Blackwood temperament modal harmony (in 15edo)

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author igliashon and made on 2013-03-15 00:00:50 UTC.

The original revision id was 415050748.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=Harmony in 15edo Blacksmith[10] //(in progress)//= 
[[toc]]
Blacksmith[10] in [[15edo]] refers to the 10-note symmetric 5L5s [[MOSscales|MOS]] scale in 15edo, which has two modes: 2 1 2 1 2 1 2 1 2 1 and 1 2 1 2 1 2 1 2 1 2. It can be thought of as a 5-limit temperament tempering out 256/243 (the Pythagorean diatonic semitone), a 7-limit temperament tempering out 28/27 and 49/48, and an 11-limit temperament tempering out 28/27, 49/48, and 55/54 (though in 15edo 121/120 and 100/99 are both tempered out as well, making the tuning identical to Ferrier and the unnamed 5c&15 temperament). In 15edo it has a period of 240 cents (5 periods per octave) and a generator of 80 or 160 cents (though it is more commonly described as having a generator of 400 cents).
==Important features of Blacksmith[10] in 15edo== 
* As an 11-limit temperament, Blacksmith is extremely simple and efficient, and while it does fairly high damage to many ratios of 3 and 9, it does a very acceptable job of approximating most ratios of 5, 7, and 11. 9/8, 7/6, 11/9, 4/3, and their octave inversions are the most heavily-damaged, but 6/5, 12/11, and their octave inversions are tuned with good to tolerable accuracy.
* Blacksmith[10] has the most 5-odd-limit consonant triads it is possible to have in a 10-note 5-limit scale.
* Because it is a 10-note scale with a period of 1/5 of an octave, any arbitrary harmony will occur either 5 or 10 times within the 10-note scale, and for otonal harmonies consisting of three or more notes, the utonal counterpart of the harmony will also occur either 5 or 10 times within the scale; this is a property that is only held by other scales with 5 periods per octave.
* Blacksmith[10] is also a "mode of limited transposition" like the Diminished and Augmented scales in 12edo: since the scale is built by applying the generator only a single time within each period, the scale has only two modes.
* Another way to think about Blacksmith[10] is as a super-position of three modes of the diatonic scale: the major mode can be seen as a superposition of ionian, lydian, and mixolydian, while the minor mode can be seen as a superposition of dorian, phrygian, and aeolian (this will be expanded on below). This has radical implications for writing tonal and modal music in Blacksmith[10].
==Interval Classes in Blacksmith[10]== 
|| Step of 15edo || Cent Value || Interval Class || Guitar Notation || Decimal Notation || Approximated Ratios ||
|| 0 || 0 || Unison || E || 1 || 1/1 ||
|| 1 || 80 || Minor 2nd, Augmented Unison* || E#, Gbb || 2b, 1# || 16/15, 21/20, 22/21, 25/24 ||
|| 2 || 160 || Major 2nd, Diminished 3rd || Gb, Ex || 2, 3b || 10/9, 11/10, 12/11, 15/14 ||
|| 3 || 240 || Perfect 3rd, Augmented 2nd, Diminished 4th || G || 3, 2#, 4bb || 7/6, 8/7, 9/8 ||
|| 4 || 320 || Minor 4th, Augmented 3rd || G#, Abb || 4b, 3# || 6/5, 11/9 ||
|| 5 || 400 || Major 4th, Diminished 5th || Ab, Gx || 4, 5b || 5/4, 14/11, ||
|| 6 || 480 || Perfect 5th, Augmented 4th, Diminished 6th || A || 5, 4#, 6bb || 4/3, 21/16, 9/7 ||
|| 7 || 560 || Minor 6th, Augmented 5th || A#, Bbb || 6b, 5# || 7/5, 11/8, ||
|| 8 || 640 || Major 6th, Diminished 7th || Bb, Ax || 6, 7b || 10/7, 16/11 ||
|| 9 || 720 || Perfect 7th, Augmented 6th, Diminished 8th || B || 7, 6#, 8bb || 3/2, 32/21, 14/9 ||
|| 10 || 800 || Minor 8th, Augmented 7th || B#, Dbb || 8b, 7# || 8/5, 11/7, ||
|| 11 || 880 || Major 8th, Diminished 9th || Db, Bx || 8, 9b || 5/3, 18/11 ||
|| 12 || 960 || Perfect 9th, Augmented 8th, Diminished 10th || D || 9, 8#, 0bb || 12/7, 7/4, 16/9 ||
|| 13 || 1040 || Minor 10th, Augmented 9th || D#, Ebb || 0b, 9# || 9/5, 20/11, 11/6, 28/15 ||
|| 14 || 1120 || Major 10th, Diminished Undecave || Eb, Dx || 0, 1b || 15/8, 40/21, 48/25 ||
|| 15 || 1200 || Undecave ("Octave") || E || 1 || 2/1 ||
*Augmented and diminished intervals do not occur in the 10-note MOS scale, but can occur in chromatically-altered MODMOSs.

