Ben Johnston's notation: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference: ~~

~~: This revision was by author [[User:xenwolf~~|~~xenwolf]] and made on <tt>2011-06-27 06:27:14 UTC</tt>. ~~

~~: The original revision id was <tt>238919263</tt>. ~~

~~: The revision comment was: <tt></tt> ~~

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. ~~

~~<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 JI~~ notation ~~by the composer [[http://en.wikipedia.org/wiki/Ben_Johnston_%28composer%29|Ben Johnston]]~~

* http://tonalsoft.~~com/enc/j/johnston~~.~~aspx~~

'''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.

* 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>~~

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–Zarlino "intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals:

~~<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>Ben~~ Johnston's notation</~~title~~></~~head~~><~~body>...a JI notation by the composer <a class="wiki_link_ext" href="http:~~//~~en.wikipedia.org~~/~~wiki~~/~~Ben_Johnston_%28composer%~~29~~" rel="nofollow">Ben~~ Johnston</a><~~br /~~>

{| class="wikitable center-all"

<~~br /~~>

|+ style="font-size: 105%;" | Accidentals in Johnston's notation

<ul><li>~~<!-- ws:start:WikiTextUrlRule:11:http:~~/~~/tonalsoft.com/enc/j/johnston.aspx --~~><~~a class="wiki_link_ext" href="http://tonalsoft.com/enc/j/johnston.aspx" rel="nofollow"~~>~~http:~~/~~/tonalsoft.com/enc/j/johnston.aspx~~</a><~~!-- ws:end:WikiTextUrlRule:11 --~~></li><li><~~!-- ws:start:WikiTextUrlRule:12:http:~~//~~adagio.calarts.edu~~/~~~msabat~~/ms/~~pdfs~~/~~EJItext.pdf --~~><~~a class="wiki_link_ext" href="http:~~//~~adagio.calarts.edu~~/~~~msabat/ms/pdfs/EJItext.pdf" rel="nofollow"~~>~~http:~~/~~/adagio~~.~~calarts~~.~~edu/~msabat/ms/pdfs/EJItext~~.~~pdf~~</a><~~!-- ws:end:WikiTextUrlRule:12 --~~></li></ul>~~<br~~ /~~>~~

|-

~~<a class~~=~~"wiki_link_ext" href~~=~~"http~~://www.~~google~~.com/~~search?q=%22Ben+Johnston%27s+notation%22" rel="nofollow">Google: &quot;~~Ben Johnston's notation~~&quot;<~~/~~a><~~/~~body><~~/~~html><~~/~~pre></div>~~

! Symbol !! Ratio !! Symbol !! Ratio

|-

| + || [[81/80]] || − || 80/81

|-

| ♯ || [[25/24]] || ♭ || 24/25

|-

| 7 || 35/36 || {{invert|7}} || [[36/35]]

|-

| ↑ || [[33/32]] || ↓ || 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}}, ↑, ↓, 13, {{invert|13}}, etc.) with sharps (♯) and flats (♭) if symbols from both categories are present.

A chain of just fifths is given by:

... {{dash|F♭−−, C♭−−, G♭−−, D♭−−, A♭−, E♭−, B♭−, F, C, G, D, A+, E+, B+, F♯++, C♯++, G♯++, D♯++, A♯+++, E♯+++, B♯+++|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♭7, D, F↑, A♭13, B, C♯17, E♭19, F7+, F♯23+, G♯, A+, B♭29, B31|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]

[[Category:Just intonation]]

[[Category:Notation]]

@@ Line 1: / Line 1: @@
-<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 06:27:14 UTC</tt>.<br>
-: The original revision id was <tt>238919263</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">...a JI notation by the composer [[http://en.wikipedia.org/wiki/Ben_Johnston_%28composer%29|Ben Johnston]]
-* http://tonalsoft.com/enc/j/johnston.aspx
+'''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.
-* 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>
+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:
-<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;...a JI notation by the composer &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Ben_Johnston_%28composer%29" rel="nofollow"&gt;Ben Johnston&lt;/a&gt;&lt;br /&gt;
+{| class="wikitable center-all"
-&lt;br /&gt;
+|+ style="font-size: 105%;" | Accidentals in Johnston's notation
-&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:11:http://tonalsoft.com/enc/j/johnston.aspx --&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/j/johnston.aspx" rel="nofollow"&gt;http://tonalsoft.com/enc/j/johnston.aspx&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:11 --&gt;&lt;/li&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:12: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:12 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+|-
-&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>
+! 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 }}