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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
== Purpose and Principles ==
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
I{{who}} developed '''heptatonic notation''' in order to notate my microtonal music, which is written in a number of different [[EDO|edos]]. Some principles were followed in the development this [[notation]] system:
: This revision was by author [[User:jake.huryn|jake.huryn]] and made on <tt>2017-05-13 00:14:07 UTC</tt>.<br>
: The original revision id was <tt>612772593</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=Purpose and Principles=  
I developed heptatonic notation in order to notate my microtonal music, which is written in a number of different [[edo|edos]]. A number of principles were followed in the development this notation system.
* It should be nearly consistent with standard modern music notation.
* It should be consistent between different edos.
* It should be as non-arbitrary as possible.


From these principles I decided that it should be based on [[Nominal-Accidental Chains|nominal-accidental chains]], with seven nominals to an octave. In addition, accidentals should both be based on those of standard notation and give an approximation of their displacement size. From these principles is derived the fundamental rule behind this notation system:
<ul><li>It should be nearly consistent with standard modern music notation.</li><li>It should be consistent between different edos.</li><li>It should be as non-arbitrary as possible.</li></ul>
* For each edo, nominals are assigned to the first mode of the [[Maximal evenness|maximally even]] heptatonic [[MOSScales|MOS]].


=Nominals for Different Edos=  
From these principles I decided that it should be based on [[Nominal-Accidental_Chains|nominal-accidental chains]], with seven nominals to an [[octave]]. In addition, accidentals should both be based on those of standard notation and give an approximation of their displacement size. From these principles is derived the fundamental rule behind this notation system:
By finding these particular MOS scales in each edo, we can find that they follow a number of patterns:
 
* (L=1, s=0)
<ul><li>For each edo, nominals are assigned to the first mode of the [[Maximal_evenness|maximally even]] heptatonic [[MOSScales|MOS]].</li></ul>
** 1\7: LLLLLLL
 
* (2, 1)
==Nominals==
** 1\8: ssssssL
By finding these particular MOS scales in each edo, we can find that they, and thus that edo's nominals, follow a number of patterns:
** 4\9: LssLsss
 
** 3\10: LsLsLss
<ul><li>(L=1, s=0)<ul><li>1\7: LLLLLLL</li></ul></li><li>(2, 1)<ul><li>1\8: ssssssL</li><li>4\9: LssLsss</li><li>3\10: LsLsLss</li><li>3\11: sLsLsLL</li><li>5\12: sLLsLLL</li><li>2\13: LLLLLLs</li><li>2\14: LLLLLLL</li></ul></li><li>(3, 2)<ul><li>2\15: ssssssL</li><li>7\16: LssLsss</li><li>5\17: LsLsLss</li><li>5\18: sLsLsLL</li><li>7\19: sLLsLLL</li><li>3\20: LLLLLLs</li><li>3\21: LLLLLLL</li></ul></li></ul>
** 3\11: sLsLsLL
** 5\12: sLLsLLL
** 2\13: LLLLLLs
** 2\14: LLLLLLL
* (3, 2)
** 2\15: ssssssL
** 7\16: LssLsss
** 5\17: LsLsLss
** 5\18: sLsLsLL
** 7\19: sLLsLLL
** 3\20: LLLLLLs
** 3\21: LLLLLLL


These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.
These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.


=Accidentals=  
== Accidentals ==
For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each class (flat or sharp) are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation.
For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each flat/sharp are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation. I chose the following twenty-five accidentals to be usable with the [http://www.ekmelic-music.org/en/extra/ekmelily.htm Ekmelily] extension to [http://lilypond.org/ Lilypond], which I use to notate my music:
 
bb bb^ dbv db db^ bv b b^ dv d d^ nv n n^ ‡v ‡ ‡^ #v # #^ ‡#v ‡# ‡#^ xv x,
 
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:
 
<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 in was used in rounding 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>
 
This would clearly require a significant amount of memorization to be at all efficient. However, two "shorthand" systems can be made, for three and five accidentals per class:
 
<ul><li>3: bb db d n ‡ ‡# x</li><li>5: bb db bv b^ d n ‡ #v #^ ‡# x</li></ul>
 
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!)
 
