41edo modes
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[[toc]] This page lists some useful and/or interesting modes (subsets) of [[41edo]] . =MOS= (maximally even scales indicated by *) **generator = 1\41** [3] [4] [5] etc. [40*] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 **g=2 ([[hemimiracle]])** [3] [4] [5] etc. [20*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 [21*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 **g=3 ([[octacot]])** [3] [4] [5] etc. [13] 3 3 3 3 3 3 3 3 3 3 3 3 5 [14*] 3 3 3 3 3 3 3 3 3 3 3 3 3 2 [27*] 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 **g=4 ([[miracle]])** [3] [4] [5] etc. [10*] 4 4 4 4 4 4 4 4 4 5 [11] 4 4 4 4 4 4 4 4 4 4 1 [21] 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 [31*] 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1 **g=5 ([[bohpier]])** [8*] 5 5 5 5 5 5 5 6 [9] 5 5 5 5 5 5 5 5 1 [17] 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 1 [25] 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1 [33*] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 note: the non-octave [[Bohlen-Pierce]] scale is simply 5 5 5 5 5 5 5 5 5 5 5 5 5, repeating at [[3_1|3/1]] (65\[[41edo|41]]) **g=6 ([[tetracot]] / [[bunya]] / [[monkey]])** [7*] 6 6 6 6 6 6 5 [13] 1 5 1 5 1 5 1 5 1 5 1 5 5 [20] 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 4 [27] 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 3 [34*] 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 **g=7 ([[baldy]])** [6*] 7 7 7 7 7 6 [11] 1 6 1 6 1 6 1 6 1 6 6 [17] 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 5 [23] 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 4 [29] [35*] **g=8 ([[rodan]] / [[guiron]] / [[slendric]]?)** [5*] 8 8 8 8 9 [6] 8 8 8 8 8 1 [11] 7 1 7 1 7 1 7 1 7 1 1 [16] 6 1 1 6 1 1 6 1 1 6 1 1 6 1 1 1 [21] 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 1 [26] [31] [36*] **g=9 ([[septimin]])** [5] 9 9 9 9 5 [9*] 4 5 4 5 4 5 4 5 5 [14] 4 4 1 4 4 1 4 4 1 4 4 1 4 1 [23] 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 1 [32*] 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1 **g=10 ([[quasitemp]])** [4*] 10 10 10 11 [5] 10 10 10 10 1 [9] 9 1 9 1 9 1 9 1 1 [13] 8 1 1 8 1 1 8 1 1 8 1 1 1 [17] 7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1 [21] [25] [29] etc. **g=11 ([[superkleismic]] / [[orgone]]?)** [7] 3 8 3 8 3 8 8 [11] 3 3 5 3 3 5 3 3 5 3 5 [15*] 3 3 3 2 3 3 3 2 3 3 3 2 3 3 2 [26*] 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 **g=12 ([[hemififths]] / [[karadeniz]] / [[beatles]]?)** [7] 7 5 7 5 7 5 5 [10] 2 5 5 2 5 5 2 5 5 5 [17*] 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3 [24*] 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 **g=13 ([[magic]] / [[witchcraft]])** [7] 11 2 11 2 11 2 2 [10] 9 2 2 9 2 2 9 2 2 2 [13] 7 2 2 2 7 2 2 2 7 2 2 2 2 [16] 5 2 2 2 2 5 2 2 2 2 5 2 2 2 2 2 [19*] 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 [22*] 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 **g=14 ([[hocus]])** [3*] 14 14 13 [5] 1 13 1 13 13 [8] 1 1 12 1 1 12 1 12 [11] 1 1 1 11 1 1 1 11 1 1 11 [14] 1 1 1 1 10 1 1 1 1 10 1 1 1 10 [17] 1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9 [20] [23] [26] [29] etc. **g=15 ([[stacks]]?)