17edo neutral scale

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=17edo neutral scale=

A lovely system of Middle-Eastern flavored scales!

We can call the [[MOSScales|Moment of Symmetry]]  scale derived from a 5/17 generator & 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 (& its octave transposition) 0:

0 (0)

Add a note a neutral third up from 0:

0 5 (0)

Add a note a neutral third down from 0:

0 5 12 (0)

Between these notes we have intervals of:

5 7 5

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.

Add an N3 up from 5:

0 5 10 12 (0)

Add an N3 down from 12:

0 5 7 10 12 (0)

Add an N3 up from 10:

0 5 7 10 12 15 (0)

Add an N3 down from 7:

0 2 5 7 10 12 15 (0)

We have arrived again at a MOS scale.

[[#7-note]]
==7-note neutral scale:==

degrees from 0: 0 2 5 7 10 12 15 (0)
cents from 0: 0 141 353 494 706 847 1059 (1200)
interval classes from P1: P1 N2 N3 P4 P5 N6 N7 (P8)

degrees between: 2 3 2 3 2 3 2
cents between: 141 212 141 212 141 212 141
interval classes between: N2 M2 N2 M2 N2 M2 N2

===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 ||
|| 2 || dril || .0 3 5 8 10 13 15 (0) || .0 212 353 565 706 918 1059 (1200) || .P1 M2 N3 A4 P5 M6 N7 (P8) || .3 2 3 2 3 2 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 & 3rds, making it sound very different from the traditional major-minor Western harmonic & melodic system, while having a coherent structure including ample 4ths & 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) & 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, & 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, & 13, while skipping 7 & 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]]....)

Original HTML content:

<html><head><title>17edo neutral scale</title></head><body><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x17edo neutral scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->17edo neutral scale</h1>
<br />
A lovely system of Middle-Eastern flavored scales!<br />
<br />
We can call the <a class="wiki_link" href="/MOSScales">Moment of Symmetry</a>  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.<br />
<br />
Begin anywhere.  Let's call our first pitch (&amp; its octave transposition) 0:<br />
<br />
0 (0)<br />
<br />
Add a note a neutral third up from 0:<br />
<br />
0 5 (0)<br />
<br />
Add a note a neutral third down from 0:<br />
<br />
0 5 12 (0)<br />
<br />
Between these notes we have intervals of:<br />
<br />
5 7 5<br />
<br />
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.<br />
<br />
Add an N3 up from 5:<br />
<br />
0 5 10 12 (0)<br />
<br />
Add an N3 down from 12:<br />
<br />
0 5 7 10 12 (0)<br />
<br />
Add an N3 up from 10:<br />
<br />
0 5 7 10 12 15 (0)<br />
<br />
Add an N3 down from 7:<br />
<br />
0 2 5 7 10 12 15 (0)<br />
<br />
We have arrived again at a MOS scale.<br />
<br />
<!-- ws:start:WikiTextAnchorRule:6:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@7-note&quot; title=&quot;Anchor: 7-note&quot;/&gt; --><a name="7-note"></a><!-- ws:end:WikiTextAnchorRule:6 --><br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x17edo neutral scale-7-note neutral scale:"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-note neutral scale:</h2>
<br />
degrees from 0: 0 2 5 7 10 12 15 (0)<br />
cents from 0: 0 141 353 494 706 847 1059 (1200)<br />
interval classes from P1: P1 N2 N3 P4 P5 N6 N7 (P8)<br />
<br />
degrees between: 2 3 2 3 2 3 2<br />
cents between: 141 212 141 212 141 212 141<br />
interval classes between: N2 M2 N2 M2 N2 M2 N2<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x17edo neutral scale-7-note neutral scale:-modes of 7-note neutral scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->modes of 7-note neutral scale</h3>
<br />
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:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>mode<br />
</td>
        <td>name<br />
</td>
        <td>degrees from 0<br />
</td>
        <td>cents from 0<br />
</td>
        <td>intverval classes from P1<br />
</td>
        <td>degrees between<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>bish<br />
</td>
        <td>.0 2 5 7 10 12 15 (0)<br />
</td>
        <td>.0 141 353 494 706 847 1059 (1200)<br />
</td>
        <td>.P1 N2 N3 P4 P5 N6 N7 (P8)<br />
</td>
        <td>.2 3 2 3 2 3 2<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>dril<br />
</td>
        <td>.0 3 5 8 10 13 15 (0)<br />
</td>
        <td>.0 212 353 565 706 918 1059 (1200)<br />
</td>
        <td>.P1 M2 N3 A4 P5 M6 N7 (P8)<br />
</td>
        <td>.3 2 3 2 3 2 2<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>fish<br />
</td>
        <td>.0 2 5 7 10 12 14 (0)<br />
</td>
        <td>.0 141 353 494 706 847 988 (1200)<br />
</td>
        <td>.P1 N2 N3 P4 P5 N6 m7 (P8)<br />
</td>
        <td>.2 3 2 3 2 2 3<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>gil<br />
</td>
        <td>.0 3 5 8 10 12 15 (0)<br />
</td>
        <td>.0 212 353 565 706 847 1059 (1200)<br />
</td>
        <td>.P1 M2 N3 A4 P5 N6 N7 (P8)<br />
</td>
        <td>.3 2 3 2 2 3 2<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>jwl<br />
</td>
        <td>.0 2 5 7 9 12 14 (0)<br />
</td>
        <td>.0 141 353 494 635 847 988 (1200)<br />
</td>
        <td>.P1 N2 N3 P4 d5 N6 m7 (P8)<br />
</td>
        <td>.2 3 2 2 3 2 3<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>kleeth<br />
</td>
        <td>.0 3 5 7 10 12 15 (0)<br />
</td>
        <td>.0 212 353 494 706 847 1059 (1200)<br />
</td>
        <td>.P1 M2 N6 P4 P5 N6 N7 (P8)<br />
</td>
        <td>.3 2 2 3 2 3 2<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>led<br />
</td>
        <td>.0 2 4 7 9 12 14 (0)<br />
</td>
        <td>.0 141 282 494 635 847 988 (1200)<br />
</td>
        <td>.P1 N2 m3 P4 d5 N6 m7 (P8)<br />
</td>
        <td>.2 2 3 2 3 2 3<br />
</td>
    </tr>
</table>

<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
17-tonists may find these scales helpful for escaping the familiar.  Just because you <em>can</em> play diatonic music in 17edo, doesn't mean you have to.  These neutral scales give you a more xenharmonic modal system to play with.<br />
<br />
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.<br />
<br />
<br />
(Note that you will come up with similarly structured scales by using <em>other neutral thirds</em> as generators, although some of them will sound quite different.  Some equal divisions of the octave containing neutral scales: <a class="wiki_link" href="/10edo">10edo</a>, <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="/24edo">24edo</a>, <a class="wiki_link" href="/31edo">31edo</a>....)</body></html>