actuellecd

Track listing detail

Combinations for String Quartet

Tom Johnson

  • Year of composition: 2003
  • Instrumentation: string quartet
  • Commission: Quatuor Bozzini, MaerzMusik

Stereo

ISRC CAA4J2210025

Premiere

  • March 21, 2004, Maerzmusik — Berliner Festspiele, Berlin (Germany)

Performers

Recording

Tilework for String Quartet

Tom Johnson

  • Year of composition: 2003
  • Duration: 9:15
  • Instrumentation: string quartet

Stereo

ISRC CAA4J2210031

  • 44,1 kHz, 16 bits

Tilework for String Quartet is a compilation of all the ways one can tile a line of 12 points by overlapping a single six-note rhythm. The four musicians play these rhythms in canon for 10 minutes in a rapid music requiring great precision. The work was premiered in a KlangAktion concert in Münich in December, 2004.

“Tilework” has to do with fitting together little tiles to fill lines and loops. One can think of this as making mosaics in one dimension, but it is also very much like stringing beads onto necklaces in various patterns. In musical terms, the Tilework series is a collection of compositions in which individual tiles/rhythms fit together into musical sequences without simultaneities, often filling all the available points of a line or a loop.

Since the notes of different motifs come at different moments, it is possible for a single melodic instrument to play several voices at once, so “tiling” was particularly appropriate for unaccompanied melodic instruments. I gradually found so many ways of tiling musical phrases that I could not stop until I had a piece for each instrument of the orchestra. The year of 2002 was devoted almost exclusively to 14 pieces for 14 solo wind and string instruments. Tilework for Five Conductors and One Drummer, Tilework for Piano, and Tilework for String Quartet came later, in 2003.

At first, interlocking one tile with another seemed obvious, sort of like fitting together the pieces of a jigsaw puzzle. As the work went on, however, it became clear that this was not so simple. Sometimes it is not at all obvious how rhythms/tiles link together, and sometimes one can easily see six ways of solving a certain problem, without being sure if some seventh solution might also be possible, and sometimes the discussion can go way beyond the comprehension of musicians. I knew that making a loop of 16 beats by repeating one eight-note rhythm had something to do with group theory, and I was dimly aware that some mathematicians know how to determine the number of unique necklaces of length n possible using beads of m colors, never allowing two beads of the same color to touch, but I certainly hadn’t studied such things. Gradually I was entering a world I didn’t know much about.

As the Tilework project continued, I sometimes stumbled across questions that were as new and interesting for mathematicians as for myself. I owe much to the regular meetings devoted to Mathematical Music Theory at IRCAM in Paris, where I met many mathematicians, particularly Emmanuel Amiot, and Andranik Tangian, who gave me solutions to some problems. In the case of Tilework for String Quartet, which involves ways of tiling the line with six-note rhythms, I am particularly indebted to Harald Fripertinger and his most useful computer list of “rhythmic canons.”

But of course, composers, interpreters, and listeners do not need to know all this, just as we do not need to master counterpoint in order to appreciate a Bach fugue. As always, one of the wonderful things about music is that it allows us to perceive directly things that we would never understand intellectually.

[x-03]

Performers

Recording

Four-Note Chords in Four Voices

Tom Johnson

  • Year of composition: 2009
  • Instrumentation: string quartet

Stereo

ISRC CAA4J2210032

How can we classify musical harmonies? Terms like “major seventh” and “diminished ninth” can mean quite a few different things, and it was not until 1973 that this little problem of musical taxonomy was solved definitively and elegantly in Allen Forte’s book The Structure of Atonal Music. More recently Guerino Mazzola, Elliot Carter and other writers have counted and classified harmonies somewhat differently, but the Forte classifications have become the standard. Theorists today who wish to identify clearly a certain type of chord will not use terms like “minor seventh,” but will distinguish between Forte 4-19 and Forte 4-26.

As a composer I often think about what kinds of harmonies go together and how to place them in groups, and this problem is particularly apparent in the case of four-note chords, because we use them so much and hear them so well. There are 495 ways to distribute 12 notes in groups of four, and thanks to Forte, we now know that they break down into exactly 29 sets. The goal of this composition is to allow listeners to better appreciate the pure harmonic richness of all these combinations of notes and to help them hear the differences between one set and another. Wanting to place the emphasis on harmony itself, without rhythms and colors, I wrote the music simply in half notes in four lines, playable either on keyboard or by a string quartet, but also by other ensembles.

At first it seemed that the piece must have 29 short movements, following Forte’s 29 sets, but this way the music was starting and stopping all the time, and besides, sets like Forte 4-2 and Forte 4-3 sound very similar, because they have the same “bip”. Bip is another Forte term meaning “basic interval pattern,” and in this case the bip is 112, meaning that if you place the four notes as close together as possible, the distance between adjacent notes will be some ordering of 1, 1, and 2 semitones.

The piece is dedicated to Forte, not only in recognition of his important theoretical work, but also because I learned so much from him as a young naïve Yale student in 1959-61.

[i-09]

Performers

Recording

Formulas for String Quartet

Tom Johnson

  • Year of composition: 1994
  • Instrumentation: string quartet

Stereo

ISRC CAA4J2210048

Formulas is the first Johnson string quartet, premiered by the Brindisi Quartet in 1994. It comprise of eight movements, each following a mathematical formula.

“The logic of the Formulas for String Quartet is easily perceived. Even when the music goes by too fast to enable one to count notes and analyze exactly what is happening, one hears that the music is following a strict logical sequence. While composing, it was useful for me to try to define this logic more precisely and mathematically, and it seemed important to do so. I wanted to be able to show that these sequences really are formulas, and that the title is not just a metaphor.“

Performers

Recording