==Triads of Blacksmith[10]== 
===Unaltered Triads=== 
||= Decimal Notation ||= Guitar Notation ||= Cents ||= Steps of 15edo ||= Approximated 
Harmonics #1 ||= Approximated 
Harmonics #2 ||= Triad Name ||= Comments ||
||= 1-2b-3 ||= E-E#-G ||= 0-80-240 ||= 0-1-3 ||= 21:22:24 ||=   ||= Minor Cluster ||=   ||
||= 1-2-3 ||= E-Gb-G ||= 0-160-240 ||= 0-2-3 ||= 1/(21:22:24) ||=   ||= Major Cluster ||=   ||
||= 1-2b-4b ||= E-E#-G# ||= 0-80-320 ||= 0-1-4 ||= 20:21:24 ||=   ||=   ||=   ||
||= 1-3-4b ||= E-G-G# ||= 0-240-320 ||= 0-3-4 ||=   ||=   ||=   ||=   ||
|| 1-2-4 || E-Gb-Ab || 0-160-400 || 0-2-5 || 11:12:14 || 1/(8:9:10) ||   ||   ||
|| 1-3-4 || E-G-Ab || 0-240-400 || 0-3-5 || 8:9:10 || 1/(11:12:14) ||   ||   ||
|| 1-2b-5 || E-E#-A || 0-80-480 || 0-1-6 ||   ||   ||   ||   ||
|| 1-2-5 || E-Gb-A || 0-160-480 || 0-2-6 || 9:10:12 ||   ||   ||   ||
|| 1-3-5 || E-G-A || 0-240-480 || 0-3-6 || 6:7:8 || 1/(6:7:8) ||   ||   ||
|| 1-4b-5 || E-G#-A || 0-320-480 || 0-4-6 || 9:11:12 ||   ||   ||   ||
|| 1-4-5 || E-Ab-A || 0-400-480 || 0-5-6 || 16:20:21 ||   ||   ||   ||
|| 1-2b-6b || E-E#-A# || 0-80-560 || 0-1-7 || 15:16:21 ||   ||   ||   ||
|| 1-3-6b || E-G-A# || 0-240-560 || 0-3-7 || 1/(5:6:7) ||   ||   ||   ||
|| 1-4b-6b || E-G#-A# || 0-320-560 || 0-4-7 || 5:6:7 ||   || Diminished ||   ||
|| 1-5-6b || E-A-A# || 0-480-560 || 0-6-7 ||   ||   ||   ||   ||
|| 1-2-6 || E-Gb-Bb || 0-160-640 || 0-2-8 || 11:12:16 ||   ||   ||   ||
|| 1-3-6 || E-G-Bb || 0-240-640 || 0-3-8 || 7:8:10 || 1/(11:14:16) ||   ||   ||
|| 1-4-6 || E-Ab-Bb || 0-400-640 || 0-5-8 || 1/(7:8:10) || 11:14:16 || Major-Diminished ||   ||
|| 1-5-6 || E-A-Bb || 0-480-640 || 0-6-8 ||   ||   ||   ||   ||
|| 1-2b-7 || E-E#-B || 0-80-720 || 0-1-9 || 21:22:32 ||   ||   ||   ||
|| 1-2-7 || E-Gb-B || 0-160-720 || 0-2-9 ||   ||   ||   ||   ||
|| 1-3-7 || E-G-B || 0-240-720 || 0-3-9 || 6:7:9 || 8:9:12 ||   ||   ||
|| 1-4b-7 || E-G#-B || 0-320-720 || 0-4-9 || 1/(4:5:6) || 10:12:15 || Minor Triad ||   ||
|| 1-4-7 || E-Ab-B || 0-400-720 || 0-5-9 || 4:5:6 ||   || Major Triad ||   ||
=== === 

Original HTML content:

<html><head><title>Harmony in 15edo Blacksmith</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Harmony in 15edo Blacksmith[10] (in progress)"></a><!-- ws:end:WikiTextHeadingRule:0 -->Harmony in 15edo Blacksmith[10] <em>(in progress)</em></h1>
 <!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><div style="margin-left: 1em;"><a href="#Harmony in 15edo Blacksmith[10] (in progress)">Harmony in 15edo Blacksmith[10] (in progress)</a></div>
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><div style="margin-left: 2em;"><a href="#Harmony in 15edo Blacksmith[10] (in progress)-Important features of Blacksmith[10] in 15edo">Important features of Blacksmith[10] in 15edo</a></div>
<!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 2em;"><a href="#Harmony in 15edo Blacksmith[10] (in progress)-Interval Classes in Blacksmith[10]">Interval Classes in Blacksmith[10]</a></div>
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 2em;"><a href="#Harmony in 15edo Blacksmith[10] (in progress)-Triads of Blacksmith[10]">Triads of Blacksmith[10]</a></div>
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 3em;"><a href="#Harmony in 15edo Blacksmith[10] (in progress)-Triads of Blacksmith[10]-Unaltered Triads">Unaltered Triads</a></div>