** [5] 4 11 4 11 11 [8] 4 4 7 4 4 7 4 7 [11*] 4 4 4 3 4 4 4 3 4 4 3 [19] 1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 3 [30*] 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 **g=16 ([[barbad]])** [5] 7 9 7 9 9 [8] 7 7 2 7 7 2 7 2 [13] 5 2 5 2 2 5 2 5 2 2 5 2 2 [18*] 3 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2 [23*] 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 **g=17 ([[schismic]] / [[schismatic]] / [[helmholtz]] / [[garibaldi]] / [[cassandra]])** [5] 10 7 10 7 7 [7] 3 7 7 3 7 7 7 [12*] 3 3 4 3 4 3 3 4 3 4 3 4 [17] 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1 [29*] 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 **g=18 ([[trismegistus]])** [5] 13 5 13 5 5 [7] 8 5 5 8 5 5 5 [9] 3 5 5 5 3 5 5 5 5 [16*] 3 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2 [25*] 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2 **g=19 ([[kangaroo]]? / [[thuja]]?)** [5] 16 3 16 3 3 [7] 13 3 3 13 3 3 3 [9] 10 3 3 3 10 3 3 3 3 [11] 7 3 3 3 3 7 3 3 3 3 3 [13*] 4 3 3 3 3 3 4 3 3 3 3 3 3 [15] 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 [28*] 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 **g=20 ([[pluto]])** [5] 19 1 19 1 1 [7] 18 1 1 18 1 1 1 [9] 17 1 1 1 17 1 1 1 1 [11] [13] [15] [17] etc. g=21 <--> g=20 g=22 <--> g=19 etc. =Non-MOS= ==Harmonic series approximations== [5] 11 9 8 7 6 harmonic series 5:6:7:8:9:10 [6] 9 8 7 6 6 5 harmonic series 6::12 [7] 8 7 6 6 5 5 4 harmonic series 7::14 [8] 7 6 6 5 5 4 4 4 harmonic series 8::16 [12] 5 4 4 4 4 3 3 3 3 3 2 3 harmonic series 12::24 (reverse these for subharmonic scales) ==Others== from Scala: [7] 7 6 4 7 6 7 4 "just" major [7] 7 4 6 7 4 7 6 "just" minor [7] 7 4 6 7 4 6 7 natural minor [7] 7 4 6 7 6 7 4 melodic minor [7] 7 4 6 7 4 9 4 harmonic minor [7] 7 6 4 7 4 9 4 harmonic major [12] 4 3 4 2 4 3 4 4 2 4 3 4 "just" chromatic ... =Partial scales= ==Tetrachords== (from Scala) 1 1 15 (0-1-2-17) Wilson 1 2 14 (0-1-3-17) Wilson 1 6 10 (0-1-7-17) Wilson 1 7 9 (0-1-8-17) Barbour Chromatic 2 2 13 (0-2-4-17) Ptolemy 2 5 10 (0-2-7-17) Archytas' Chromatic 2 7 8 (0-2-9-17) Septimal Kürdi 2 8 7 (0-2-10-17) Archytas' Diatonic, Ptolemy's Diatonon Toniaion 3 4 10 (0-3-7-17) Pythagorean Chromatic, Gaudentius 3 4 10 (0-3-7-17) Boethius Chromatic 3 4 10 (0-3-7-17) Perrett Chromatic 3 5 9 (0-3-8-17) Ptolemy 3 5 9 (0-3-8-17) Hipkins 3 6 8 (0-3-9-17) Ptolemy's Diatonon Malakon, Soft Diatonic 3 7 7 (0-3-10-17) Kürdi 3 7 7 (0-3-10-17) Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion 3 11 3 (0-3-14-17) Xenakis 4 4 9 (0-4-8-17) Avicenna 4 5 8 (0-4-9-17) Avicenna 4 6 10 (0-4-10-20) Araban 4 7 6 (0-4-11-17) Iraq, Segâh 4 9 4 (0-4-13-17) Sedaraban, Hicaz 4 9 4 (0-4-13-17) Palmer 4 10 3 (0-4-14-17) Evicârâ 5 5 7 (0-5-10-17) Ushshaq 5 5 7 (0-5-10-17) Young exquisite 3/4 tone Hellenic lyre 5 7 5 (0-5-12-17) Dudon Mohajira 5 7 5 (0-5-12-17) Mojahira, Iraq 7 2 7 (0-7-9-16) Nahawand 7 3 7 (0-7-10-17) Buselik 7 3 7 (0-7-10-17) Busalik, Nihâvend 7 4 6 (0-7-11-17) Müstear 