String Quartet No. 3 (2010)
This score uses Ben Johnston's system for notating extended Just Intonation. In this notational system, uninflected notes represent a just-tuned C major scale, i.e. the triads C-E-G, F-A-C and G-B-D are all perfect major triads in the ratio 4:5:6. This means that D-A is not a perfect fifth and D-F not a just minor third. The symbols + and - are used to sharpen or flatten notes by a syntonic comma (a ratio of 81:80, about 20 cents) to keep fifths and thirds in tune, so for instance D/A+ and D-/A are perfect fifths, and D/F#+ and D-/F# are just major thirds. The traditional sharp/flat signs raise or lower a note by a ratio of 25:24 (about 70 cents), being the difference between a just major and minor third. The 7 and L symbols flatten and sharpen by 36/35 (about 49 cents), and represent intervals derived from the seventh tone of the harmonic series (the "flat" seventh). Then the arrows up nd down raise and lower by 33/32 (about 53 cents), the difference between a perfect fourth and the "sharp" fourth of th 11th harmonic. Finally the "13" symbol raises (or lowers when upside down) by 65/64 (about 7 cents), this being the difference between a minor sixth and the lightly sharper sixth of the 13th harmonic.
If this all sounds terribly confusing, don't worry! The thing to remember is to listen to the other players and tune yourself with them as accurately as possible. And remember that there are no enharmonic equivalents: e.g. D sharp is not the same note as E flat, but is slightly flatter, G double-sharp is slightly flatter than A, etc. etc.
The first movement traces a single line, with harmony implied by overlapping each tone in the sequence. Until the very end, the score contains only two types of note head: the white one signifies a long note, tied to a black one which signifies a short note. The long notes should be played in a single bow stroke (as long as possible), while the black note should be held long enough to establish a harmony with the player who plays the next long note. The last phrase in the viola and cello should not be played too fast.
The second movement is a sequence of chords. The players work their way through these, keeping more or less to the same group of notes as each other (though some overlap is inevitable and fine). Each player may play any combination or repetition of any of the notes in the group being played, at any register and in free rhythm. When the final single "E" is reached, the players play repeated notes and then gradually play a single held note. When everyone is playing a sustained note, this should be held for a while before the movement ends. Where the notes in a bar are presente as two chords rather than one, this is just for clarity, to show how some tones relate to earlier ones. These bars should b approached in the same way as the others.
In the final movement, the players begin all playing repeated "G"s, then proceed independently through the following sequence of note-pairs, playing each pair over and over at their own speed (but probably a fairly regular pulse). The players should probably try not to get more than four pairs apart from each other. When each player reaches the penultimate sequence (with repeat marks), they remain playing it until all four players are playing that sequence. Then each player completes the sequence and moves to the final held "G". When everyone is playing the final note, hold it for a while and then fade out.
The recording above is an ersatz version - it's a multi-track rcording using all cellos rather than a proper quartet lineup. It's a bit rough but should give you the idea.
If this all sounds terribly confusing, don't worry! The thing to remember is to listen to the other players and tune yourself with them as accurately as possible. And remember that there are no enharmonic equivalents: e.g. D sharp is not the same note as E flat, but is slightly flatter, G double-sharp is slightly flatter than A, etc. etc.
The first movement traces a single line, with harmony implied by overlapping each tone in the sequence. Until the very end, the score contains only two types of note head: the white one signifies a long note, tied to a black one which signifies a short note. The long notes should be played in a single bow stroke (as long as possible), while the black note should be held long enough to establish a harmony with the player who plays the next long note. The last phrase in the viola and cello should not be played too fast.
The second movement is a sequence of chords. The players work their way through these, keeping more or less to the same group of notes as each other (though some overlap is inevitable and fine). Each player may play any combination or repetition of any of the notes in the group being played, at any register and in free rhythm. When the final single "E" is reached, the players play repeated notes and then gradually play a single held note. When everyone is playing a sustained note, this should be held for a while before the movement ends. Where the notes in a bar are presente as two chords rather than one, this is just for clarity, to show how some tones relate to earlier ones. These bars should b approached in the same way as the others.
In the final movement, the players begin all playing repeated "G"s, then proceed independently through the following sequence of note-pairs, playing each pair over and over at their own speed (but probably a fairly regular pulse). The players should probably try not to get more than four pairs apart from each other. When each player reaches the penultimate sequence (with repeat marks), they remain playing it until all four players are playing that sequence. Then each player completes the sequence and moves to the final held "G". When everyone is playing the final note, hold it for a while and then fade out.
The recording above is an ersatz version - it's a multi-track rcording using all cellos rather than a proper quartet lineup. It's a bit rough but should give you the idea.