<!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 3em;"><a href="#toc5"> </a></div>
<!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --></div>
<!-- ws:end:WikiTextTocRule:19 -->Blacksmith[10] in <a class="wiki_link" href="/15edo">15edo</a> refers to the 10-note symmetric 5L5s <a class="wiki_link" href="/MOSscales">MOS</a> scale in 15edo, which has two modes: 2 1 2 1 2 1 2 1 2 1 and 1 2 1 2 1 2 1 2 1 2. It can be thought of as a 5-limit temperament tempering out 256/243 (the Pythagorean diatonic semitone), a 7-limit temperament tempering out 28/27 and 49/48, and an 11-limit temperament tempering out 28/27, 49/48, and 55/54 (though in 15edo 121/120 and 100/99 are both tempered out as well, making the tuning identical to Ferrier and the unnamed 5c&amp;15 temperament). In 15edo it has a period of 240 cents (5 periods per octave) and a generator of 80 or 160 cents (though it is more commonly described as having a generator of 400 cents).<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Harmony in 15edo Blacksmith[10] (in progress)-Important features of Blacksmith[10] in 15edo"></a><!-- ws:end:WikiTextHeadingRule:2 -->Important features of Blacksmith[10] in 15edo</h2>
 <ul><li>As an 11-limit temperament, Blacksmith is extremely simple and efficient, and while it does fairly high damage to many ratios of 3 and 9, it does a very acceptable job of approximating most ratios of 5, 7, and 11. 9/8, 7/6, 11/9, 4/3, and their octave inversions are the most heavily-damaged, but 6/5, 12/11, and their octave inversions are tuned with good to tolerable accuracy.</li><li>Blacksmith[10] has the most 5-odd-limit consonant triads it is possible to have in a 10-note 5-limit scale.</li><li>Because it is a 10-note scale with a period of 1/5 of an octave, any arbitrary harmony will occur either 5 or 10 times within the 10-note scale, and for otonal harmonies consisting of three or more notes, the utonal counterpart of the harmony will also occur either 5 or 10 times within the scale; this is a property that is only held by other scales with 5 periods per octave.</li><li>Blacksmith[10] is also a &quot;mode of limited transposition&quot; like the Diminished and Augmented scales in 12edo: since the scale is built by applying the generator only a single time within each period, the scale has only two modes.</li><li>Another way to think about Blacksmith[10] is as a super-position of three modes of the diatonic scale: the major mode can be seen as a superposition of ionian, lydian, and mixolydian, while the minor mode can be seen as a superposition of dorian, phrygian, and aeolian (this will be expanded on below). This has radical implications for writing tonal and modal music in Blacksmith[10].</li></ul><!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Harmony in 15edo Blacksmith[10] (in progress)-Interval Classes in Blacksmith[10]"></a><!-- ws:end:WikiTextHeadingRule:4 -->Interval Classes in Blacksmith[10]</h2>
 

<table class="wiki_table">
    <tr>
        <td>Step of 15edo<br />
</td>
        <td>Cent Value<br />
</td>
        <td>Interval Class<br />
</td>
        <td>Guitar Notation<br />
</td>
        <td>Decimal Notation<br />
</td>