7 4 9 (0-7-11-20) Neveser 7 5 5 (0-7-12-17) Rast 7 5 5 (0-7-12-17) Rast, Nagdi, Neutral Diatonic, Islamic Diatonic 7 5 5 (0-7-12-17) Modern Rast, Avicenna 7 6 4 (0-7-13-17) Turkish Rast 7 7 3 (0-7-14-17) Mahur 7 7 3 (0-7-14-17) Çargâh 8 7 2 (0-8-15-17) Septimal 'Ajam ==Pentachords== (from Scala) 3 7 7 7 (0-3-10-17-24) Kürdi 4 4 9 7 (0-4-8-17-24) Iranian 4 6 4 7 (0-4-10-14-21) Hicaz 4 7 6 7 (0-4-11-17-24) Segâh 5 5 7 7 (0-5-10-17-24) Huseyni 7 2 7 8 (0-7-9-16-24) Busalik 7 3 7 7 (0-7-10-17-24) Buselik 7 3 7 7 (0-7-10-17-24) Busalik 7 4 6 7 (0-7-11-17-24) Müstear 7 4 9 4 (0-7-11-20-24) Nikriz 7 5 5 7 (0-7-12-17-24) Rast 7 6 4 7 (0-7-13-17-24) Turkish Rast 7 7 3 7 (0-7-14-17-24) Çargâh 7 7 6 4 (0-7-14-20-24) Pencgâh
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<html><head><title>41edo modes</title></head><body><!-- ws:start:WikiTextTocRule:14:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#MOS">MOS</a></div> <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#Non-MOS">Non-MOS</a></div> <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#Non-MOS-Harmonic series approximations">Harmonic series approximations</a></div> <!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 2em;"><a href="#Non-MOS-Others">Others</a></div> <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 1em;"><a href="#Partial scales">Partial scales</a></div> <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 2em;"><a href="#Partial scales-Tetrachords">Tetrachords</a></div> <!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 2em;"><a href="#Partial scales-Pentachords">Pentachords</a></div> <!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --></div> <!-- ws:end:WikiTextTocRule:22 -->This page lists some useful and/or interesting modes (subsets) of <a class="wiki_link" href="/41edo">41edo</a> .<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="MOS"></a><!-- ws:end:WikiTextHeadingRule:0 -->MOS</h1> (maximally even scales indicated by *)<br /> <br /> <strong>generator = 1\41</strong><br /> [3] [4] [5] etc.<br /> [40*] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 <br /> <br /> <strong>g=2 (<a class="wiki_link" href="/hemimiracle">hemimiracle</a>)</strong><br /> [3] [4] [5] etc.<br /> [20*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 <br /> [21*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 <br /> <br /> <strong>g=3 (<a class="wiki_link" href="/octacot">octacot</a>)</strong><br /> [3] [4] [5] etc.<br /> [13] 3 3 3 3 3 3 3 3 3 3 3 3 5 <br /> [14*] 3 3 3 3 3 3 3 3 3 3 3 3 3 2<br /> [27*] 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 <br /> <br /> <strong>g=4 (<a class="wiki_link" href="/miracle">miracle</a>)</strong><br /> [3] [4] [5] etc.