;mish&quot;</a> in the form of modes of ssLsLsL &quot;led&quot;.<br />
<br />
(ascending)<br />
s s s L s s L s s L - Mode Keter<br />
s s L s s L s s L s - Chesed<br />
s L s s L s s L s s - Netzach<br />
L s s L s s L s s s - Malkuth<br />
s s L s s L s s s L - Binah<br />
s L s s L s s s L s - Tiferet<br />
L s s L s s s L s s - Yesod<br />
s s L s s s L s s L - Chokmah<br />
s L s s s L s s L s - Gevurah<br />
L s s s L s s L s s - Hod<br />
<br />
--<br />


<table class="wiki_table">
    <tr>
        <td>3/10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>360<br />
</td>
        <td>120<br />
</td>
        <td>120<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19/63<br />
</td>
        <td>361.905<br />
</td>
        <td>133.333<br />
</td>
        <td>114.286<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>16/53<br />
</td>
        <td><br />
</td>
        <td>362.264<br />
</td>
        <td>135.849<br />
</td>
        <td>113.208<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13/43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>362.791<br />
</td>
        <td>139.535<br />
</td>
        <td>111.63<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>10/33<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>363.636<br />
</td>
        <td>145.455<br />
</td>
        <td>109.091<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17/56<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>364.286<br />
</td>
        <td>150<br />
</td>
        <td>107.143<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>7/23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>365.217<br />
</td>
        <td>156.522<br />
</td>
        <td>104.348<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>11/36<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>366.667<br />
</td>
        <td>166.667<br />
</td>
        <td>100<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>15/49<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>367.347<br />
</td>
        <td>171.429<br />
</td>
        <td>97.959<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4/13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>369.231<br />
</td>
        <td>184.615<br />
</td>
        <td>92.308<br />
</td>
        <td>Boundary of propriety<br />
(smaller generators are proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>372.414<br />
</td>
        <td>206.897<br />
</td>
        <td>82.759<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14/45<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>373.333<br />
</td>
        <td>213.333<br />
</td>
        <td>80<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>375<br />
</td>
        <td>225<br />
</td>
        <td>75<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>6/19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>378.947<br />
</td>
        <td>252.632<br />
</td>
        <td>63.158<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19/60<br />
</td>
        <td>380<br />
</td>
        <td>260<br />
</td>
        <td>60<br />
</td>
        <td>Magic is in here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13/41<br />
</td>
        <td><br />
</td>
        <td>380.488<br />
</td>
        <td>263.415<br />
</td>
        <td>58.537<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>20/63<br />
</td>
        <td>380.952<br />
</td>
        <td>266.667<br />
</td>
        <td>57.143<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7/22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>381.818<br />
</td>
        <td>272.727<br />
</td>
        <td>54.545<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>15/47<br />
</td>
        <td>382.979<br />
</td>
        <td>331.915<br />
</td>
        <td>51.064<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8/25<br />
</td>
        <td><br />
</td>
        <td>384<br />
</td>
        <td>336<br />
</td>
        <td>48<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/28<br />
</td>
        <td>385.714<br />
</td>
        <td>342.857<br />
</td>
        <td>42.857<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1/3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400<br />
</td>
        <td>400<br />
</td>
        <td>0<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
L=1 s=1 <a class="wiki_link" href="/10edo">10edo</a><br />
L=2 s=1 <a class="wiki_link" href="/13edo">13edo</a><br />
<br />
(L=3 s=1 <a class="wiki_link" href="/16edo">16edo</a>)<br />
L=3 s=2 <a class="wiki_link" href="/23edo">23edo</a><br />
<br />
(L=4 s=1 <a class="wiki_link" href="/19edo">19edo</a>)<br />
L=4 s=3 <a class="wiki_link" href="/33edo">33edo</a><br />
<br />
(L=5 s=1 <a class="wiki_link" href="/22edo">22edo</a>)<br />
(L=5 s=2 <a class="wiki_link" href="/29edo">29edo</a>)<br />
L=5 s=3 <a class="wiki_link" href="/36edo">36edo</a><br />
L=5 s=4 <a class="wiki_link" href="/43edo">43edo</a><br />
<br />
(L=6 s=1 <a class="wiki_link" href="/25edo">25edo)</a><br />
L=6 s=5 <a class="wiki_link" href="/53edo">53edo</a><br />
<br />
L=7 s=6 <a class="wiki_link" href="/63edo">63edo</a><br />
L=7 s=5 <a class="wiki_link" href="/56edo">56edo</a><br />
L=7 s=4 <a class="wiki_link" href="/49edo">49edo</a><br />
etc.</body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-06-07 11:14:14 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-07 11:20:33 UTC</tt>.<br>
-: The original revision id was <tt>343547626</tt>.<br>
+: The original revision id was <tt>343549570</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>
@@ Line 51: / Line 51: @@
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 ||   || 5/16 ||   ||   ||   ||   || 375 || 225 || 75 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
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@@ Line 57: / Line 58: @@
 ||   ||   ||   ||   ||   || 19/60 || 380 || 260 || 60 || Magic is in here ||
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-||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 20/63 || 380.952 || 266.667 || 57.143 ||   ||
 ||   ||   ||   || 7/22 ||   ||   || 381.818 || 272.727 || 54.545 ||   ||
-||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 15/47 || 382.979 || 331.915 || 51.064 ||   ||
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 ||   ||   ||   ||   ||   || 9/28 || 385.714 || 342.857 || 42.857 ||   ||
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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+        &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
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+         &lt;td&gt;15/47&lt;br /&gt;
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+         &lt;td&gt;382.979&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;

3L 7s: Difference between revisions

Revision as of 11:20, 7 June 2012

IMPORTED REVISION FROM WIKISPACES

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