Rational comma notation: Difference between revisions
Wikispaces>daveryan23 **Imported revision 605224327 - Original comment: ** |
Wikispaces>daveryan23 **Imported revision 605224593 - 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:daveryan23|daveryan23]] and made on <tt>2017-02-01 | : This revision was by author [[User:daveryan23|daveryan23]] and made on <tt>2017-02-01 07:04:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>605224593</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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**Key features of RCN:** | **Key features of RCN:** | ||
Every rational-numbered frequency can be given a notation in this system of the form Lz[x/y] where L is note label, z is octave number, [x/y] is a rational comma comprising prime commas multiplied together. | Every rational-numbered frequency can be given a notation in this system of the form Lz[x/y] where L is a 3-limit note label, z is octave number, [x/y] is a rational comma comprising prime commas multiplied together. | ||
All pitch classes can be represented with a notation L[x/y] | All pitch classes can be represented with a notation L[x/y] | ||
3-limit frequencies have the simplest notations, and have no comma, so their form is Lz or L(-z) for negative octave number, similar to Scientific Pitch Notation | 3-limit frequencies have the simplest notations, and have no comma, so their form is Lz or L(-z) for negative octave number, similar to Scientific Pitch Notation | ||
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Note that this system (Jan 2017) has had the algorithm, the notation style, and the octave numbering amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups. It is recommended to use the style Lz[x/y] set out in the papers above, and not the style from previous drafts! | Note that this system (Jan 2017) has had the algorithm, the notation style, and the octave numbering amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups. It is recommended to use the style Lz[x/y] set out in the papers above, and not the style from previous drafts! | ||
**Prime and Rational Comma examples under DR algorithm:** | |||
__Prime__: | |||
[5] = 80/81 | |||
[7] = 63/64 | |||
[11] = 33/32 | |||
[13] = 26/27 | |||
[17] = 2176/2187 | |||
[19] = 513/512 | |||
__Rational__: | |||
[1/5] = 1/[5] = 81/80 | |||
[35] = [5]*[7] = 35/36 | |||
[5/13] = [5]/[13] = 40/39 | |||
**Notation examples:** | **Notation examples:** | ||
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* Dave Ryan's SoundCloud page: http://soundcloud.com/daveryan23/tracks | * Dave Ryan's SoundCloud page: http://soundcloud.com/daveryan23/tracks | ||
In future work, it is hoped to develop a computer based / online free-JI scoring system where the comma numbers (5, 1/7, 65/77, etc) are annotated directly onto notes in order to retune them from Pythagorean notes. The score would be Pythagorean, and commas used as accidentals to be able to compose in free-JI and enable anyone to make free-JI music online. If anyone wants to help with this project, please contact David Ryan.</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>Rational Comma Notation (RCN)</title></head><body>A system using either plaintext (ASCII) or richtext to notate any frequency in Just Intonation (JI).<br /> | <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>Rational Comma Notation (RCN)</title></head><body>A system using either plaintext (ASCII) or richtext to notate any frequency in Just Intonation (JI).<br /> | ||
Also names the pitch classes, which are notes up to octave equivalence.<br /> | Also names the pitch classes, which are notes up to octave equivalence.<br /> | ||
Developed in 2015-2017 by the musician and music theorist David Ryan<br /> | Developed in 2015-2017 by the musician and music theorist David Ryan<br /> | ||
