Heptatonic notation: Difference between revisions
Wikispaces>jake.huryn **Imported revision 612807055 - Original comment: ** |
Wikispaces>jake.huryn **Imported revision 612807115 - 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:jake.huryn|jake.huryn]] and made on <tt>2017-05-14 00: | : This revision was by author [[User:jake.huryn|jake.huryn]] and made on <tt>2017-05-14 00:30:04 UTC</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> | ||
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* 6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x | * 6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x | ||
* 7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x | * 7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x | ||
* 8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x | * 8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion was used to determine these to be the most intuitive.) | ||
* 9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x | * 9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x | ||
* 10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x | * 10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x | ||
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* 5: bb db bv b^ d n ‡ #v #^ ‡# x | * 5: bb db bv b^ d n ‡ #v #^ ‡# x | ||
These simply remove extraneous arrows. Now, given that you know the four-accidental (quartertone) system, these two follow easily; three accidentals simply removes the sharp/flat and five splits them into up-arrow and down-arrow versions. These systems—two to five accidentals per class—are easy to memorize, intuitive, and able to notate up to 35edo, which is sufficient for a significant amount of music. | |||
(To be continued. Feedback welcome, as I'm sure there are ways to make it better!) | (To be continued. Feedback welcome, as I'm sure there are ways to make it better!) | ||
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where bb is a double flat, db is a three-half flat, b is a flat, d is a half-flat, n is a natural, ‡ is a half-sharp, # is a sharp, ‡# is a three-half sharp, and x is a double sharp. The v and ^ are arrows which are attached to the bottom and top of the accidentals, respectively. Because there are twelve flats and twelve sharps, these accidentals allow notation up to 84edo with full enharmonicity, as described above. In order to notate edos which use fewer accidentals, the accidentals used are chosen to best approximate the required modification value, assuming that the above accidentals are in increments of perfect twelfth-accidentals. For example, suppose we wish to notate 45edo; 45 = 7*6+3, so seven sharp and seven flat accidentals are required. To determine, say, the three-sevenths sharp we multiply that value by twelve: 12*3/7 = 5.14 ≈ 5, so we use the five-twelfths sharp, or #v. Doing this for all sets of fewer than or equal to twelve accidentals per sharp/flat class, we find the following:<br /> | where bb is a double flat, db is a three-half flat, b is a flat, d is a half-flat, n is a natural, ‡ is a half-sharp, # is a sharp, ‡# is a three-half sharp, and x is a double sharp. The v and ^ are arrows which are attached to the bottom and top of the accidentals, respectively. Because there are twelve flats and twelve sharps, these accidentals allow notation up to 84edo with full enharmonicity, as described above. In order to notate edos which use fewer accidentals, the accidentals used are chosen to best approximate the required modification value, assuming that the above accidentals are in increments of perfect twelfth-accidentals. For example, suppose we wish to notate 45edo; 45 = 7*6+3, so seven sharp and seven flat accidentals are required. To determine, say, the three-sevenths sharp we multiply that value by twelve: 12*3/7 = 5.14 ≈ 5, so we use the five-twelfths sharp, or #v. Doing this for all sets of fewer than or equal to twelve accidentals per sharp/flat class, we find the following:<br /> | ||
<ul><li>For two accidentals: bb b n # x</li><li>3: bb db^ dv n ‡^ ‡#v x</li><li>4: bb db b d n ‡ # ‡# x</li><li>5: bb dbv bv b^ d^ n ‡v #v #^ ‡#^ x</li><li>6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x</li><li>7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x</li><li>8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x</li><li>9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x</li><li>10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x</li><li>11: bb bb^ dbv db db^ bv b b^ dv d d^ nv n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li><li>12: bb bb^ dbv db db^ bv b b^ dv d d^ nv n n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li></ul><br /> | <ul><li>For two accidentals: bb b n # x</li><li>3: bb db^ dv n ‡^ ‡#v x</li><li>4: bb db b d n ‡ # ‡# x</li><li>5: bb dbv bv b^ d^ n ‡v #v #^ ‡#^ x</li><li>6: bb dbv db^ b dv d^ n ‡v ‡^ # ‡#v ‡#^ x</li><li>7: bb dbv db bv b^ d d^ n ‡v ‡ #v #^ ‡# ‡#^ x</li><li>8: bb dbv db bv b b^ d d^ n ‡v ‡ #v # #^ ‡# ‡#^ x (Because this results in values exactly in between twelfths, some discretion was used to determine these to be the most intuitive.)</li><li>9: bb bb^ db db^ bv b^ dv d nv n n^ ‡ ‡^ #v #^ ‡#v ‡# xv x</li><li>10: bb bb^ dbv db^ bv b b^ dv d^ nv n n^ ‡v ‡^ #v # #^ ‡#v ‡#^ xv x</li><li>11: bb bb^ dbv db db^ bv b b^ dv d d^ nv n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li><li>12: bb bb^ dbv db db^ bv b b^ dv d d^ nv n n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x</li></ul><br /> | ||
This would clearly require a significant amount of memorization to be at all efficient. However, two &quot;shorthand&quot; systems can be made, for three and five accidentals per class:<br /> | This would clearly require a significant amount of memorization to be at all efficient. However, two &quot;shorthand&quot; systems can be made, for three and five accidentals per class:<br /> | ||
<ul><li>3: bb db d n ‡ ‡# x</li><li>5: bb db bv b^ d n ‡ #v #^ ‡# x</li></ul><br /> | <ul><li>3: bb db d n ‡ ‡# x</li><li>5: bb db bv b^ d n ‡ #v #^ ‡# x</li></ul><br /> | ||
These simply remove extraneous arrows. Now, given that you know the four-accidental (quartertone) system, these two follow easily; three accidentals simply removes the sharp/flat and five splits them into up-arrow and down-arrow versions. These systems—two to five accidentals per class—are easy to memorize, intuitive, and able to notate up to 35edo, which is sufficient for a significant amount of music.<br /> | |||
<br /> | <br /> | ||
(To be continued. Feedback welcome, as I'm sure there are ways to make it better!)<br /> | (To be continued. Feedback welcome, as I'm sure there are ways to make it better!)<br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Scores and score-videos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Scores and score-videos</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Scores and score-videos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Scores and score-videos</h1> | ||
<a class="wiki_link_ext" href="https://www.youtube.com/watch?v=jagxI__W-Mg" rel="nofollow" target="_blank">Palinkalin Viharo (Flowers in the Mist)</a> by Jake Huryn (<a class="wiki_link_ext" href="https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view" rel="nofollow" target="_blank">Score</a>): 22edo</body></html></pre></div> | <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=jagxI__W-Mg" rel="nofollow" target="_blank">Palinkalin Viharo (Flowers in the Mist)</a> by Jake Huryn (<a class="wiki_link_ext" href="https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view" rel="nofollow" target="_blank">Score</a>): 22edo</body></html></pre></div> | ||