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Ryan ASCII notation: Difference between revisions

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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>2016-12-15 06:19:09 UTC</tt>.<br>
: This revision was by author [[User:daveryan23|daveryan23]] and made on <tt>2016-12-15 06:29:59 UTC</tt>.<br>
: The original revision id was <tt>602219214</tt>.<br>
: The original revision id was <tt>602219946</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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//Individual notes://
//Individual notes://
E'4 = E4[5] = 5/4
E'4 = E4[5] = 5/4
Ab4. = Ab4[1/5] = 4/5
Ab.4 = Ab4[1/5] = 4/5
A'4 = 5/3
A'4 = A4[5] = 5/3
Db.4 = 16/15
Db.4 = Db4[1/5] = 16/15


__//7-limit//__
__//7-limit//__
//Octave equivalence classes://
//Octave equivalence classes://
Bb~7 = {...7/16, 7/8, 7/4, 7/2, 7/1, 14/1...}
Bb~7 = Bb[7] = {...7/16, 7/8, 7/4, 7/2, 7/1, 14/1...}
D_7 = {...1/14, 1/7, 2/7, 4/7, 8/7, 16/7...}
D_7 = D[1/7] = {...1/14, 1/7, 2/7, 4/7, 8/7, 16/7...}
//Individual notes://
//Individual notes://
`0Bb~7 = 7/8 (definition of ~7 modifier)
Bb4[7] = 7/4
`0D_7 = 8/7 (definition of _7 modifier)
D4[7] = 8/7
`0F~7 = 21/16
F4[7] = 21/16
`Bb~7 = 7/4
Eb4[7] = 7/6
`F~7 = 21/16
`0Eb~7 = 7/6


__//Higher p-limits//__
__//Higher p-limits//__
`0F#~11 = 11/8 (definition of ~11 modifier)
F4[11] = 11/8
`0Gb_11 = 8/11 (definition of _11 modifier)
A4[13] = 13/8
``F#~11 = 11/2
C#4[17] = 17/16
`0B~11 = 11/6
Eb4[19] = 19/16
`0Ab~13 = 13/16 (definition of ~13 modifier)
F#4[23] = 23/16
`0C#~17 = 17/16
Bb4[29] = 29/16
`0Eb~19 = 19/16
C4[31] = 31/32 (which is itself a prime comma!)
`0F#~23 = 23/32
D4[37] = 37/32
etc (separate definition for each prime) and octave equivalence classes can be found using the procedure above.
Notations can be derived for p/2^n for all higher p, using the prime comma algorithm.


**Calculation examples**
**Other links**
The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions; fractions with notation already known. In particular, separate out the fractions for each higher prime.


55/32 = (11/8)*(5/4) = `0F#~11 * `0E' = `0A#'~11
Calculation examples are given in the second paper listed above.
7/5 = (7/8)*(4/5)*(2/1) = `0Bb~7 * `0Ab. * `1C = `1Bb.~7 * `0Ab = `1Gb.~7
30/1 = (2/1)*(3/1)*(5/1) = (32/1)*(3/4)*(5/4) = `````C * `0G * `0E' = `````G' * `0E = `````B' (Notice how modifiers ` for octave and ' for prime 5 can be moved about freely)
19/13 = (19/16) * (16/13) = `0Eb~19 * (`0Ab~13)^-1 = `0Eb~19 * `0E_13 = `0G~19_13


