Canonic Offerings

Videos of the performances can be found here.

Musician biographies can be found here.

CALLENDER    Canonic Offerings

T'ang Quartet

Ng Yu-Ying, violin

Ang Chek-meng, violin

Lionel Tan, viola

Leslie Tan, cello

TYMOCZKO    S Sensation Something (world premiere)

T'ang Quartet

Ng Yu-Ying, violin

Ang Chek-meng, violin

Lionel Tan, viola

Leslie Tan, cello

Jacob Abela, piano

J.S. BACH/EMMERSON    Goldberg Variations for two pianos

Bernard Lanskey, piano

Stephen Emmerson, piano

Canonic Offerings

Canonic Offerings is based on my work with canons that have an infinite number of solutions. These are maximally self-similar melodic lines that can be combined successfully and performed simultaneously by any number of voices, each voice at its own tempo yielding either rational or irrational tempo ratios, with the melody moving either forward or backward. In Canonic Offerings I have selected a small number of these combinations based on three such melodies, attempting to give the flavor of the combinatorial possibilities within the context of a unified (and finite) composition.

Introduction

Canon 1

canon 4:3:1

Canon 2 sempre accelerando

canons 2:1, 9:6:4, 11:8

Canon 3

cannons 7:5, 4:3

Cannon 4 sempre ritardando, sempre accelerando, sempre accelerando e ritardando

canon  , table canon 2:3 ritardando against 2:3 accelerando

Canon 5

round 24:12:7:3 (48:24:12:7)

— Clifton Callender

S Sensation Something

S Sensation Something is a kind of private diary, a network of allusions and references to musical, theoretical, and mathematical ideas that have intrigued me over the past few years.  The first third of the piece is a canon that evokes well-known progressions from popular music, implicitly suggesting that we can learn to hear the structure latent in those original sources.  The last third builds on a well-known association between pitch and rhythm, with each chord or scale exemplifying the groove it represents.  Sprinkled in between are various other allusions, both cryptic and overt, including a slow passage based on the sound of a laser printer, a rhythmic joke about quintuplets and salsa music, and the impossible project of approximating one collection of notes with another.

What is the listener supposed to take from all this?  That is the question implicit in the title, which refers to the philosopher Wittenstein's famous (and obscure) meditation on language, communication, and privacy.  I’ll be perfectly content if most listeners ignore my associations, experiencing the music as an exotic trip through a succession of psychedelic musical spaces.  But I am also happy to welcome a smaller and more dedicated group into my private compositional workshop, inviting them to examine in detail the more esoteric thinking behind the notes.

In this sense, I think the piece summarizes my feelings about the relation between theory (or mathematics) and music.  Personally, I am not so interested in pieces that wear their conceptual motivations on their sleeves, like a theorem expressed in notes; instead I like my theory buried and subterranean, a rigorous starting point that has been polished, defaced, rethought, and embellished to the point where it is only occasionally apparent, like a fossilized skeleton protruding through the surface of the earth.

Is it worthwhile in the end? Are these conceptual structures just a kind of trick I play to create the illusion that my notes have some extra meaning? In the end, that’s close to the question I want to pose. This piece, like much classical music, is about the sense of a meaningfulness that we can only partially grasp—the poetry of an impossible language always just beyond us. — Dmitri Tymoczko

Goldberg Variations for Two Pianos

Johann Sebastian Bach's Aria with Thirty Variations, BWV 988, usually referred to as the Goldberg Variations, is universally recognised as a landmark in Western music. Beyond being the most substantial keyboard work of the 18th century, the set is widely admired for its virtuosic and ingenious counterpoint as well as its rigorous architectural organisation and construction. Surprisingly, for around two centuries it was viewed as a collection of rather arcane counterpoint exercises and relatively rarely performed but, especially since Glenn Gould’s notorious 1955 recording, its dazzling textures and wide expressive range have since made it among his most popular works, certainly on record. (In this respect it resembles the case of Vivaldi’s Four Seasons whose popularity is again surprisingly recent.) Charles Rosen has even referred to it as Bach’s most successful work in performance. Originally composed for a two-manual harpsichord, the popularity of the Goldberg Variations has largely been as a work played on piano but the reduction to one keyboard does raise certain difficulties. This arrangement of the work for two pianos (made by Stephen Emmerson in 2012) reimagines the work by exploiting the sense of dialogue between the pianists to clarify the relationships between the contrapuntal lines (and adding some extra ones!). As such, it sits within a rich and vibrant tradition of arranging the Goldberg Variations for different instrumental combinations (that have included string trio, jazz trio, brass or wind quintet, harp, guitars to name just a few). — Stephen Emmerson