==Scores and score-videos==
[https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]): 22edo


(To be continued.)
{{Navbox notation}}


=Scores and score-videos=
[[Category:notation]]
[[@https://www.youtube.com/watch?v=jagxI__W-Mg|//Palinkalin Viharo// (Flowers in the Mist)]] by Jake Huryn ([[@https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view|Score]]): 22edo</pre></div>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Heptatonic Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Purpose and Principles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Purpose and Principles&lt;/h1&gt;
I developed heptatonic notation in order to notate my microtonal music, which is written in a number of different &lt;a class="wiki_link" href="/edo"&gt;edos&lt;/a&gt;. A number of principles were followed in the development this notation system.&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;It should be nearly consistent with standard modern music notation.&lt;/li&gt;&lt;li&gt;It should be consistent between different edos.&lt;/li&gt;&lt;li&gt;It should be as non-arbitrary as possible.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
From these principles I decided that it should be based on &lt;a class="wiki_link" href="/Nominal-Accidental%20Chains"&gt;nominal-accidental chains&lt;/a&gt;, with seven nominals to an octave. In addition, accidentals should both be based on those of standard notation and give an approximation of their displacement size. From these principles is derived the fundamental rule behind this notation system:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;For each edo, nominals are assigned to the first mode of the &lt;a class="wiki_link" href="/Maximal%20evenness"&gt;maximally even&lt;/a&gt; heptatonic &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Nominals for Different Edos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Nominals for Different Edos&lt;/h1&gt;
By finding these particular MOS scales in each edo, we can find that they follow a number of patterns:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;(L=1, s=0)&lt;ul&gt;&lt;li&gt;1\7: LLLLLLL&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(2, 1)&lt;ul&gt;&lt;li&gt;1\8: ssssssL&lt;/li&gt;&lt;li&gt;4\9: LssLsss&lt;/li&gt;&lt;li&gt;3\10: LsLsLss&lt;/li&gt;&lt;li&gt;3\11: sLsLsLL&lt;/li&gt;&lt;li&gt;5\12: sLLsLLL&lt;/li&gt;&lt;li&gt;2\13: LLLLLLs&lt;/li&gt;&lt;li&gt;2\14: LLLLLLL&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(3, 2)&lt;ul&gt;&lt;li&gt;2\15: ssssssL&lt;/li&gt;&lt;li&gt;7\16: LssLsss&lt;/li&gt;&lt;li&gt;5\17: LsLsLss&lt;/li&gt;&lt;li&gt;5\18: sLsLsLL&lt;/li&gt;&lt;li&gt;7\19: sLLsLLL&lt;/li&gt;&lt;li&gt;3\20: LLLLLLs&lt;/li&gt;&lt;li&gt;3\21: LLLLLLL&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
These periodic patterns occur because the sum of step sizes must equal the edo's order, and for any (L, s) MOS there is only one scale-step pattern.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Accidentals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Accidentals&lt;/h1&gt;
For edos 7(n-1)+1 to 7n, the large step is n edo-intervals, so n-1 unique accidentals of each class (flat or sharp) are required, plus a natural accidental. This ensures that the maximum or minimum accidentals always modify a nominal to a neighboring nominal, as in the double-flats and double-sharps of standard notation.&lt;br /&gt;
&lt;br /&gt;
(To be continued.)&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Scores and score-videos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Scores and score-videos&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=jagxI__W-Mg" rel="nofollow" target="_blank"&gt;//Palinkalin Viharo// (Flowers in the Mist)&lt;/a&gt; by Jake Huryn (&lt;a class="wiki_link_ext" href="https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view" rel="nofollow" target="_blank"&gt;Score&lt;/a&gt;): 22edo&lt;/body&gt;&lt;/html&gt;</pre></div>
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