David Ryan's notation: Difference between revisions
Wikispaces>daveryan23 **Imported revision 566300119 - Original comment: ** |
Wikispaces>daveryan23 **Imported revision 566301293 - 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>2015-11-13 04: | : This revision was by author [[User:daveryan23|daveryan23]] and made on <tt>2015-11-13 04:30:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>566301293</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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* Preprint: http://arxiv.org/pdf/1508.07739 | * Preprint: http://arxiv.org/pdf/1508.07739 | ||
Abstract: | **Abstract:** | ||
Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described. | Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described. | ||
Key features: | **Key features:** | ||
Can be inputted by computer keyboard alone (ASCII characters) | Can be inputted by computer keyboard alone (ASCII characters) | ||
Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied | Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied | ||
| Line 22: | Line 22: | ||
Good for describing all the notes on a 5-limit or 7-limit tone lattice | Good for describing all the notes on a 5-limit or 7-limit tone lattice | ||
Challenges: | **Challenges:** | ||
Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)</pre></div> | Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.) | ||
**Notation examples:** | |||
//2-limit:// | |||
C = 1/1 | |||
`C = 2/1 (definition of octave modifier using ` character to prefix) | |||
,C = 1/2 (definition of octave modifier using , character to prefix) | |||
,,,C = 1/8 | |||
//3-limit:// | |||
F = 4/3 C = 1/1 G = 3/4 D = 9/16 A = 27/64 E = 81/256 B = 243/1024 | |||
Bb = 16/9 | |||
F# = 729/4096 | |||
C# = 2187/16384 (this is equivalent to a sharp # character) | |||
Cb = 16384/2187 (this is equivalent to a flat b character) | |||
`G = 3/2 | |||
```D = 9/2 | |||
//5-limit:// | |||
E' = 5/4 (definition of ' modifier) | |||
Ab. = 4/5 (definition of . modifier) | |||
A' = 4/3 | |||
``E' = 5/1 | |||
`B' = 15/8 | |||
//7-limit// | |||
Bb~7 = 7/8 (definition of ~7 modifier) | |||
D_7 = 8/7 (definition of _7 modifier) | |||
F~7 = 21/16 | |||
`Bb~7 = 7/4 | |||
`F~7 = 21/16 | |||
Eb~7 = 7/6 | |||
//Higher p-limits// | |||
F#~11 = 11/8 (definition of ~11 modifier) | |||
Gb_11 = 8/11 (definition of _11 modifier) | |||
``F#~11 = 11/2 | |||
B~11 = 11/6 | |||
A#'~11 = 55/32 ( 11/8 * 5/4 = F#~11 * E' multiplied as notations) | |||
etc! | |||
The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions or fractions already known. In particular, separating out fractions for each higher prime.</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>David Ryan's notation</title></head><body>A system of notating any fractional frequency in Just Intonation, created by the musician and theorist David Ryan<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>David Ryan's notation</title></head><body>A system of notating any fractional frequency in Just Intonation, created by the musician and theorist David Ryan<br /> | ||
<br /> | <br /> | ||
<ul><li>Preprint: <!-- ws:start:WikiTextUrlRule: | <ul><li>Preprint: <!-- ws:start:WikiTextUrlRule:62:http://arxiv.org/pdf/1508.07739 --><a class="wiki_link_ext" href="http://arxiv.org/pdf/1508.07739" rel="nofollow">http://arxiv.org/pdf/1508.07739</a><!-- ws:end:WikiTextUrlRule:62 --></li></ul><br /> | ||
Abstract:<br /> | <strong>Abstract:</strong><br /> | ||
Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described.<br /> | Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described.<br /> | ||
<br /> | <br /> | ||
Key features:<br /> | <strong>Key features:</strong><br /> | ||
Can be inputted by computer keyboard alone (ASCII characters)<br /> | Can be inputted by computer keyboard alone (ASCII characters)<br /> | ||
Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied<br /> | Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied<br /> | ||
| Line 40: | Line 82: | ||
Good for describing all the notes on a 5-limit or 7-limit tone lattice<br /> | Good for describing all the notes on a 5-limit or 7-limit tone lattice<br /> | ||
<br /> | <br /> | ||
Challenges:<br /> | <strong>Challenges:</strong><br /> | ||
Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)</body></html></pre></div> | Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)<br /> | ||
<br /> | |||
<strong>Notation examples:</strong><br /> | |||
<br /> | |||
<em>2-limit:</em><br /> | |||
C = 1/1<br /> | |||
`C = 2/1 (definition of octave modifier using ` character to prefix)<br /> | |||
,C = 1/2 (definition of octave modifier using , character to prefix)<br /> | |||
,,,C = 1/8<br /> | |||
<br /> | |||
<em>3-limit:</em><br /> | |||
F = 4/3 C = 1/1 G = 3/4 D = 9/16 A = 27/64 E = 81/256 B = 243/1024<br /> | |||
Bb = 16/9<br /> | |||
F# = 729/4096<br /> | |||
C# = 2187/16384 (this is equivalent to a sharp # character)<br /> | |||
Cb = 16384/2187 (this is equivalent to a flat b character)<br /> | |||
`G = 3/2<br /> | |||
```D = 9/2<br /> | |||
<br /> | |||
<em>5-limit:</em><br /> | |||
E' = 5/4 (definition of ' modifier)<br /> | |||
Ab. = 4/5 (definition of . modifier)<br /> | |||
A' = 4/3<br /> | |||
``E' = 5/1<br /> | |||
`B' = 15/8<br /> | |||
<br /> | |||
<em>7-limit</em><br /> | |||
Bb~7 = 7/8 (definition of ~7 modifier)<br /> | |||
D_7 = 8/7 (definition of _7 modifier)<br /> | |||
F~7 = 21/16<br /> | |||
`Bb~7 = 7/4<br /> | |||
`F~7 = 21/16<br /> | |||
Eb~7 = 7/6<br /> | |||
<br /> | |||
<em>Higher p-limits</em><br /> | |||
F#~11 = 11/8 (definition of ~11 modifier)<br /> | |||
Gb_11 = 8/11 (definition of _11 modifier)<br /> | |||
``F#~11 = 11/2<br /> | |||
B~11 = 11/6<br /> | |||
A#'~11 = 55/32 ( 11/8 * 5/4 = F#~11 * E' multiplied as notations)<br /> | |||
etc!<br /> | |||
<br /> | |||
The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions or fractions already known. In particular, separating out fractions for each higher prime.</body></html></pre></div> | |||