Blackwood temperament modal harmony (in 15edo): Difference between revisions
Wikispaces>igliashon **Imported revision 414999724 - Original comment: ** |
Wikispaces>igliashon **Imported revision 415050748 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2013-03- | : This revision was by author [[User:igliashon|igliashon]] and made on <tt>2013-03-15 00:00:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>415050748</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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* 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]. | * 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]== | ==Interval Classes in Blacksmith[10]== | ||
|| Step of 15edo || Cent Value || Interval Class || Guitar Notation || Decimal Notation || | || Step of 15edo || Cent Value || Interval Class || Guitar Notation || Decimal Notation || Approximated Ratios || | ||
|| 0 || 0 || Unison || E || 1 || | || 0 || 0 || Unison || E || 1 || 1/1 || | ||
|| 1 || 80 || Minor 2nd, Augmented Unison* || E#, Gbb || 2b, 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 || | || 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 || | || 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# || | || 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 || 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 || | || 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 || 560 || Minor 6th, Augmented 5th || A#, Bbb || 6b, 5# || 7/5, 11/8, || | ||
|| 8 || 640 || Major 6th, Diminished 7th || Bb, Ax || 6, 7b || | || 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 || | || 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# || | || 10 || 800 || Minor 8th, Augmented 7th || B#, Dbb || 8b, 7# || 8/5, 11/7, || | ||
|| 11 || 880 || Major 8th, Diminished 9th || Db, Bx || 8, 9b || | || 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 || 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# || | || 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 || | || 14 || 1120 || Major 10th, Diminished Undecave || Eb, Dx || 0, 1b || 15/8, 40/21, 48/25 || | ||
|| 15 || 1200 || Undecave (Octave) || E || 1 || | || 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.</pre></div> | *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 || || | |||
=== === </pre></div> | |||
<h4>Original HTML content:</h4> | <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"><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> | <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"><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: | <!-- 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: | <!-- 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: | <!-- 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: | <!-- 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: | <!-- 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> | <!-- 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> | <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> | ||
| Line 56: | Line 90: | ||
</td> | </td> | ||
<td>Decimal Notation<br /> | <td>Decimal Notation<br /> | ||
</td> | |||
<td>Approximated Ratios<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 68: | Line 104: | ||
</td> | </td> | ||
<td>1<br /> | <td>1<br /> | ||
</td> | |||
<td>1/1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 80: | Line 118: | ||
</td> | </td> | ||
<td>2b, 1#<br /> | <td>2b, 1#<br /> | ||
</td> | |||
<td>16/15, 21/20, 22/21, 25/24<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 92: | Line 132: | ||
</td> | </td> | ||
<td>2, 3b<br /> | <td>2, 3b<br /> | ||
</td> | |||
<td>10/9, 11/10, 12/11, 15/14<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 104: | Line 146: | ||
</td> | </td> | ||
<td>3, 2#, 4bb<br /> | <td>3, 2#, 4bb<br /> | ||
</td> | |||
<td>7/6, 8/7, 9/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 116: | Line 160: | ||
</td> | </td> | ||
<td>4b, 3#<br /> | <td>4b, 3#<br /> | ||
</td> | |||
<td>6/5, 11/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 128: | Line 174: | ||
</td> | </td> | ||
<td>4, 5b<br /> | <td>4, 5b<br /> | ||
</td> | |||
<td>5/4, 14/11,<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 140: | Line 188: | ||
</td> | </td> | ||
<td>5, 4#, 6bb<br /> | <td>5, 4#, 6bb<br /> | ||
</td> | |||
<td>4/3, 21/16, 9/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 152: | Line 202: | ||
</td> | </td> | ||
<td>6b, 5#<br /> | <td>6b, 5#<br /> | ||
</td> | |||
<td>7/5, 11/8,<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 164: | Line 216: | ||
</td> | </td> | ||
<td>6, 7b<br /> | <td>6, 7b<br /> | ||
</td> | |||
<td>10/7, 16/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 176: | Line 230: | ||
</td> | </td> | ||
<td>7, 6#, 8bb<br /> | <td>7, 6#, 8bb<br /> | ||
</td> | |||
<td>3/2, 32/21, 14/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 188: | Line 244: | ||
</td> | </td> | ||
<td>8b, 7#<br /> | <td>8b, 7#<br /> | ||
</td> | |||
<td>8/5, 11/7,<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 200: | Line 258: | ||
</td> | </td> | ||
<td>8, 9b<br /> | <td>8, 9b<br /> | ||
</td> | |||
<td>5/3, 18/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 212: | Line 272: | ||
</td> | </td> | ||
<td>9, 8#, 0bb<br /> | <td>9, 8#, 0bb<br /> | ||
</td> | |||
<td>12/7, 7/4, 16/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 224: | Line 286: | ||
</td> | </td> | ||
<td>0b, 9#<br /> | <td>0b, 9#<br /> | ||
</td> | |||
<td>9/5, 20/11, 11/6, 28/15<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 236: | Line 300: | ||
</td> | </td> | ||
<td>0, 1b<br /> | <td>0, 1b<br /> | ||
</td> | |||
<td>15/8, 40/21, 48/25<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 243: | Line 309: | ||
<td>1200<br /> | <td>1200<br /> | ||
</td> | </td> | ||
<td>Undecave (Octave)<br /> | <td>Undecave (&quot;Octave&quot;)<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td>E<br /> | ||
</td> | </td> | ||
<td>1<br /> | <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> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h3> | |||
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