        <td>Approximated Ratios<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>Unison<br />
</td>
        <td>E<br />
</td>
        <td>1<br />
</td>
        <td>1/1<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>80<br />
</td>
        <td>Minor 2nd, Augmented Unison*<br />
</td>
        <td>E#, Gbb<br />
</td>
        <td>2b, 1#<br />
</td>
        <td>16/15, 21/20, 22/21, 25/24<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>160<br />
</td>
        <td>Major 2nd, Diminished 3rd<br />
</td>
        <td>Gb, Ex<br />
</td>
        <td>2, 3b<br />
</td>
        <td>10/9, 11/10, 12/11, 15/14<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>240<br />
</td>
        <td>Perfect 3rd, Augmented 2nd, Diminished 4th<br />
</td>
        <td>G<br />
</td>
        <td>3, 2#, 4bb<br />
</td>
        <td>7/6, 8/7, 9/8<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>320<br />
</td>
        <td>Minor 4th, Augmented 3rd<br />
</td>
        <td>G#, Abb<br />
</td>
        <td>4b, 3#<br />
</td>
        <td>6/5, 11/9<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>400<br />
</td>
        <td>Major 4th, Diminished 5th<br />
</td>
        <td>Ab, Gx<br />
</td>
        <td>4, 5b<br />
</td>
        <td>5/4, 14/11,<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>480<br />
</td>
        <td>Perfect 5th, Augmented 4th, Diminished 6th<br />
</td>
        <td>A<br />
</td>
        <td>5, 4#, 6bb<br />
</td>
        <td>4/3, 21/16, 9/7<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>560<br />
</td>
        <td>Minor 6th, Augmented 5th<br />
</td>
        <td>A#, Bbb<br />
</td>
        <td>6b, 5#<br />
</td>
        <td>7/5, 11/8,<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>640<br />
</td>
        <td>Major 6th, Diminished 7th<br />
</td>
        <td>Bb, Ax<br />
</td>
        <td>6, 7b<br />
</td>
        <td>10/7, 16/11<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>720<br />
</td>
        <td>Perfect 7th, Augmented 6th, Diminished 8th<br />
</td>
        <td>B<br />
</td>
        <td>7, 6#, 8bb<br />
</td>
        <td>3/2, 32/21, 14/9<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>800<br />
</td>
        <td>Minor 8th, Augmented 7th<br />
</td>
        <td>B#, Dbb<br />
</td>
        <td>8b, 7#<br />
</td>
        <td>8/5, 11/7,<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>880<br />
</td>
        <td>Major 8th, Diminished 9th<br />
</td>
        <td>Db, Bx<br />
</td>
        <td>8, 9b<br />
</td>
        <td>5/3, 18/11<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>960<br />
</td>
        <td>Perfect 9th, Augmented 8th, Diminished 10th<br />
</td>
        <td>D<br />
</td>
        <td>9, 8#, 0bb<br />
</td>
        <td>12/7, 7/4, 16/9<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>1040<br />
</td>
        <td>Minor 10th, Augmented 9th<br />
</td>
        <td>D#, Ebb<br />
</td>
        <td>0b, 9#<br />
</td>
        <td>9/5, 20/11, 11/6, 28/15<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>1120<br />
</td>
        <td>Major 10th, Diminished Undecave<br />
</td>
        <td>Eb, Dx<br />
</td>
        <td>0, 1b<br />
</td>
        <td>15/8, 40/21, 48/25<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>1200<br />
</td>
        <td>Undecave (&quot;Octave&quot;)<br />