<br /> [10*] 4 4 4 4 4 4 4 4 4 5<br /> [11] 4 4 4 4 4 4 4 4 4 4 1 <br /> [21] 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 <br /> [31*] 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1 <br /> <br /> <strong>g=5 (<a class="wiki_link" href="/bohpier">bohpier</a>)</strong><br /> [8*] 5 5 5 5 5 5 5 6 <br /> [9] 5 5 5 5 5 5 5 5 1 <br /> [17] 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 1 <br /> [25] 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1 <br /> [33*] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 <br /> note: the non-octave <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale is simply 5 5 5 5 5 5 5 5 5 5 5 5 5, repeating at <a class="wiki_link" href="/3_1">3/1</a> (65\<a class="wiki_link" href="/41edo">41</a>)<br /> <br /> <strong>g=6 (<a class="wiki_link" href="/tetracot">tetracot</a> / <a class="wiki_link" href="/bunya">bunya</a> / <a class="wiki_link" href="/monkey">monkey</a>)</strong><br /> [7*] 6 6 6 6 6 6 5 <br /> [13] 1 5 1 5 1 5 1 5 1 5 1 5 5<br /> [20] 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 4 <br /> [27] 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 3 <br /> [34*] 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 <br /> <br /> <strong>g=7 (<a class="wiki_link" href="/baldy">baldy</a>)</strong><br /> [6*] 7 7 7 7 7 6 <br /> [11] 1 6 1 6 1 6 1 6 1 6 6 <br /> [17] 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 5 <br /> [23] 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 4 <br /> [29] [35*]<br /> <br /> <strong>g=8 (<a class="wiki_link" href="/rodan">rodan</a> / <a class="wiki_link" href="/guiron">guiron</a> / <a class="wiki_link" href="/slendric">slendric</a>?)</strong><br /> [5*] 8 8 8 8 9 <br /> [6] 8 8 8 8 8 1 <br /> [11] 7 1 7 1 7 1 7 1 7 1 1 <br /> [16] 6 1 1 6 1 1 6 1 1 6 1 1 6 1 1 1 <br /> [21] 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 1 <br /> [26] [31] [36*]<br /> <br /> <strong>g=9 (<a class="wiki_link" href="/septimin">septimin</a>)</strong><br /> [5] 9 9 9 9 5 <br /> [9*] 4 5 4 5 4 5 4 5 5 <br /> [14] 4 4 1 4 4 1 4 4 1 4 4 1 4 1<br /> [23] 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 1 <br /> [32*] 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1 <br /> <br /> <strong>g=10 (<a class="wiki_link" href="/quasitemp">quasitemp</a>)</strong><br /> [4*] 10 10 10 11 <br /> [5] 10 10 10 10 1 <br /> [9] 9 1 9 1 9 1 9 1 1 <br /> [13] 8 1 1 8 1 1 8 1 1 8 1 1 1 <br /> [17] 7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1 <br /> [21] [25] [29] etc.<br /> <br /> <strong>g=11 (<a class="wiki_link" href="/superkleismic">superkleismic</a> / <a class="wiki_link" href="/orgone">orgone</a>?)</strong><br /> [7] 3 8 3 8 3 8 8 <br /> [11] 3 3 5 3 3 5 3 3 5 3 5 <br /> [15*] 3 3 3 2 3 3 3 2 3 3 3 2 3 3 2 <br /> [26*] 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 <br /> <br /> <strong>g=12 (<a class="wiki_link" href="/hemififths">hemififths</a> / <a class="wiki_link" href="/karadeniz">karadeniz</a> / <a class="wiki_link" href="/beatles">beatles</a>?)</strong><br /> [7] 7 5 7 5 7 5 5 <br /> [10] 2 5 5 2 5 5 2 5 5 5 <br /> [17*] 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3 <br /> [24*] 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 <br /> <br /> <strong>g=13 (<a class="wiki_link" href="/magic">magic</a> / <a class="wiki_link" href="/witchcraft">witchcraft</a>)</strong><br /> [7] 11 2 11 2 11 2 2 <br /> [10] 9 2 2 9 2 2 9 2 2 2 <br /> [13] 7 2 2 2 7 2 2 2 7 2 2 2 2<br /> [16] 5 2 2 2 2 5 2 2 2 2 5 2 2 2 2 