Xenharmonic Wiki

3L 7s: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>Kosmorsky
**Imported revision 268473548 - Original comment: **
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(67 intermediate revisions by 17 users not shown)
Line 1: Line 1:
<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>2011-10-25 15:20:28 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>268473548</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
= =  
}}
Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic). (13 edo tempers 5/4 ~ 16/13.) This MOS can also represent tempered-flat 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, which together are a stable harmony. Furthermore and curiously, 13, 21, and 34 are Fibonacci numbers. If L=s, which are 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 end where the large and small steps are more distinct, well, I'm not sure what else but a flat 13th harmonic it is, but somebody out there might like it; the popular 16-tone is among these.
{{MOS intro}}
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''


Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but descending, reminiscent of ancient Greek practice in that way. 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. See for more details [[http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf]]
== Scale properties ==
{{TAMNAMS use}}


There are probably improper forms, 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".
=== Intervals ===
{{MOS intervals}}


(ascending)
=== Generator chain ===
s s s L s s L s s L - Mode Keter
{{MOS genchain}}
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


L=1 s=1 [[10edo]]
=== Modes ===
L=2 s=1 [[13edo]]
{{MOS mode degrees}}


(L=3 s=1 [[16edo]])
=== Proposed Names ===
L=3 s=2 [[23edo]]
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 $
}}


(L=4 s=1 [[19edo]])
== Theory ==
L=4 s=3 [[33edo]]
=== The ''modi sephiratorum'' ===
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).


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


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


L=7 s=6 [[63edo]]
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.  
L=7 s=5 [[56edo]]
 
L=7 s=4 [[49edo]]
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".
etc.</pre></div>
 
<h4>Original HTML content:</h4>
== Scale tree ==
<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;3L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x3L+7s &amp;quot;Fair Mosh&amp;quot; (Modi Sephirotorum)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;3L+7s &amp;quot;Fair Mosh&amp;quot; (Modi Sephirotorum)&lt;/h1&gt;
{{MOS tuning spectrum
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h1&gt;
| 6/5 = [[Submajor (temperament)|Submajor]]
Fair Mosh is found in &lt;a class="wiki_link" href="/Magic"&gt;magic&lt;/a&gt; (chains of the 5th harmonic). (13 edo tempers 5/4 ~ 16/13.) This MOS can also represent tempered-flat 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, which together are a stable harmony. Furthermore and curiously, 13, 21, and 34 are Fibonacci numbers. If L=s, which are 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 end where the large and small steps are more distinct, well, I'm not sure what else but a flat 13th harmonic it is, but somebody out there might like it; the popular 16-tone is among these.&lt;br /&gt;
| 13/8 = Unnamed golden tuning
&lt;br /&gt;
| 5/2 = [[Sephiroth]]
Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical - not ascending but descending, reminiscent of ancient Greek practice in that way. 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. See for more details &lt;a class="wiki_link_ext" href="http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf" rel="nofollow"&gt;http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf&lt;/a&gt;&lt;br /&gt;
| 13/5 = Golden sephiroth
&lt;br /&gt;
| 11/3 = [[Muggles]]
There are probably improper forms, 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 &lt;a class="wiki_link" href="/3L%204s"&gt;4s+3L &amp;quot;mish&amp;quot;&lt;/a&gt; in the form of modes of ssLsLsL &amp;quot;led&amp;quot;.&lt;br /&gt;
| 4/1 = [[Magic]] / horcrux
&lt;br /&gt;
| 9/2 = Magic / witchcraft / necromancy
(ascending)&lt;br /&gt;
| 5/1 = Magic / telepathy
s s s L s s L s s L - Mode Keter&lt;br /&gt;
| 6/1 = [[Würschmidt]] ↓
s s L s s L s s L s - Chesed&lt;br /&gt;
}}
s L s s L s s L s s - Netzach&lt;br /&gt;
 
L s s L s s L s s s - Malkuth&lt;br /&gt;
== External links ==
s s L s s L s s s L - Binah&lt;br /&gt;
* [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky
s L s s L s s s L s - Tiferet&lt;br /&gt;
 
L s s L s s s L s s - Yesod&lt;br /&gt;
[[Category:10-tone scales]]
s s L s s s L s s L - Chokmah&lt;br /&gt;
s L s s s L s s L s - Gevurah&lt;br /&gt;
L s s s L s s L s s - Hod&lt;br /&gt;
&lt;br /&gt;
L=1 s=1 &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;&lt;br /&gt;
L=2 s=1 &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
(L=3 s=1 &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;)&lt;br /&gt;
L=3 s=2 &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
(L=4 s=1 &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;)&lt;br /&gt;
L=4 s=3 &lt;a class="wiki_link" href="/33edo"&gt;33edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
(L=5 s=1 &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;)&lt;br /&gt;
(L=5 s=2 &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;)&lt;br /&gt;
L=5 s=3 &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;&lt;br /&gt;
L=5 s=4 &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
(L=6 s=1 &lt;a class="wiki_link" href="/25edo"&gt;25edo)&lt;/a&gt;&lt;br /&gt;
L=6 s=5 &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
L=7 s=6 &lt;a class="wiki_link" href="/63edo"&gt;63edo&lt;/a&gt;&lt;br /&gt;
L=7 s=5 &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;&lt;br /&gt;
L=7 s=4 &lt;a class="wiki_link" href="/49edo"&gt;49edo&lt;/a&gt;&lt;br /&gt;
etc.&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/3L_7s"