</td>
        <td>E<br />
</td>
        <td>1<br />
</td>
        <td>2/1<br />
</td>
    </tr>
</table>

*Augmented and diminished intervals do not occur in the 10-note MOS scale, but can occur in chromatically-altered MODMOSs.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Harmony in 15edo Blacksmith[10] (in progress)-Triads of Blacksmith[10]"></a><!-- ws:end:WikiTextHeadingRule:6 -->Triads of Blacksmith[10]</h2>
 <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Harmony in 15edo Blacksmith[10] (in progress)-Triads of Blacksmith[10]-Unaltered Triads"></a><!-- ws:end:WikiTextHeadingRule:8 -->Unaltered Triads</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;">Decimal Notation<br />
</td>
        <td style="text-align: center;">Guitar Notation<br />
</td>
        <td style="text-align: center;">Cents<br />
</td>
        <td style="text-align: center;">Steps of 15edo<br />
</td>
        <td style="text-align: center;">Approximated <br />
Harmonics #1<br />
</td>
        <td style="text-align: center;">Approximated <br />
Harmonics #2<br />
</td>
        <td style="text-align: center;">Triad Name<br />
</td>
        <td style="text-align: center;">Comments<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1-2b-3<br />
</td>
        <td style="text-align: center;">E-E#-G<br />
</td>
        <td style="text-align: center;">0-80-240<br />
</td>
        <td style="text-align: center;">0-1-3<br />
</td>
        <td style="text-align: center;">21:22:24<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">Minor Cluster<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1-2-3<br />
</td>
        <td style="text-align: center;">E-Gb-G<br />
</td>
        <td style="text-align: center;">0-160-240<br />
</td>
        <td style="text-align: center;">0-2-3<br />
</td>
        <td style="text-align: center;">1/(21:22:24)<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">Major Cluster<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1-2b-4b<br />
</td>
        <td style="text-align: center;">E-E#-G#<br />
</td>
        <td style="text-align: center;">0-80-320<br />
</td>
        <td style="text-align: center;">0-1-4<br />
</td>
        <td style="text-align: center;">20:21:24<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1-3-4b<br />
</td>
        <td style="text-align: center;">E-G-G#<br />
</td>
        <td style="text-align: center;">0-240-320<br />
</td>
        <td style="text-align: center;">0-3-4<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1-2-4<br />
</td>
        <td>E-Gb-Ab<br />
</td>
        <td>0-160-400<br />
</td>
        <td>0-2-5<br />
</td>
        <td>11:12:14<br />
</td>
        <td>1/(8:9:10)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-4<br />
</td>
        <td>E-G-Ab<br />
</td>
        <td>0-240-400<br />
</td>
        <td>0-3-5<br />
</td>
        <td>8:9:10<br />
</td>
        <td>1/(11:12:14)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2b-5<br />
</td>
        <td>E-E#-A<br />
</td>
        <td>0-80-480<br />
</td>
        <td>0-1-6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-5<br />
</td>
        <td>E-Gb-A<br />
</td>
        <td>0-160-480<br />
</td>
        <td>0-2-6<br />
</td>
