Isotropes

(2002)
For Piano Quartet

Duration: ca. 10 minutes

First performances:

December 5, 2003
at Los Angeles Harbor College &

December 7, 2003
 at Pacific Unitarian Church

as part of the The South Bay Chamber Music Society
2003 - 2004 Concert Series

by:

Thies Piano Quartet

Robert Edward Thies - piano
Roger Wilkie - violin
Brian Dembow - viola
Cécilia Tsan - violoncello

Special thanks to:

Robert Edward Thies, a brilliant pianist, friend
and supporter of my work.  Without his encouragement
this piece would not exist.

Program Notes

The title of this work does not refer to a misspelled scientific term relating to atomic particles, but rather to musical ideas of the Middle Ages. The main concept on which this piano quartet is based is the Medieval process of troping. Essentially a trope is a new section of music and/or text which is interpolated between an existing plainchant. Although it is unknown at what time and place this procedure began, it appears in some of the oldest music manuscripts still in existence. This indicates that troping was in use by the late eighth or early ninth centuries and it continued to prosper through the twelfth century. Notker Balbulus “the Stammerer” (ca. 840-912), the best known author of tropes suggested that by adding new text to a melisma (i.e. a series of notes sung on a single syllable) it was used as a pneumatic device to help singers remember melodies. These new texts often augment or embellish the original (i.e. Kyrie elesion - Lord have mercy - becomes Kyrie Orbis factor elesion - Lord, creator of the world, have mercy). As the process flourished, new music was added to the chants and in some instances both new text and melodies were used to elaborate chants to the point that whole new genres of liturgical music were created.

Isotropes employs the processes of melodic troping along with other Medieval musical procedures by applying it to an ensemble of a much later period, the classic piano quartet. Essentially a 17-measure theme is presented and troped in various ways throughout the piece.

Another important compositional device of the Middle Ages is isorhythm. This procedure involves two elements: the talea - a rhythmic pattern and the color - a melodic pattern. For example, the talea could be 10 notes long while the color might consist of 30 notes. If one were to apply the melody to the rhythmic pattern, it would take three repetitions of the talea to equal one presentation of the color. This process plays in important role in the latter half of the present work, albeit in a more complicated manner.

The final Medieval concept used extensively in Isotropes is the mensuration canon. Fundamentally, this is the presentation of a melodic idea which is imitated by the other voices in an ensemble but these new presentations are occurring at different rhythmic intervals. For example, a few beats after the first melody begins, the next line enters but is half as fast (i.e. original is in quarter note values and the second line is in half notes). Then another voice enters at 150% of the rate of the original (i.e. dotted quarter notes against the original). This gives the impression of concurrent multiple tempos. However, in keeping with the concept of troping in this piano quartet, these canons are themselves troped, but not necessarily by melodic material of the same rhythmic value.

Obviously, the title of this work comes from a combination of the words isorhythm and trope. However iso is a generic prefix which in its simplest form means similar, but not quite the same. Just as in science an isotope is an atom of the same atomic number but with a different mass number than its “normal” version. Thus the title Isotropes gives some indication to the informed listener of what compositional devices are employed in the work while eluding to the familiar scientific term.



Isotropes begins with a mensural device although it is not a strict canon. The violin and viola both begin on the natural harmonic of their open D strings and ascend and descend between the harmonics on their four open strings each a fifth apart. The violin is moving in dotted half note values while the viola maintains strict wholes. Almost immediately the piano enters with a minimalist figure which gradually expands one measure at a time until it is six measures long. Over this hypnotic tapestry of sound, the cello presents the first half of the main theme (m.11). The upper strings then meet back at their opening D harmonics and play the second half of the theme in harmony while the cello reverts to an accompanimental role (m. 19). A bass ostinato in the cello and piano propels (m. 29) the piece forward leading the piano to present an ornamented version of the whole theme with the other instruments becoming more prominent throughout this embellished restatement. Virtually all of the material presented in this short 90-second introduction comprises the musical gestures which appear in various guises in the rest of the work.

The bass ostinato sets up the development of the following musical ideas: the main theme, the expanding minimalist piano figure, the open string harmonics, and the ostinato itself. The latter is the first to be developed (m. 48) as a mensuration canon with the piano playing it two (right hand) against one (left hand) against one and a half in the cello. The violin then plays the theme with the viola troping it at various breaks with the expanding minimalist figure. In the midst of this, the piano breaks the canon by restating previous gestures in the right hand while maintaining the ostinato figure with the cello.

The middle section (mm. 83-150) of the piece involves the troped mensuration cannons. The cello begins with half note values, followed by the viola in dotted quarter notes and the violin performing in quarter notes. All of these are troped by fragments of the minimalist figure but in various note values, with some presented as retrogrades. The left hand of the piano plays an non-troped version of the theme in whole note values in octaves with periodic presentations of the minimalist figure in the right hand.

Following the troped canon is an Interlude in which the piano performs a solo variation of the theme that in the latter portion makes use of the minimalist pattern by placing it in rapid sixteenth notes in the bass against the melody.

The concluding half of the work (m. 168) is based around isorhythmic principles by employing the theme and its isorhythmic variations as a cantus firmus (fixed tune) that appears throughout the four instruments. The main theme is heard once again in the violin with the other strings playing polyphonically against it in the style of a viol consort while deriving its melodic ideas from the minimalist pattern and retrogrades of the main theme. The isorhythmic variations are set up as follows. Since the theme begins and ends with the same pitch D, the color (i.e. the melodic pattern) omits the final D thus creating an elision with the next repetition. In other words, the final note and the beginning note become one and the same. Since there is one less note in the melodic pattern now and the corresponding talea (i.e. the rhtyhmic pattern) stays the same, the theme sounds familiar but the rhythms line up differently. Each instrument plays an isorhythmic cell in the following order: violin, cello, viola and left hand of the piano. Continuing this process, four more isorhythmic presentations ensue in the same order. Several figures derived from the theme, the minimalist pattern, the open string harmonics, and the ostinato are set contrapuntally against these isorhythmic variations. There is an important melody which is formed by taking small fragments of the theme and the minimalist gesture. It appears several times in the latter half of the work. The piece ends with this new tune played by the violin and right hand of the piano with a subsequent repetition that is harmonized by the viola while the left hand of the piano performs the last isorhythmic variation with the cello playing the ostinato in dotted quarter note values bringing the piece to a dramatic conclusion.
 

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