Calculating using octave equivalence classes is easier, since you don't have to keep track of the powers of two:
55/32 class = 5 class * 11 class = E' * F#~11 = A#'~11
7/5 class = 7 class * (1/5) class = Bb~7 * Ab. = Gb.~7
**Other links**
Some music created using this notation is available at:
Some music created using this notation is available at:
* Dave Ryan's SoundCloud page: https://soundcloud.com/daveryan23/tracks</pre></div>
* Dave Ryan's SoundCloud page: https://soundcloud.com/daveryan23/tracks</pre></div>
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Also names the pitch classes, which are notes up to octave equivalence.&lt;br /&gt;
Also names the pitch classes, which are notes up to octave equivalence.&lt;br /&gt;
Developed in 2015-2016 by the musician and music theorist David Ryan&lt;br /&gt;
Developed in 2015-2016 by the musician and music theorist David Ryan&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Paper (pre-print) for defining all the prime commas by algorithm and the basic notation: &lt;!-- ws:start:WikiTextUrlRule:117:http://arxiv.org/abs/1612.01860 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/1612.01860" rel="nofollow"&gt;http://arxiv.org/abs/1612.01860&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:117 --&gt;&lt;/li&gt;&lt;li&gt;Paper (pre-print) for defining how the notation breaks down into components and enables key changes and transposition: &lt;!-- ws:start:WikiTextUrlRule:118:http://arxiv.org/abs/1508.07739 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/1508.07739" rel="nofollow"&gt;http://arxiv.org/abs/1508.07739&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:118 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Paper (pre-print) for defining all the prime commas by algorithm and the basic notation: &lt;!-- ws:start:WikiTextUrlRule:103:http://arxiv.org/abs/1612.01860 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/1612.01860" rel="nofollow"&gt;http://arxiv.org/abs/1612.01860&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:103 --&gt;&lt;/li&gt;&lt;li&gt;Paper (pre-print) for defining how the notation breaks down into components and enables key changes and transposition: &lt;!-- ws:start:WikiTextUrlRule:104:http://arxiv.org/abs/1508.07739 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/abs/1508.07739" rel="nofollow"&gt;http://arxiv.org/abs/1508.07739&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:104 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;strong&gt;Abstract (for 2 papers above):&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Abstract (for 2 papers above):&lt;/strong&gt;&lt;br /&gt;
In Just Intonation every rational frequency has a prime factorisation. This can be reconstructed from an approximate 3-limit component, and a series of microtonal 'prime comma' adjustments, one for each higher prime (5 and above) present in the original prime factorisation. Each prime comma is of the form [p] = 2^a 3^b p. This means that different prime commas don't interact, which is helpful for notation since the effect of each higher prime is separated out, which will aid mapping between notations and frequencies. Prime commas are assigned by algorithm. The algorithm performs a tradeoff between using low numbers in the comma fraction, and keeping the comma as small as possible. All commas are microtonal, less than a semitone, the widest comma is thought to be [13]=26/27. Commas are only considered between a specific set of bounds for 3^b, since larger values of b become unmusical. Plaintext (ASCII) nnotations are defined of the form Lz[x/y] which have alternative forms in richtext. The notation breaks down into a set of four components: octave number, diatonic scale note, sharps/flats, prime commas or rational comma. This aids inversion, multiplication, division of notations, and enables transposition of music into any other key.&lt;br /&gt;
In Just Intonation every rational frequency has a prime factorisation. This can be reconstructed from an approximate 3-limit component, and a series of microtonal 'prime comma' adjustments, one for each higher prime (5 and above) present in the original prime factorisation. Each prime comma is of the form [p] = 2^a 3^b p. This means that different prime commas don't interact, which is helpful for notation since the effect of each higher prime is separated out, which will aid mapping between notations and frequencies. Prime commas are assigned by algorithm. The algorithm performs a tradeoff between using low numbers in the comma fraction, and keeping the comma as small as possible. All commas are microtonal, less than a semitone, the widest comma is thought to be [13]=26/27. Commas are only considered between a specific set of bounds for 3^b, since larger values of b become unmusical. Plaintext (ASCII) nnotations are defined of the form Lz[x/y] which have alternative forms in richtext. The notation breaks down into a set of four components: octave number, diatonic scale note, sharps/flats, prime commas or rational comma. This aids inversion, multiplication, division of notations, and enables transposition of music into any other key.&lt;br /&gt;
