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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Wikipedia| Ben Johnston (composer) #Staff notation}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-27 06:07:49 UTC</tt>.<br>
: The original revision id was <tt>238917881</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>
<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">
http://adagio.calarts.edu/~msabat/ms/pdfs/EJItext.pdf


[[http://www.google.com/search?q=%22Ben+Johnston%27s+notation%22|Google: "Ben Johnston's notation"]]</pre></div>
'''Ben Johnston's notation''' is a staff notation system for [[just intonation]] developed by composer [[Ben Johnston]], which supports prime harmonics up to and including 31. It is employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered only occasionally in his music.
<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;Ben Johnston's notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
The base notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D|med}} consists of three stacked 4:5:6 chords, i.e. {{dash|F, A, C|med}}, {{dash|C, E, G|med}}, and {{dash|G, B, D|med}} are just major triads. This in turn makes {{dash|C, D, E, F, G, A, B, C|med}} a justly-intonated [[Zarlino|Ptolemy&ndash;Zarlino "intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals:
&lt;!-- ws:start:WikiTextUrlRule:4:http://adagio.calarts.edu/~msabat/ms/pdfs/EJItext.pdf --&gt;&lt;a class="wiki_link_ext" href="http://adagio.calarts.edu/~msabat/ms/pdfs/EJItext.pdf" rel="nofollow"&gt;http://adagio.calarts.edu/~msabat/ms/pdfs/EJItext.pdf&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4 --&gt;&lt;br /&gt;
 
&lt;br /&gt;
{| class="wikitable center-all"
&lt;a class="wiki_link_ext" href="http://www.google.com/search?q=%22Ben+Johnston%27s+notation%22" rel="nofollow"&gt;Google: &amp;quot;Ben Johnston's notation&amp;quot;&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
|+ style="font-size: 105%;" | Accidentals in Johnston's notation
|-
! Symbol !! Ratio !! Symbol !! Ratio
|-
| + || [[81/80]] || &minus; || 80/81
|-
| &#x266F; || [[25/24]] || &#x266D; || 24/25
|-
| 7 || 35/36 || {{invert|7}} || [[36/35]]
|-
| &uarr; || [[33/32]] || &darr; || 32/33
|-
| 13 || [[65/64]] || {{invert|13}} || 64/65
|-
| 17 || [[51/50]] || {{invert|17}} || 50/51
|-
| 19 || 95/96 || {{invert|19}} || [[96/95]]
|-
| 23 || [[46/45]] || {{invert|23}} || 45/46
|-
| 29 || [[145/144]] || {{invert|29}} || 144/145
|-
| 31 || [[31/30]] || {{invert|31}} || 30/31
|}
 
Johnston combines numeric accidentals (7, {{invert|7}}, &uarr;, &darr;, 13, {{invert|13}}, etc.) with sharps (&#x266F;) and flats (&#x266D;) if symbols from both categories are present.
 
A chain of just fifths is given by:
 
... {{dash|F&#x266D;<sup>&minus;&minus;</sup>, C&#x266D;<sup>&minus;&minus;</sup>, G&#x266D;<sup>&minus;&minus;</sup>, D&#x266D;<sup>&minus;&minus;</sup>, A&#x266D;<sup>&minus;</sup>, E&#x266D;<sup>&minus;</sup>, B&#x266D;<sup>&minus;</sup>, F, C, G, D, A<sup>+</sup>, E<sup>+</sup>, B<sup>+</sup>, F&#x266F;<sup>++</sup>, C&#x266F;<sup>++</sup>, G&#x266F;<sup>++</sup>, D&#x266F;<sup>++</sup>, A&#x266F;<sup>+++</sup>, E&#x266F;<sup>+++</sup>, B&#x266F;<sup>+++</sup>|hair|long}} ...
 
with a plus or minus added for every loop around the ends of the core {{dash|F, A, C, E, G, B, D|med}} sequence.
 
The odd harmonic series up to 31 starting on C is given by:
 
{{dash|C, G, E, B&#x266D;<sup>7</sup>, D, F&uarr;, A&#x266D;<sup>13</sup>, B, C&#x266F;<sup>17</sup>, E&#x266D;<sup>19</sup>, F<sup>7+</sup>, F&#x266F;<sup>23+</sup>, G&#x266F;, A<sup>+</sup>, B&#x266D;<sup>29</sup>, B<sup>31</sup>|hair|long}}.
 
Johnston's notation sacrifices some mathematical intuition compared to [[Helmholtz–Ellis notation]], as it bases the natural notes on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer accidentals needed for music that emphasizes the 5-limit.
 
== See also ==
* [[Johnston–Copper notation]]
* [[Helmholtz–Ellis notation]]
* [[Functional Just System]]
* [[Color notation]]
 
== External links ==
* [https://www.kylegann.com/BJNotation.html Kyle Gann - How to Use Ben Johnston's Just Intonation Notation]
* [http://tonalsoft.com/enc/j/johnston.aspx Johnston notation] on the [[Tonalsoft encyclopedia]]
* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]
 
{{Navbox notation}}
 
[[Category:Just intonation]]
[[Category:Notation]]
 
{{Todo| expand }}
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