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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox MOS |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = sephiroid |
| : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-07-19 23:19:59 UTC</tt>.<br>
| | | Periods = 1 |
| : The original revision id was <tt>242046277</tt>.<br>
| | | nLargeSteps = 3 |
| : The revision comment was: <tt></tt><br>
| | | nSmallSteps = 7 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | Equalized = 3 |
| <h4>Original Wikitext content:</h4>
| | | Collapsed = 1 |
| <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">=3L+7s "Fair Mosh" "Modi Sephirotorum"=
| | | Pattern = LssLssLsss |
| | }} |
| | {{MOS intro}} |
| | == Name == |
| | [[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.'' |
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| This MOS can, presumably among other things, represent tempered chains of the 13th harmonic. The region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward, together a stable harmony. If L=s, which are multiples of 10edo, the 13th harmonic becomes nearly perfect, 121 edo being the first to accurately represent the comma (which might as well be represented accurately as it's quite small). Towards the end where the large and small steps are more distinct, well, I'm not sure what it would represent harmonically but somebody out there might like the sound of such scales.
| | == Scale properties == |
| I have named the modes of this EDO according to the Sephiroth, hence "Modi Sephirotorum". There are probably improper forms, but I haven't explored them yet.
| | {{TAMNAMS use}} |
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| s s s L s s L s s L - Mode Keter
| | === Intervals === |
| s s L s s L s s L s - Chesed
| | {{MOS intervals}} |
| s L s s L s s L s s - Netzach
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| L s s L s s L s s s - Malkuth
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| s s L s s L s s s L - Binah
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| s L s s L s s s L s - Tiferet
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| L s s L s s s L s s - Yesod
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| s s L s s s L s s L - Chokmah
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| s L s s s L s s L s - Gevurah
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| L s s s L s s L s s - Hod
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| L=1 s=1 10edo
| | === Generator chain === |
| L=2 s=1 13edo
| | {{MOS genchain}} |
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| (L=3 s=1 16edo)
| | === Modes === |
| L=3 s=2 23edo
| | {{MOS mode degrees}} |
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| (L=4 s=1 19edo)
| | === Proposed Names === |
| L=4 s=3 33edo
| | Mode names are described by Kosmorsky, which use names from the [[wikipedia:Sefirot|Sefirot]] (or sephiroth). Kosmorsky describes the mode Keter to be akin to the lydian mode of 5L 2s, and the mode Malkuth like the locrian mode. |
| | {{MOS modes |
| | | Mode Names= |
| | Malkuth $ |
| | Yesod $ |
| | Hod $ |
| | Netzach $ |
| | Tiferet $ |
| | Gevurah $ |
| | Chesed $ |
| | Binah $ |
| | Chokmah $ |
| | Keter $ |
| | }} |
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| (L=5 s=1 22edo)
| | == Theory == |
| (L=5 s=2 29edo)
| | === The ''modi sephiratorum'' === |
| L=5 s=3 36edo
| | This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). |
| L=5 s=4 43edo
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| L=6 s=5 53edo
| | With sephiroid scales with a soft-of-basic step ratio (around {nowrap|L:s {{=}} 3:2}}, or 23edo), the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum. |
| (L=6 s=1 25edo) | |
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| L=7 s=6 63edo | | Scales approaching an equalized step ratio ({{nowrap|L:s {{=}} 1:1}}, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio ({{nowrap|L:s {{=}} 1:0}}, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others. |
| L=7 s=5 56edo
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| L=7 s=4 49edo
| | Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10){{Clarify}} 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. |
| etc.</pre></div>
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| <h4>Original HTML content:</h4>
| | There are MODMOS as well, but Kosmorsky has not explored them yet, as "there's enough undiscovered harmonic resources 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". |
| <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>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L+7s &quot;Fair Mosh&quot; &quot;Modi Sephirotorum&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L+7s &quot;Fair Mosh&quot; &quot;Modi Sephirotorum&quot;</h1>
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| <br />
| | == Scale tree == |
| This MOS can, presumably among other things, represent tempered chains of the 13th harmonic. The region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward, together a stable harmony. If L=s, which are multiples of 10edo, the 13th harmonic becomes nearly perfect, 121 edo being the first to accurately represent the comma (which might as well be represented accurately as it's quite small). Towards the end where the large and small steps are more distinct, well, I'm not sure what it would represent harmonically but somebody out there might like the sound of such scales.<br />
| | {{MOS tuning spectrum |
| I have named the modes of this EDO according to the Sephiroth, hence &quot;Modi Sephirotorum&quot;. There are probably improper forms, but I haven't explored them yet.<br />
| | | 6/5 = [[Submajor (temperament)|Submajor]] |
| <br />
| | | 13/8 = Unnamed golden tuning |
| s s s L s s L s s L - Mode Keter<br />
| | | 5/2 = [[Sephiroth]] |
| s s L s s L s s L s - Chesed<br />
| | | 13/5 = Golden sephiroth |
| s L s s L s s L s s - Netzach<br />
| | | 11/3 = [[Muggles]] |
| L s s L s s L s s s - Malkuth<br />
| | | 4/1 = [[Magic]] / horcrux |
| s s L s s L s s s L - Binah<br />
| | | 9/2 = Magic / witchcraft / necromancy |
| s L s s L s s s L s - Tiferet<br />
| | | 5/1 = Magic / telepathy |
| L s s L s s s L s s - Yesod<br />
| | | 6/1 = [[Würschmidt]] ↓ |
| s s L s s s L s s L - Chokmah<br />
| | }} |
| s L s s s L s s L s - Gevurah<br />
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| L s s s L s s L s s - Hod<br />
| | == External links == |
| <br />
| | * [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky |
| L=1 s=1 10edo<br />
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| L=2 s=1 13edo<br />
| | [[Category:10-tone scales]] |
| <br />
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| (L=3 s=1 16edo)<br />
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| L=3 s=2 23edo<br />
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| <br />
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| (L=4 s=1 19edo)<br />
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| L=4 s=3 33edo<br />
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| <br />
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| (L=5 s=1 22edo)<br />
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| (L=5 s=2 29edo)<br />
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| L=5 s=3 36edo<br />
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| L=5 s=4 43edo<br />
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| <br />
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| L=6 s=5 53edo<br />
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| (L=6 s=1 25edo)<br />
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| <br />
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| L=7 s=6 63edo<br />
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| L=7 s=5 56edo<br />
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| L=7 s=4 49edo<br />
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| etc.</body></html></pre></div>
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