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&lt;em&gt;Individual notes:&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;Individual notes:&lt;/em&gt;&lt;br /&gt;
E'4 = E4[5] = 5/4&lt;br /&gt;
E'4 = E4[5] = 5/4&lt;br /&gt;
Ab4. = Ab4[1/5] = 4/5&lt;br /&gt;
Ab.4 = Ab4[1/5] = 4/5&lt;br /&gt;
A'4 = 5/3&lt;br /&gt;
A'4 = A4[5] = 5/3&lt;br /&gt;
Db.4 = 16/15&lt;br /&gt;
Db.4 = Db4[1/5] = 16/15&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;em&gt;7-limit&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
&lt;u&gt;&lt;em&gt;7-limit&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
&lt;em&gt;Octave equivalence classes:&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;Octave equivalence classes:&lt;/em&gt;&lt;br /&gt;
Bb~7 = {...7/16, 7/8, 7/4, 7/2, 7/1, 14/1...}&lt;br /&gt;
Bb~7 = Bb[7] = {...7/16, 7/8, 7/4, 7/2, 7/1, 14/1...}&lt;br /&gt;
D_7 = {...1/14, 1/7, 2/7, 4/7, 8/7, 16/7...}&lt;br /&gt;
D_7 = D[1/7] = {...1/14, 1/7, 2/7, 4/7, 8/7, 16/7...}&lt;br /&gt;
&lt;em&gt;Individual notes:&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;Individual notes:&lt;/em&gt;&lt;br /&gt;
`0Bb~7 = 7/8 (definition of ~7 modifier)&lt;br /&gt;
Bb4[7] = 7/4&lt;br /&gt;
`0D_7 = 8/7 (definition of _7 modifier)&lt;br /&gt;
D4[7] = 8/7&lt;br /&gt;
`0F~7 = 21/16&lt;br /&gt;
F4[7] = 21/16&lt;br /&gt;
`Bb~7 = 7/4&lt;br /&gt;
Eb4[7] = 7/6&lt;br /&gt;
`F~7 = 21/16&lt;br /&gt;
`0Eb~7 = 7/6&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;u&gt;&lt;em&gt;Higher p-limits&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
&lt;u&gt;&lt;em&gt;Higher p-limits&lt;/em&gt;&lt;/u&gt;&lt;br /&gt;
`0F#~11 = 11/8 (definition of ~11 modifier)&lt;br /&gt;
F4[11] = 11/8&lt;br /&gt;
`0Gb_11 = 8/11 (definition of _11 modifier)&lt;br /&gt;
A4[13] = 13/8&lt;br /&gt;
``F#~11 = 11/2&lt;br /&gt;
C#4[17] = 17/16&lt;br /&gt;
`0B~11 = 11/6&lt;br /&gt;
Eb4[19] = 19/16&lt;br /&gt;
`0Ab~13 = 13/16 (definition of ~13 modifier)&lt;br /&gt;
F#4[23] = 23/16&lt;br /&gt;
`0C#~17 = 17/16&lt;br /&gt;
Bb4[29] = 29/16&lt;br /&gt;
`0Eb~19 = 19/16&lt;br /&gt;
C4[31] = 31/32 (which is itself a prime comma!)&lt;br /&gt;
`0F#~23 = 23/32&lt;br /&gt;
D4[37] = 37/32&lt;br /&gt;
etc (separate definition for each prime) and octave equivalence classes can be found using the procedure above.&lt;br /&gt;
Notations can be derived for p/2^n for all higher p, using the prime comma algorithm.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Calculation examples&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Other links&lt;/strong&gt;&lt;br /&gt;
The golden rule in this notation is: to derive notation for a more complicated fraction, break it down into simpler fractions; fractions with notation already known. In particular, separate out the fractions for each higher prime.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
55/32 = (11/8)*(5/4) = `0F#~11 * `0E' = `0A#'~11&lt;br /&gt;
Calculation examples are given in the second paper listed above.&lt;br /&gt;
7/5 = (7/8)*(4/5)*(2/1) = `0Bb~7 * `0Ab. * `1C = `1Bb.~7 * `0Ab = `1Gb.~7&lt;br /&gt;
30/1 = (2/1)*(3/1)*(5/1) = (32/1)*(3/4)*(5/4) = &lt;!-- ws:start:WikiTextRawRule:00:```` --&gt;&lt;!-- ws:end:WikiTextRawRule:00 --&gt;`C * `0G * `0E' = &lt;!-- ws:start:WikiTextRawRule:01:```` --&gt;&lt;!-- ws:end:WikiTextRawRule:01 --&gt;`G' * `0E = &lt;!-- ws:start:WikiTextRawRule:02:```` --&gt;&lt;!-- ws:end:WikiTextRawRule:02 --&gt;`B' (Notice how modifiers ` for octave and ' for prime 5 can be moved about freely)&lt;br /&gt;
19/13 = (19/16) * (16/13) = `0Eb~19 * (`0Ab~13)^-1 = `0Eb~19 * `0E_13 = `0G~19_13&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Calculating using octave equivalence classes is easier, since you don't have to keep track of the powers of two:&lt;br /&gt;
55/32 class = 5 class * 11 class = E' * F#~11 = A#'~11&lt;br /&gt;
7/5 class = 7 class * (1/5) class = Bb~7 * Ab. = Gb.~7&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Other links&lt;/strong&gt;&lt;br /&gt;
Some music created using this notation is available at:&lt;br /&gt;
Some music created using this notation is available at:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Dave Ryan's SoundCloud page: &lt;!-- ws:start:WikiTextUrlRule:119:https://soundcloud.com/daveryan23/tracks --&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/daveryan23/tracks" rel="nofollow"&gt;https://soundcloud.com/daveryan23/tracks&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:119 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;Dave Ryan's SoundCloud page: &lt;!-- ws:start:WikiTextUrlRule:105:https://soundcloud.com/daveryan23/tracks --&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/daveryan23/tracks" rel="nofollow"&gt;https://soundcloud.com/daveryan23/tracks&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:105 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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