        <td>9:10:12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-5<br />
</td>
        <td>E-G-A<br />
</td>
        <td>0-240-480<br />
</td>
        <td>0-3-6<br />
</td>
        <td>6:7:8<br />
</td>
        <td>1/(6:7:8)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4b-5<br />
</td>
        <td>E-G#-A<br />
</td>
        <td>0-320-480<br />
</td>
        <td>0-4-6<br />
</td>
        <td>9:11:12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4-5<br />
</td>
        <td>E-Ab-A<br />
</td>
        <td>0-400-480<br />
</td>
        <td>0-5-6<br />
</td>
        <td>16:20:21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2b-6b<br />
</td>
        <td>E-E#-A#<br />
</td>
        <td>0-80-560<br />
</td>
        <td>0-1-7<br />
</td>
        <td>15:16:21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-6b<br />
</td>
        <td>E-G-A#<br />
</td>
        <td>0-240-560<br />
</td>
        <td>0-3-7<br />
</td>
        <td>1/(5:6:7)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4b-6b<br />
</td>
        <td>E-G#-A#<br />
</td>
        <td>0-320-560<br />
</td>
        <td>0-4-7<br />
</td>
        <td>5:6:7<br />
</td>
        <td><br />
</td>
        <td>Diminished<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-5-6b<br />
</td>
        <td>E-A-A#<br />
</td>
        <td>0-480-560<br />
</td>
        <td>0-6-7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-6<br />
</td>
        <td>E-Gb-Bb<br />
</td>
        <td>0-160-640<br />
</td>
        <td>0-2-8<br />
</td>
        <td>11:12:16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-6<br />
</td>
        <td>E-G-Bb<br />
</td>
        <td>0-240-640<br />
</td>
        <td>0-3-8<br />
</td>
        <td>7:8:10<br />
</td>
        <td>1/(11:14:16)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4-6<br />
</td>
        <td>E-Ab-Bb<br />
</td>
        <td>0-400-640<br />
</td>
        <td>0-5-8<br />
</td>
        <td>1/(7:8:10)<br />
</td>
        <td>11:14:16<br />
</td>
        <td>Major-Diminished<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-5-6<br />
</td>
        <td>E-A-Bb<br />
</td>
        <td>0-480-640<br />
</td>
        <td>0-6-8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2b-7<br />
</td>
        <td>E-E#-B<br />
</td>
        <td>0-80-720<br />
</td>
        <td>0-1-9<br />
</td>
        <td>21:22:32<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-7<br />
</td>
        <td>E-Gb-B<br />
</td>
        <td>0-160-720<br />
</td>
        <td>0-2-9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-7<br />
</td>
        <td>E-G-B<br />
</td>
        <td>0-240-720<br />
</td>
        <td>0-3-9<br />
</td>
        <td>6:7:9<br />
</td>
        <td>8:9:12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4b-7<br />
</td>
        <td>E-G#-B<br />
</td>
        <td>0-320-720<br />
</td>
        <td>0-4-9<br />
</td>
        <td>1/(4:5:6)<br />
</td>
        <td>10:12:15<br />
</td>
        <td>Minor Triad<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4-7<br />
</td>
        <td>E-Ab-B<br />
</td>
        <td>0-400-720<br />
</td>
        <td>0-5-9<br />
</td>
        <td>4:5:6<br />
</td>
        <td><br />
</td>
        <td>Major Triad<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h3>
</body></html>