Ben Johnston's notation: Difference between revisions

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~~...a JI notation by the composer [[wikipedia:~~Ben Johnston (composer)~~|Ben Johnston]]~~

~~<ul>~~

'''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.

~~<li>[https://www.kylegann.com/BJNotation.html Kyle Gann - How to Use~~ Ben Johnston's ~~Just Intonation Notation~~]~~</li>~~

~~<li>~~[~~http://tonalsoft.com/enc/j/johnston.aspx Joe Monzo -~~ Johnston ~~notation~~]~~</li>~~

~~<li>[http://www~~.~~marcsabat~~.~~com/pdfs/EJItext.pdf Marc Sabat~~ - ~~On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation~~]~~</li>~~

~~</ul>~~

[~~http~~://~~www~~.~~google~~.~~com~~/~~search?q=%22Ben~~+Johnston~~%27s+~~notation~~%22 Google~~: "Ben Johnston's notation"]

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:

{| class="wikitable center-all"

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

|-

! 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]]

~~[[Category:~~Todo~~:add definition]]~~

@@ Line 1: / Line 1: @@
-...a JI notation by the composer [[wikipedia:Ben Johnston (composer)|Ben Johnston]]
+{{Wikipedia| Ben Johnston (composer) #Staff notation}}
-<ul>
+'''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.
-<li>[https://www.kylegann.com/BJNotation.html Kyle Gann - How to Use Ben Johnston's Just Intonation Notation]</li>
-<li>[http://tonalsoft.com/enc/j/johnston.aspx Joe Monzo - Johnston notation]</li>
-<li>[http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]</li>
-</ul>
-[http://www.google.com/search?q=%22Ben+Johnston%27s+notation%22 Google: "Ben Johnston's notation"]
+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:
+{| class="wikitable center-all"
+|+ 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]]
-[[Category:Todo:add definition]]
+{{Todo| expand }}