Heptatonic notation
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- This revision was by author jake.huryn and made on 2017-05-12 18:35:20 UTC.
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=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 giving an approximation of their displacement size. From these principles is derived the generating rule behind this notation system: * For each edo, nominals are assigned to the first mode of the [[Maximal evenness|maximally even]] heptatonic [[MOSScales|MOS]]. =Nominals for Different Edos= By finding these particular MOS scales in each edo, we can find that they follow a number of patterns: * (L=1, s=0) ** 1\7: LLLLLLL * (2, 1) ** 1\8: ssssssL ** 4\9: LssLsss ** 3\10: LsLsLss ** 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. =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 nominals, as in the double-flats and double-sharps of standard notation. (To be continued.)
Original HTML content:
<html><head><title>Heptatonic Notation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Purpose and Principles"></a><!-- ws:end:WikiTextHeadingRule:0 -->Purpose and Principles</h1> I developed heptatonic notation in order to notate my microtonal music, which is written in a number of different <a class="wiki_link" href="/edo">edos</a>. A number of principles were followed in the development this notation system. <br /> <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><br /> From these principles I decided that it should be based on <a class="wiki_link" href="/Nominal-Accidental%20Chains">nominal-accidental chains</a>, with seven nominals to an octave. In addition, accidentals should both be based on those of standard notation, and giving an approximation of their displacement size. From these principles is derived the generating rule behind this notation system:<br /> <ul><li>For each edo, nominals are assigned to the first mode of the <a class="wiki_link" href="/Maximal%20evenness">maximally even</a> heptatonic <a class="wiki_link" href="/MOSScales">MOS</a>.</li></ul><br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Nominals for Different Edos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Nominals for Different Edos</h1> By finding these particular MOS scales in each edo, we can find that they follow a number of patterns:<br /> <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><br /> 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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Accidentals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Accidentals</h1> 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 nominals, as in the double-flats and double-sharps of standard notation.<br /> <br /> (To be continued.)</body></html>