Miracle/Chords: Difference between revisions
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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: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2014-11-28 15:22:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>533042792</tt>.<br> | ||
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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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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=Triads= | =Triads= | ||
Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this [[@http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf|PDF]] (uses 41 EDO sagittal notation) and can be heard using [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3|piano]], [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3|oud]], or [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3|sine wave]] timbres (all links in MP3 format and tuned to 41 EDO). Finally, here is a [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid|tuned MIDI file]]. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest. | Each of the triads below has three "inversions", i.e., can be written starting on any one of the three tones in the triad. | ||
<span style="line-height: 1.5;">Note that the tones in the triad are noted in order of generator steps, not pitch. For example, </span>look at triad #21. 1/1 - 8/5 - 6/5 is listed in order of generator steps, 0 - 7 - 13. Seven generator steps, or 8/5, is 813.7 cents. Thirteen generator steps, or 6/5, is 315.6 cents. If you put the triad in pitch order, you get 1/1 - 6/5 - 8/5, or <span style="line-height: 1.5;">0.0 - 315.6 - 813.7 cents.</span> | |||
<span style="line-height: 1.5;">Also note that you won't see the traditional five-limit major triad, 1/1 - 5/4 - 3/2 in this list. That's because this list contains an inversion of the five-limit major triad: number 21. 1/1 - 6/5 - 8/5 is the first inversion of 1/1 - 5/4 - 3/2. In other words, to get the major chord from the list below, you need to take the second inversion of triad 21. The same may be true of other triads you're interested in.</span> | |||
All three inversions for all 63 chords are notated in this [[@http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf|PDF]] (uses 41 EDO sagittal notation) and can be heard using [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3|piano]], [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3|oud]], or [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3|sine wave]] timbres (all links in MP3 format and tuned to 41 EDO). Finally, here is a [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid|tuned MIDI file]]. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest. | |||
|| Number || Chord || Transversal || Type || Hash || | || Number || Chord || Transversal || Type || Hash || | ||
|| 1 || 0-2-5 || 1-8/7-7/5 || werckismic || 5.209453 || | || 1 || 0-2-5 || 1-8/7-7/5 || werckismic || 5.209453 || | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | ||
Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf" rel="nofollow" target="_blank">PDF</a> (uses 41 EDO sagittal notation) and can be heard using <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3" rel="nofollow">piano</a>, <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3" rel="nofollow">oud</a>, or <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3" rel="nofollow">sine wave</a> timbres (all links in MP3 format and tuned to 41 EDO). Finally, here is a <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid" rel="nofollow">tuned MIDI file</a>. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest.<br /> | Each of the triads below has three &quot;inversions&quot;, i.e., can be written starting on any one of the three tones in the triad. <br /> | ||
<br /> | |||
<span style="line-height: 1.5;">Note that the tones in the triad are noted in order of generator steps, not pitch. For example, </span>look at triad #21. 1/1 - 8/5 - 6/5 is listed in order of generator steps, 0 - 7 - 13. Seven generator steps, or 8/5, is 813.7 cents. Thirteen generator steps, or 6/5, is 315.6 cents. If you put the triad in pitch order, you get 1/1 - 6/5 - 8/5, or <span style="line-height: 1.5;">0.0 - 315.6 - 813.7 cents.</span><br /> | |||
<br /> | |||
<span style="line-height: 1.5;">Also note that you won't see the traditional five-limit major triad, 1/1 - 5/4 - 3/2 in this list. That's because this list contains an inversion of the five-limit major triad: number 21. 1/1 - 6/5 - 8/5 is the first inversion of 1/1 - 5/4 - 3/2. In other words, to get the major chord from the list below, you need to take the second inversion of triad 21. The same may be true of other triads you're interested in.</span><br /> | |||
<br /> | |||
All three inversions for all 63 chords are notated in this <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf" rel="nofollow" target="_blank">PDF</a> (uses 41 EDO sagittal notation) and can be heard using <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3" rel="nofollow">piano</a>, <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3" rel="nofollow">oud</a>, or <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3" rel="nofollow">sine wave</a> timbres (all links in MP3 format and tuned to 41 EDO). Finally, here is a <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid" rel="nofollow">tuned MIDI file</a>. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest.<br /> | |||