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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>2016-03-19 04:04:03 UTC</tt>.<br>
: This revision was by author [[User:daveryan23|daveryan23]] and made on <tt>2016-12-15 06:06:38 UTC</tt>.<br>
: The original revision id was <tt>577873835</tt>.<br>
: The original revision id was <tt>602218512</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>
<h4>Original Wikitext content:</h4>
<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">A system of using ASCII characters / computer-friendly input to notate **any fractional frequency** in Just Intonation (JI).
<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">A system using either plaintext (ASCII) or richtext to notate any frequency in Just Intonation (JI).
Also a system for naming **octave equivalence classes** in JI.
Also names the pitch classes, which are notes up to octave equivalence.
Created by the musician and theorist David Ryan
Developed in 2015-2016 by the musician and music theorist David Ryan
* Paper (pre-print) for defining all the prime commas by algorithm and the basic notation: http://arxiv.org/abs/1612.01860
* Paper (pre-print) for defining how the notation breaks down into components and thus transposition: http://arxiv.org/abs/1508.07739


* Preprint: http://arxiv.org/pdf/1508.07739
**Abstract (for 2 papers above):**
 
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. 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.
**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. The paper (link above) 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. Also the differences between exact note names and note names up to octave equivalence are discussed.


**Key features:**
**Key features:**
Can be inputted by computer keyboard alone (ASCII characters)
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 of prime commas multiplied together.
Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied
All pitch classes can be represented with a notation L[x/y]
Simple notations exist for 3-limit, 5-limit, 7-limit JI notes
3-limit frequencies have the simplest notations, and have no comma
Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc)
3-limit notations correspond to notes on a standard musical stave, which may need one or more sharps or flats
Algorithm for deriving these notations
The plaintext version of the notation can be inputted by computer keyboard alone (ASCII characters)
Very compact notation for octave equivalence classes
Can transpose any JI music into any other key, by multiplying notations together. (In a computerised stave, this could be automated)
Good for describing all the notes on a 5-limit or 7-limit tone lattice
Shorthand exists for 5-limit notations such as L' = L[5], L'' = L[25], L. = L[1/5], etc
Shorthand exists for pitch classes, of form L~a_b which is the same pitch class as L[x/y]
These shorthands allow the 7-limit tone lattice of pitch classes (3-dimensional) to be drawn accurately in ASCII


**Challenges:**
Note that this system (Dec 2016) is amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups on the algorithm, notation style, and octave numbering.
For some notations it might not be clear whether exact frequencies or octave equivalence classes are being referenced.
- The suggested solution is to always include an item of octave information when the exact note is being described. E.g. use `0C for 1/1, not C
For a series of notes in ascending order of frequency, the octave numbering is not sequential.
- An example: the scale (1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1) has notations (`0C `1D' `0E' `0F `1G `0A' `1B' `1C) - the octave numbers are not sequential.


**Notation examples:**
**Notation examples:**
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* Dave Ryan's SoundCloud page: https://soundcloud.com/daveryan23/tracks</pre></div>
* Dave Ryan's SoundCloud page: https://soundcloud.com/daveryan23/tracks</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ryan ASCII notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A system of using ASCII characters / computer-friendly input to notate &lt;strong&gt;any fractional frequency&lt;/strong&gt; in Just Intonation (JI).&lt;br /&gt;
<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;Ryan ASCII notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A system using either plaintext (ASCII) or richtext to notate any frequency in Just Intonation (JI).&lt;br /&gt;
Also a system for naming &lt;strong&gt;octave equivalence classes&lt;/strong&gt; in JI.&lt;br /&gt;
Also names the pitch classes, which are notes up to octave equivalence.&lt;br /&gt;
Created by the musician and theorist David Ryan&lt;br /&gt;
Developed in 2015-2016 by the musician and music theorist David Ryan&lt;br /&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:112: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:112 --&gt;&lt;/li&gt;&lt;li&gt;Paper (pre-print) for defining how the notation breaks down into components and thus transposition: &lt;!-- ws:start:WikiTextUrlRule:113: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:113 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Preprint: &lt;!-- ws:start:WikiTextUrlRule:113:http://arxiv.org/pdf/1508.07739 --&gt;&lt;a class="wiki_link_ext" href="http://arxiv.org/pdf/1508.07739" rel="nofollow"&gt;http://arxiv.org/pdf/1508.07739&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:113 --&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:&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. 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;
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. The paper (link above) 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. Also the differences between exact note names and note names up to octave equivalence are discussed.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Key features:&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Key features:&lt;/strong&gt;&lt;br /&gt;
Can be inputted by computer keyboard alone (ASCII characters)&lt;br /&gt;
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 of prime commas multiplied together.&lt;br /&gt;
Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied&lt;br /&gt;
All pitch classes can be represented with a notation L[x/y]&lt;br /&gt;
Simple notations exist for 3-limit, 5-limit, 7-limit JI notes&lt;br /&gt;
3-limit frequencies have the simplest notations, and have no comma&lt;br /&gt;
Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc)&lt;br /&gt;
3-limit notations correspond to notes on a standard musical stave, which may need one or more sharps or flats&lt;br /&gt;
Algorithm for deriving these notations&lt;br /&gt;
The plaintext version of the notation can be inputted by computer keyboard alone (ASCII characters)&lt;br /&gt;
Very compact notation for octave equivalence classes&lt;br /&gt;
Can transpose any JI music into any other key, by multiplying notations together. (In a computerised stave, this could be automated)&lt;br /&gt;
Good for describing all the notes on a 5-limit or 7-limit tone lattice&lt;br /&gt;
Shorthand exists for 5-limit notations such as L' = L[5], L'' = L[25], L. = L[1/5], etc&lt;br /&gt;
Shorthand exists for pitch classes, of form L~a_b which is the same pitch class as L[x/y]&lt;br /&gt;
These shorthands allow the 7-limit tone lattice of pitch classes (3-dimensional) to be drawn accurately in ASCII&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Challenges:&lt;/strong&gt;&lt;br /&gt;
Note that this system (Dec 2016) is amended from previous drafts (e.g. Sept 2015) due to feedback from relevant Facebook groups on the algorithm, notation style, and octave numbering.&lt;br /&gt;
For some notations it might not be clear whether exact frequencies or octave equivalence classes are being referenced.&lt;br /&gt;
- The suggested solution is to always include an item of octave information when the exact note is being described. E.g. use `0C for 1/1, not C&lt;br /&gt;
For a series of notes in ascending order of frequency, the octave numbering is not sequential.&lt;br /&gt;
- An example: the scale (1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1) has notations (`0C `1D' `0E' `0F `1G `0A' `1B' `1C) - the octave numbers are not sequential.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;Notation examples:&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Notation examples:&lt;/strong&gt;&lt;br /&gt;
Retrieved from "https://en.xen.wiki/w/Ryan_ASCII_notation"