Johnston–Copper notation: Difference between revisions

Line 13:

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).

To distinguish the cases when an altered sharp or a normal sharp is required, the same 5-limit basis as the diatonic scale dictates the usage. To stay in a chromatic key-based just intonation, we use a normal sharp sign for the sharp 4th of the key and the sharp root of the key. In C major, of course, these are F# and C#. Continuing higher by fifths (this process often called following the Pythagorean spine), the succeeding sharps must be identified by an altered sharp sign, the sharp with a small arrow on the lower right leg. Thus, the sharp 5th, sharp 2nd, sharp 6th, sharp 3rd, sharp 7th, etc. In C major, these are vG#, vD#, vA#, vE#, vB# using the usual convention when typing, with the preceding 'v' indicating a comma-low marking.

In the same way, the cases for an altered flat or a normal flat follow the 5-limit basis of the diatonic scale: the flat 7th uses a normal flat sign. From the flat third, continuing lower by fifths, the usual tuning will require an altered flat for the 3rd, 6th, 2nd, 5th, etc. In C major, these become Bb (ordinary flat) then ^Eb, ^Ab, ^Db, ^Gb, ^Cb, and the preceding '^' indicates a comma-high marking.

Because in practice music rarely stays purely diatonic or completely centered on the same harmonies, any particular individual moment of music may require a tuning that is different than the just intonation basis. When a comma higher than the altered sharp sign would indicate is needed, the notation uses a regular sharp sign. When a comma lower than the altered flat sign would indicate is needed, the notation uses a regular flat sign. It is very rare that a tuning is needed that is two commas higher than the altered sharp sign, or two commas lower than the altered flat sign, but in such cases an additional comma modifier may be used. It is not uncommon, however, for a musical moment to require a comma ''higher'' than the altered flat or ''lower'' than the altered sharp, and in the notation being described here the relevant accidental is 'decorated' with two small arrow heads, up in the case of the double high flat or down in the case of the double low sharp.

@@ Line 13: / Line 13: @@
 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).
+To distinguish the cases when an altered sharp or a normal sharp is required, the same 5-limit basis as the diatonic scale dictates the usage.  To stay in a chromatic key-based just intonation, we use a normal sharp sign for the sharp 4th of the key and the sharp root of the key.  In C major, of course, these are F# and C#.  Continuing higher by fifths (this process often called following the Pythagorean spine), the succeeding sharps must be identified by an altered sharp sign, the sharp with a small arrow on the lower right leg.  Thus, the sharp 5th, sharp 2nd, sharp 6th, sharp 3rd, sharp 7th, etc.  In C major, these are vG#, vD#, vA#, vE#, vB# using the usual convention when typing, with the preceding 'v' indicating a comma-low marking.
+In the same way, the cases for an altered flat or a normal flat follow the 5-limit basis of the diatonic scale: the flat 7th uses a normal flat sign.  From the flat third, continuing lower by fifths, the usual tuning will require an altered flat for the 3rd, 6th, 2nd, 5th, etc.  In C major, these become Bb (ordinary flat) then ^Eb, ^Ab, ^Db, ^Gb, ^Cb, and the preceding '^' indicates a comma-high marking.
+Because in practice music rarely stays purely diatonic or completely centered on the same harmonies, any particular individual moment of music may require a tuning that is different than the just  intonation basis.  When a comma higher than the altered sharp sign would indicate is needed, the notation uses a regular sharp sign.  When a comma lower than the altered flat sign would indicate is needed, the notation uses a regular flat sign. It is very rare that a tuning is needed that is two commas higher than the altered sharp sign, or two commas lower than the altered flat sign, but in such cases an additional comma modifier may be used.  It is not uncommon, however, for a musical moment to require a comma ''higher'' than the altered flat or ''lower'' than the altered sharp, and in the notation being described here the relevant accidental is 'decorated' with two small arrow heads, up in the case of the double high flat or down in the case of the double low sharp.