17edo neutral scale: Difference between revisions

<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">=17edo neutral scale=  

We can call the [[MOSScales|Moment of Symmetry]] scale derived from a 5/17 generator &amp; an octave repeat the **17edo Neutral Scale**. We build it by stacking neutral thirds, the generator of the [[maqamic|maqamic temperament]]. In 17edo that means the interval of five degrees of 17.

We have arrived again at a MOS scale, of type 3L+4s ("mosh" according to the [[MOSNamingScheme]]).

==7-note neutral scale:==  

===modes of 7-note neutral scale===  

|| mode 3 : fish || from bottom || in between ||

|| degrees || 0 2 5 7 10 12 14 (0) || 2 3 2 3 2 2 3 ||

|| cents || 0 141 353 494 706 847 988 (1200) || 141 212 141 212 141 141 212 ||

|| interval classes || P1 N2 N3 P4 P5 N6 m7 (P8) || N2 M2 N2 M2 N2 N2 M2 ||

|| solfege || do ru mu fa sol lu te (do) || ru re ru re ru ru re ||

|| mode 4 : gil || from bottom || in between ||

|| degrees || 0 3 5 8 10 12 15 (0) || 3 2 3 2 2 3 2 ||

|| cents || 0 212 353 565 706 847 1059 (1200) || 212 131 212 141 141 212 141 ||

|| interval classes || P1 M2 N3 A4 P5 N6 N7 (P8) || M2 N2 M2 N2 N2 M2 N2 ||

|| solfege || do re mu fu sol lu tu (do) || re ru re ru ru re ru ||

|| mode 5 : jwl || from bottom || in between ||

|| degrees || 0 2 5 7 9 12 14 (0) || 2 3 2 2 3 2 3 ||

|| cents || 0 141 353 494 635 847 988 (1200) || 141 212 141 141 212 141 212 ||

|| interval classes || P1 N2 N3 P4 d5 N6 m7 (P8) || N2 M2 N2 N2 M2 N2 M2 ||

|| solfege || do ru mu fa su lu te (do) || ru re ru ru re ru re ||

|| mode 6 : kleeth || from bottom || in between ||

|| degrees || 0 3 5 7 10 12 15 (0) || 3 2 2 3 2 3 2 ||

|| cents || 0 212 353 494 706 847 1059 (1200) || 212 141 141 212 141 212 141 ||

|| interval classes || P1 M2 N3 P4 P5 N6 N7 (P8) || M2 N2 N2 M2 N2 M2 N2 ||

|| solfege || do re mu fa sol lu tu (do) || re ru ru re ru re ru ||

|| mode 7 : led || from bottom || in between ||

|| degrees || 0 2 4 7 9 12 14 (0) || 2 2 3 2 3 2 3 ||

|| cents || 0 141 282 494 635 847 988 (1200) || 141 141 212 141 212 141 212 ||

|| interval classes || P1 N2 m3 P4 d5 N6 m7 (P8) || N2 N2 M2 N2 M2 N2 M2 ||

|| solfege || do ru me fa su lu te (do) || ru ru re ru re ru re ||

17-tonists may find these scales helpful for escaping the familiar. Just because you //can// play diatonic music in 17edo, doesn't mean you have to. These neutral scales give you a more xenharmonic modal system to play with.

==Some brief note on the 3, 7 and 10 note MOS.==  

(Note that you will come up with similarly structured scales by using //other neutral thirds// as generators, although some of them will sound quite different. A neutral sixth about sharp of the 13th harmonic leads to 7L+3s like in 17-tone, whereas going flat of the 13th harmonic can lead to 7s+3L. (This boast is possible because 10-edo sits right on it.) Some equal divisions of the octave containing neutral scales: [[10edo]], [[13edo]], [[16edo]], [[19edo]], [[24edo]], [[31edo]]....)</pre></div>

<h4>Original HTML content:</h4>

<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;17edo neutral scale&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="x17edo neutral scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;17edo neutral scale&lt;/h1&gt;

Add a note a neutral third (five degrees) up from 0:&lt;br /&gt;

Add a note a neutral third down from 0 (remember, in 17edo, 0=17):&lt;br /&gt;

Add an N3 up from 5:&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x17edo neutral scale-7-note neutral scale:-modes of 7-note neutral scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;modes of 7-note neutral scale&lt;/h3&gt;

Naturally, with seven notes we have seven modes, depending on which note we make the starting pitch (tonic) of the scale. I have given these modes a one-syllable name for my own use. Feel free to name (or not name) these modes as you see fit:&lt;br /&gt;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

        &lt;td&gt;mode 7 : led&lt;br /&gt;

 

As you can see, these modes contain many neutral 2nds &amp;amp; 3rds, making it sound very different from the traditional major-minor Western harmonic &amp;amp; melodic system, while having a coherent structure including ample 4ths &amp;amp; 5ths that help ground the scale. The 17edo neutral sixths, at 847 cents, come very close to the 13th harmonic - JI interval 13/8 - 841 cents. Thus, their inversions, the 17edo neutral thirds come very close to 16/13.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x17edo neutral scale-Some brief note on the 3, 7 and 10 note MOS."&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Some brief note on the 3, 7 and 10 note MOS.&lt;/h2&gt;

You might also find that the 10-note scale can be formed by two 17-tone pythagoresque pentatonic scales a neutral interval apart, implying something of a different approach. And one of the loveliest things I find about them is the ease with which one can play 8:11:13 chords, so there are some frightening blues licks in this decatonic scale. R'lyeh blues anyone?&lt;br /&gt;