Johnston–Copper notation: Difference between revisions

'''Johnston-Copper notation''' is a [[musical notation]] system for [[just intonation]] based on [[Ben Johnston's notation]] but extended by means of {{W|key signature}}s. This is the notation used by [[William Copper]] in the works composed by the techniques of [[intonalism]].

When the music demands a note to be tuned differently than the 'basis' then special accidentals are used: an altered sharp sign, an altered flat sign, two altered natural signs (up and down) and two neutral signs (up and down). In Johnston-Copper Notation each such change is exactly a comma, the specific comma indicated by the ratio 81/80 and often called a [[syntonic comma]].

In Johnston's hand-engraved score the neutral sign looks somewhat like a thick dash or hyphen; in Copper's notation, made with the Score computer engraving program ([[scor4]]) , it is an arrow with a flag at the top (used for the 'down one comma' neutral indication). Both are used for exactly the same purpose: in C major, Johnston's score, the note D if unaltered would sound too high, since it is tuned by default as a perfect fifth above the G according to the three 4:5:6 chords. in beginning as he does, he wants the D to be tuned lower and in fact, tuned exactly to the open D string. In D major, Copper's score, the equivalent note is an E , a perfect fifth above the A according to the same three 4:5:6 chords in D major; and for the same reason, the note E if unaltered would sound too high in bar 3 if not altered down by a comma. This gives a first orientation toward understanding how Johnston's notation is modified by Johnston-Copper notation: the addition of a key signature changes which notes need alteration. Copper's notation in C major is identical to Johnston's, with the minor difference of symbol designs.

To indicate a 'neutral' comma higher, Johnston uses two symbols: the same thick dash or hyphen plus a small arrow pointing up. In Johnston-Copper Notation, this symbol is condensed into the simpler flagged arrow pointing up. Johnston also uses (especially in later works, such as the 6th string quartet) a modified sharp sign with a down arrow; Johnston-Copper notation uses the same symbol to indicate a note that is 'sharp', according to the key signature, and tuned down by a comma. In a flat key, such a note is indicated by a natural sign modified to add a small down arrow on the lower 'leg' of the natural sign. When a note is modified by a flat sign and at the same time must be tuned higher by a comma it is notated as a flat sign with an additional up-pointing arrow head. In a sharp key, such a note is indicated by a natural sign modified to add a small up arrow on the upper 'leg' of the natural sign. It is an interesting feature of just intonation, pointed out by Mozart in one of his letters to his father, that "flat notes are tuned sharp and sharp notes are tuned flat". For this reason, there is very rarely a need to indicate a "sharp note tuned sharp" or a "flat note tuned flat". In these rare instances, the notation used is the combination of a sharp sign with a preceding up arrow sign, or a flat sign with a preceding down arrow sign. Almost always, such notation is found when the sharp or flat is simply used to return to the base key, but the music requires a high-tuned note in the base key (for the sharp) or a low-tuned note in the base key (for the flat).

* [[Functional just system]]

* [[Helmholtz-Ellis notation]]