3L 7s: Difference between revisions

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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:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-~~25 15~~:20:28 UTC</tt>.<br>

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-22 16:47:38 UTC</tt>.<br>

: The original revision id was <tt>~~268473548~~</tt>.<br>

: The original revision id was <tt>288214562</tt>.<br>

: The revision comment was: <tt></tt><br>

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<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)=

= =

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.

Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic).

~~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]]~~

This MOS can also 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.

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".

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)

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Line 30:

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]]

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<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><h1 id="toc0"><a name="x3L+7s &quot;Fair Mosh&quot; (Modi Sephirotorum)"></a>3L+7s &quot;Fair Mosh&quot; (Modi Sephirotorum)</h1>

<h1 id="toc1"> </h1>

Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (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~~.<br />

Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (chains of the 5th harmonic). <br />

<br />

This MOS can also 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 />

~~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~~ <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 />

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 />

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 <a class="wiki_link" href="/3L%204s">4s+3L &quot;mish&quot;</a> in the form of modes of ssLsLsL &quot;led&quot;.<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 />

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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 />

<br />

L=1 s=1 <a class="wiki_link" href="/10edo">10edo</a><br />

@@ Line 1: / Line 1: @@
 <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:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 15:20:28 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-22 16:47:38 UTC</tt>.<br>
-: The original revision id was <tt>268473548</tt>.<br>
+: The original revision id was <tt>288214562</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 8: / Line 8: @@
 <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)=
 = =
-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.
+Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic).
-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]]
+This MOS can also 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.
-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".
+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)
@@ Line 25: / Line 30: @@
 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]]
@@ Line 50: / Line 57: @@
 <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;
   &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;
-  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;
+  Fair Mosh is found in &lt;a class="wiki_link" href="/Magic"&gt;magic&lt;/a&gt; (chains of the 5th harmonic). &lt;br /&gt;
+&lt;br /&gt;
+This MOS can also 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. &lt;br /&gt;
 &lt;br /&gt;
-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;
+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 &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, and so on. This ends at s=0 which gives multiples of &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-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;
+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 &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;
+(I know it should be &amp;quot;tractatus&amp;quot;, changing it is just a bother)&lt;br /&gt;
+&lt;br /&gt;
+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: &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;
 &lt;br /&gt;
 (ascending)&lt;br /&gt;
@@ Line 67: / Line 79: @@
 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;
+--&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;