View source for Ben Johnston's notation

{{Wikipedia| Ben Johnston (composer) #Staff notation}}

'''Ben Johnston's notation''' is a staff notation system for [[just intonation]]. [[Ben Johnston]] developed it up to the [[31-limit]], employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered mostly incidentally in his music.

The natural notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D|s=hair|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash|F, A, C|s=hair|d=med}}, {{dash|C, E, G|s=hair|d=med}}, and {{dash|G, B, D|s=hair|d=med}} are just major triads. Then the following accidentals are used for inflections, all of which denote [[superparticular]] ratios or their reciprocals:

{| class="wikitable center-all"
|+ Accidentals in Johnston's notation
|-
! Symbol !! Ratio !! Symbol !! Ratio
|-
| + || [[81/80]] || &#x2212; || 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 the symbols 7 {{invert|7}} ↑ ↓ with sharps (♯) and flats (♭) if symbols from both categories are present.

A circle of just fifths is given by:

... {{dash|G♭<sup>&#x2212;&#x2212;</sup>, D♭<sup>&#x2212;&#x2212;</sup>, A♭<sup>&#x2212;</sup>, E♭<sup>&#x2212;</sup>, B♭<sup>&#x2212;</sup>, F, C, G, D, A<sup>+</sup>, E<sup>+</sup>, B<sup>+</sup>, F♯<sup>+</sup><sup>+</sup>, C♯<sup>+</sup><sup>+</sup>|s=hair|d=long}} ...

with a plus or minus added for every loop around the ends of the core F A C E G B D sequence.

The odd harmonic series up to 31 starting on C is given by:

{{dash|C, G, E, B♭<sup>7</sup>, D, F↑, A♭<sup>13</sup>, B, C♯<sup>17</sup>, E♭<sup>19</sup>, F<sup>7+</sup>, F♯<sup>23+</sup>, G♯, A<sup>+</sup>, B♭<sup>29</sup>, B<sup>31</sup>|s=hair|d=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.

== 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]]

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