2 <br /> [19*] 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 <br /> [22*] 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 <br /> <br /> <strong>g=14 (<a class="wiki_link" href="/hocus">hocus</a>)</strong><br /> [3*] 14 14 13 <br /> [5] 1 13 1 13 13 <br /> [8] 1 1 12 1 1 12 1 12 <br /> [11] 1 1 1 11 1 1 1 11 1 1 11 <br /> [14] 1 1 1 1 10 1 1 1 1 10 1 1 1 10 <br /> [17] 1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9 <br /> [20] [23] [26] [29] etc.<br /> <br /> <strong>g=15 (<a class="wiki_link" href="/stacks">stacks</a>?)</strong><br /> [5] 4 11 4 11 11 <br /> [8] 4 4 7 4 4 7 4 7 <br /> [11*] 4 4 4 3 4 4 4 3 4 4 3 <br /> [19] 1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 3 <br /> [30*] 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 <br /> <br /> <strong>g=16 (<a class="wiki_link" href="/barbad">barbad</a>)</strong><br /> [5] 7 9 7 9 9 <br /> [8] 7 7 2 7 7 2 7 2 <br /> [13] 5 2 5 2 2 5 2 5 2 2 5 2 2 <br /> [18*] 3 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2 <br /> [23*] 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 <br /> <br /> <strong>g=17 (<a class="wiki_link" href="/schismic">schismic</a> / <a class="wiki_link" href="/schismatic">schismatic</a> / <a class="wiki_link" href="/helmholtz">helmholtz</a> / <a class="wiki_link" href="/garibaldi">garibaldi</a> / <a class="wiki_link" href="/cassandra">cassandra</a>)</strong><br /> [5] 10 7 10 7 7 <br /> [7] 3 7 7 3 7 7 7 <br /> [12*] 3 3 4 3 4 3 3 4 3 4 3 4 <br /> [17] 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1 <br /> [29*] 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 <br /> <br /> <strong>g=18 (<a class="wiki_link" href="/trismegistus">trismegistus</a>)</strong><br /> [5] 13 5 13 5 5 <br /> [7] 8 5 5 8 5 5 5 <br /> [9] 3 5 5 5 3 5 5 5 5 <br /> [16*] 3 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2 <br /> [25*] 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2 <br /> <br /> <strong>g=19 (<a class="wiki_link" href="/kangaroo">kangaroo</a>? / <a class="wiki_link" href="/thuja">thuja</a>?)</strong><br /> [5] 16 3 16 3 3 <br /> [7] 13 3 3 13 3 3 3 <br /> [9] 10 3 3 3 10 3 3 3 3 <br /> [11] 7 3 3 3 3 7 3 3 3 3 3 <br /> [13*] 4 3 3 3 3 3 4 3 3 3 3 3 3 <br /> [15] 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 <br /> [28*] 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 <br /> <br /> <strong>g=20 (<a class="wiki_link" href="/pluto">pluto</a>)</strong><br /> [5] 19 1 19 1 1 <br /> [7] 18 1 1 18 1 1 1 <br /> [9] 17 1 1 1 17 1 1 1 1 <br /> [11] [13] [15] [17] etc.<br /> <br /> g=21 <--> g=20<br /> g=22 <--> g=19<br /> etc.<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Non-MOS"></a><!-- ws:end:WikiTextHeadingRule:2 -->Non-MOS</h1> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Non-MOS-Harmonic series approximations"></a><!-- ws:end:WikiTextHeadingRule:4 -->Harmonic series approximations</h2> [5] 11 9 8 7 6 harmonic series 5:6:7:8:9:10<br /> [6] 9 8 7 6 6 5 harmonic series 6::12<br /> [7] 8 7 6 6 5 5 4 harmonic series 7::14<br /> [8] 7 6 6 5 5 4 4 4 harmonic series 8::16<br /> [12] 5 4 4 4 4 3 3 3 3 3 2 3 harmonic series 12::24<br /> (reverse these for subharmonic scales)<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Non-MOS-Others"></a><!