<ul><li>Paper (pre-print) for defining all the prime commas by algorithm and the basic notation: <!-- ws:start:WikiTextUrlRule: | <ul><li>Paper (pre-print) for defining all the prime commas by algorithm and the basic notation: <!-- ws:start:WikiTextUrlRule:129:http://arxiv.org/abs/1612.01860 --><a class="wiki_link_ext" href="http://arxiv.org/abs/1612.01860" rel="nofollow">http://arxiv.org/abs/1612.01860</a><!-- ws:end:WikiTextUrlRule:129 --> - also compares between some different choices for algorithm.</li><li>Paper (pre-print) for defining how the notation breaks down into components and enables key changes and transposition: <!-- ws:start:WikiTextUrlRule:130:http://arxiv.org/abs/1508.07739 --><a class="wiki_link_ext" href="http://arxiv.org/abs/1508.07739" rel="nofollow">http://arxiv.org/abs/1508.07739</a><!-- ws:end:WikiTextUrlRule:130 --></li></ul>The two links above give the abstract pages on arXiv, and the PDFs are free to download from arXiv.<br /> | ||
<br /> | <br /> | ||
<strong>Rational Comma Notation (RCN)</strong> is a combination of:<br /> | <strong>Rational Comma Notation (RCN)</strong> is a combination of:<br /> | ||
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<br /> | <br /> | ||
<strong>Key features of RCN:</strong><br /> | <strong>Key features of RCN:</strong><br /> | ||
Every rational-numbered frequency can be given a notation in this system of the form Lz[x/y] where L is note label, z is octave number, [x/y] is a rational comma comprising prime commas multiplied together.<br /> | Every rational-numbered frequency can be given a notation in this system of the form Lz[x/y] where L is a 3-limit note label, z is octave number, [x/y] is a rational comma comprising prime commas multiplied together.<br /> | ||
All pitch classes can be represented with a notation L[x/y]<br /> | All pitch classes can be represented with a notation L[x/y]<br /> | ||
3-limit frequencies have the simplest notations, and have no comma, so their form is Lz or L(-z) for negative octave number, similar to Scientific Pitch Notation<br /> | 3-limit frequencies have the simplest notations, and have no comma, so their form is Lz or L(-z) for negative octave number, similar to Scientific Pitch Notation<br /> | ||
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<br /> | <br /> | ||
Note that this system (Jan 2017) has had the algorithm, the notation style, and the octave numbering amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups. It is recommended to use the style Lz[x/y] set out in the papers above, and not the style from previous drafts!<br /> | Note that this system (Jan 2017) has had the algorithm, the notation style, and the octave numbering amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups. It is recommended to use the style Lz[x/y] set out in the papers above, and not the style from previous drafts!<br /> | ||
<br /> | |||
<strong>Prime and Rational Comma examples under DR algorithm:</strong><br /> | |||
<br /> | |||
<u>Prime</u>:<br /> | |||
[5] = 80/81<br /> | |||
[7] = 63/64<br /> | |||
[11] = 33/32<br /> | |||
[13] = 26/27<br /> | |||
[17] = 2176/2187<br /> | |||
[19] = 513/512<br /> | |||
<br /> | |||
<u>Rational</u>:<br /> | |||
[1/5] = 1/[5] = 81/80<br /> | |||
[35] = [5]*[7] = 35/36<br /> | |||
[5/13] = [5]/[13] = 40/39 <br /> | |||
<br /> | <br /> | ||
<strong>Notation examples:</strong><br /> | <strong>Notation examples:</strong><br /> | ||
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<br /> | <br /> | ||
Some music created using this notation is available at:<br /> | Some music created using this notation is available at:<br /> | ||
<ul><li>Dave Ryan's SoundCloud page: <!-- ws:start:WikiTextUrlRule: | <ul><li>Dave Ryan's SoundCloud page: <!-- ws:start:WikiTextUrlRule:131:http://soundcloud.com/daveryan23/tracks --><a class="wiki_link_ext" href="http://soundcloud.com/daveryan23/tracks" rel="nofollow">http://soundcloud.com/daveryan23/tracks</a><!-- ws:end:WikiTextUrlRule:131 --></li></ul><br /> | ||
In future work, it is hoped to develop a computer based / online free-JI scoring system where the comma numbers (5, 1/7, 65/77, etc) are annotated directly onto notes in order to retune them from Pythagorean notes. The score would be Pythagorean, and commas used as accidentals to be able to compose in free-JI and enable anyone to make free-JI music online. If anyone wants to help with this project, please contact David Ryan.</body></html></pre></div> | |||