17edo neutral scale: Difference between revisions

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=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; in 17edo that means the interval of five degrees of 17.

Begin anywhere. Let's call our first pitch (&amp; its octave transposition) 0:

Add a note a neutral third up from 0:

Add a note a neutral third down from 0:

Since we have two different step sizes, we have arrived at a three-note MOS scale. But let's continue; three-note scales don't give us much to work with.

We have arrived again at a MOS scale.

[[#seven-note]]

==7-note neutral scale:==

===modes of 7-note neutral scale===

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:

|| mode || name || degrees from 0 || cents from 0 || intverval classes from P1 || degrees between ||

|| 1 || bish || .0 2 5 7 10 12 15 (0) || .0 141 353 494 706 847 1059 (1200) || .P1 N2 N3 P4 P5 N6 N7 (P8) || .2 3 2 3 2 3 2 ||

|| 3 || fish || .0 2 5 7 10 12 14 (0) || .0 141 353 494 706 847 988 (1200) || .P1 N2 N3 P4 P5 N6 m7 (P8) || .2 3 2 3 2 2 3 ||

|| 4 || gil || .0 3 5 8 10 12 15 (0) || .0 212 353 565 706 847 1059 (1200) || .P1 M2 N3 A4 P5 N6 N7 (P8) || .3 2 3 2 2 3 2 ||

|| 5 || jwl || .0 2 5 7 9 12 14 (0) || .0 141 353 494 635 847 988 (1200) || .P1 N2 N3 P4 d5 N6 m7 (P8) || .2 3 2 2 3 2 3 ||

|| 6 || kleeth || .0 3 5 7 10 12 15 (0) || .0 212 353 494 706 847 1059 (1200) || .P1 M2 N6 P4 P5 N6 N7 (P8) || .3 2 2 3 2 3 2 ||

|| 7 || led || .0 2 4 7 9 12 14 (0) || .0 141 282 494 635 847 988 (1200) || .P1 N2 m3 P4 d5 N6 m7 (P8) || .2 2 3 2 3 2 3 ||

As you can see, these modes contain many neutral 2nds &amp; 3rds, making it sound very different from the traditional major-minor Western harmonic &amp; melodic system, while having a coherent structure including ample 4ths &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.

The 17edo neutral 2nds, at 141 cents, fall between 13/12 (139 cents) &amp; 12/11 (151) cents. I've found that they generally function as 13/12, since they fall 3/2 away from 13/8. But you can discover these things for yourself, if you like, &amp; feel free to think of them in different ways entirely.

Interestingly, the 7-note neutral scale does not allow you to build any minor or major triads whatsoever. You have only one minor 3rd, which occurs with a diminished 5th, but no perfect fifth, allowing you to build a diminished triad, but no minor triad. You have no major thirds at all. In JI-terms, you might say that it contains harmonies based on 2, 3, &amp; 13, while skipping 7 &amp; 11.

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.

If you continue stacking neutral thirds, you will soon come to a rather lovely 10-note neutral scale. I (or someone) will come back to that sooner or later.

(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.  Some equal divisions of the octave containing neutral scales: [[10edo]], [[13edo]], [[16edo]], [[19edo]], [[24edo]], [[31edo]]....)</pre></div>

We can call the &lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt;  scale derived from a 5/17 generator &amp;amp; an octave repeat the 17edo Neutral Scale.  We build it by stacking neutral thirds; in 17edo that means the interval of five degrees of 17.&lt;br /&gt;

0 5 12 (0)&lt;br /&gt;

Since we have two different step sizes, we have arrived at a three-note MOS scale. But let's continue; three-note scales don't give us much to work with.&lt;br /&gt;

0 5 10 12 (0)&lt;br /&gt;

&lt;br /&gt;

0 5 7 10 12 15 (0)&lt;br /&gt;

0 2 5 7 10 12 15 (0)&lt;br /&gt;

&lt;!-- ws:start:WikiTextAnchorRule:6:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@seven-note&amp;quot; title=&amp;quot;Anchor: seven-note&amp;quot;/&amp;gt; --&gt;&lt;a name="seven-note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:6 --&gt;&lt;br /&gt;

degrees between: 2 3 2 3 2 3 2&lt;br /&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;.0 3 5 8 10 13 15 (0)&lt;br /&gt;

        &lt;td&gt;.0 212 353 565 706 918 1059 (1200)&lt;br /&gt;

        &lt;td&gt;.P1 M2 N3 A4 P5 M6 N7 (P8)&lt;br /&gt;

        &lt;td&gt;.0 2 5 7 10 12 14 (0)&lt;br /&gt;

        &lt;td&gt;.P1 N2 N3 P4 P5 N6 m7 (P8)&lt;br /&gt;

        &lt;td&gt;.2 3 2 3 2 2 3&lt;br /&gt;

        &lt;td&gt;.0 3 5 8 10 12 15 (0)&lt;br /&gt;

        &lt;td&gt;.0 212 353 565 706 847 1059 (1200)&lt;br /&gt;

        &lt;td&gt;.P1 M2 N3 A4 P5 N6 N7 (P8)&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;

The 17edo neutral 2nds, at 141 cents, fall between 13/12 (139 cents) &amp;amp; 12/11 (151) cents.  I've found that they generally function as 13/12, since they fall 3/2 away from 13/8.  But you can discover these things for yourself, if you like, &amp;amp; feel free to think of them in different ways entirely.&lt;br /&gt;

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

(Note that you will come up with similarly structured scales by using &lt;em&gt;other neutral thirds&lt;/em&gt; as generators, although some of them will sound quite different.  Some equal divisions of the octave containing neutral scales: &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &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="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;....)&lt;/body&gt;&lt;/html&gt;</pre></div>