-- ws:end:WikiTextHeadingRule:6 -->Others</h2> from Scala:<br /> [7] 7 6 4 7 6 7 4 "just" major<br /> [7] 7 4 6 7 4 7 6 "just" minor<br /> [7] 7 4 6 7 4 6 7 natural minor<br /> [7] 7 4 6 7 6 7 4 melodic minor<br /> [7] 7 4 6 7 4 9 4 harmonic minor<br /> [7] 7 6 4 7 4 9 4 harmonic major<br /> [12] 4 3 4 2 4 3 4 4 2 4 3 4 "just" chromatic<br /> <br /> ...<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Partial scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->Partial scales</h1> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Partial scales-Tetrachords"></a><!-- ws:end:WikiTextHeadingRule:10 -->Tetrachords</h2> (from Scala)<br /> 1 1 15 (0-1-2-17) Wilson <br /> 1 2 14 (0-1-3-17) Wilson <br /> 1 6 10 (0-1-7-17) Wilson <br /> 1 7 9 (0-1-8-17) Barbour Chromatic <br /> 2 2 13 (0-2-4-17) Ptolemy <br /> 2 5 10 (0-2-7-17) Archytas' Chromatic <br /> 2 7 8 (0-2-9-17) Septimal Kürdi <br /> 2 8 7 (0-2-10-17) Archytas' Diatonic, Ptolemy's Diatonon Toniaion <br /> 3 4 10 (0-3-7-17) Pythagorean Chromatic, Gaudentius <br /> 3 4 10 (0-3-7-17) Boethius Chromatic <br /> 3 4 10 (0-3-7-17) Perrett Chromatic <br /> 3 5 9 (0-3-8-17) Ptolemy <br /> 3 5 9 (0-3-8-17) Hipkins <br /> 3 6 8 (0-3-9-17) Ptolemy's Diatonon Malakon, Soft Diatonic <br /> 3 7 7 (0-3-10-17) Kürdi <br /> 3 7 7 (0-3-10-17) Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion<br /> 3 11 3 (0-3-14-17) Xenakis <br /> 4 4 9 (0-4-8-17) Avicenna <br /> 4 5 8 (0-4-9-17) Avicenna <br /> 4 6 10 (0-4-10-20) Araban <br /> 4 7 6 (0-4-11-17) Iraq, Segâh <br /> 4 9 4 (0-4-13-17) Sedaraban, Hicaz <br /> 4 9 4 (0-4-13-17) Palmer <br /> 4 10 3 (0-4-14-17) Evicârâ <br /> 5 5 7 (0-5-10-17) Ushshaq <br /> 5 5 7 (0-5-10-17) Young exquisite 3/4 tone Hellenic lyre <br /> 5 7 5 (0-5-12-17) Dudon Mohajira <br /> 5 7 5 (0-5-12-17) Mojahira, Iraq <br /> 7 2 7 (0-7-9-16) Nahawand <br /> 7 3 7 (0-7-10-17) Buselik <br /> 7 3 7 (0-7-10-17) Busalik, Nihâvend <br /> 7 4 6 (0-7-11-17) Müstear <br /> 7 4 9 (0-7-11-20) Neveser <br /> 7 5 5 (0-7-12-17) Rast <br /> 7 5 5 (0-7-12-17) Rast, Nagdi, Neutral Diatonic, Islamic Diatonic <br /> 7 5 5 (0-7-12-17) Modern Rast, Avicenna <br /> 7 6 4 (0-7-13-17) Turkish Rast <br /> 7 7 3 (0-7-14-17) Mahur <br /> 7 7 3 (0-7-14-17) Çargâh <br /> 8 7 2 (0-8-15-17) Septimal 'Ajam <br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Partial scales-Pentachords"></a><!-- ws:end:WikiTextHeadingRule:12 -->Pentachords</h2> (from Scala)<br /> 3 7 7 7 (0-3-10-17-24) Kürdi <br /> 4 4 9 7 (0-4-8-17-24) Iranian <br /> 4 6 4 7 (0-4-10-14-21) Hicaz <br /> 4 7 6 7 (0-4-11-17-24) Segâh <br /> 5 5 7 7 (0-5-10-17-24) Huseyni <br /> 7 2 7 8 (0-7-9-16-24) Busalik <br /> 7 3 7 7 (0-7-10-17-24) Buselik <br /> 7 3 7 7 (0-7-10-17-24) Busalik <br /> 7 4 6 7 (0-7-11-17-24) Müstear <br /> 7 4 9 4 (0-7-11-20-24) Nikriz <br /> 7 5 5 7 (0-7-12-17-24) Rast <br /> 7 6 4 7 (0-7-13-17-24) Turkish Rast<br /> 7 7 3 7 (0-7-14-17-24) Çargâh <br /> 7 7 6 4 (0-7-14-20-24) Pencgâh</body></html>