3L 7s
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=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. 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]] 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". (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 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.
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<html><head><title>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x3L+7s "Fair Mosh" (Modi Sephirotorum)"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L+7s "Fair Mosh" (Modi Sephirotorum)</h1> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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). (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 /> <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 /> <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 "mish"</a> in the form of modes of ssLsLsL "led".<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 /> 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>