After Hindemith

For piano trio.

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Writers, poets and visual artists regularly make reference to masterworks of the past and those who created them. Composers do so less often, and all too rarely acknowledge it when they do! In this single movement piano trio the reference to a major composer of the 20C is embedded in the music’s very mode of construction, essentially exploring a composer’s working method in the light of the new computer tools able to prototype musical design. There’s no attempt here to reflect the chosen composer’s sound world or theoretical aspects surrounding his music, purely his approach to getting to that point where specific thematic material begins to appear.
After Hindemith is also a reflection on the medium of the piano trio in our time. In its composition two very particular influences were present: Beethoven’s Op.1 No.2 trio in which the composer boldy moves away the model his teacher Haydn invented; Alexander Goehr’s remarkable Piano Trio which explores that composer’s discovery of American music, and Charles Ives in particular. Nigel Morgan’s piano trio was written for Martin Storey and the Gould Trio. Paul Hindemith, as far as we know, never wrote a piano trio . . .

from the manuscript of Hindemith’s Hérodiade (Moldenhauer Archives).

Paul Hindemith was not only an extraordinarily prolific composer but an important theorist and teacher. In Eckart Richter’s essay ‘A Glimpse into the Workshop of Paul Hindemith’ there is a description of Hindemith’s working method as presented to a class at Yale in 1951. Hindemith later ‘converted’ this procedure into a guide for listening in a lecture he gave at the University of Zurich in 1955. This ‘working method’ involved a 4 stage process:

1. The general determination of the character, medium and the basic purpose of the piece, as well as its expressive character, and even place of performance.

2. A master plan of formal design, including the overall shape, the number and character of sections, changes in mode and tempo, rhythmic character, texture and the degree of activity, the gauge being the amount of effort the listener must expend to comprehend.

3. Then ‘came the tonal layout in which the basic tonalities of each section and their relative degrees of tonal stability and complexity, as well as the modulations, were mapped by means of a diagram.’

4. Specific thematic material.

Plan for After Hindemith, showing handwritten and algorithmically composed( Symbolic Composer) sections.

My piano trio adopts Hindemith’s 4-stage process, but with a contemporary twist: the integration of algorithmic techniques with traditional methods of composition. The music is a sequence of playful ‘sections’ (algorithmically composed with a computer) with more meditative ‘episodes and interludes’ (freely composed on paper).

Testing Hindemith’s approach in a real musical composition (rather than a student exercise) proved a formative part of my collaboration with information scientist Professor John Cook in realization of a guided tutor for students of music composition called MetaMuse. This has been described as A Teaching Agent for Supporting Musical Reflection and Self-Explanation and developed in Lisp using for its musical routines the Symbolic Composer application. You can read more about their work on this unique project here.

Alongside the notated study score of this work there is also a separate volume containing a detailed analysis and annotation of the computer code used to create the four ‘sections’ that intersperse the ‘episodes and interludes’. After Hindemith is unique in being one of the few computer-mediated scores of Nigel Morgan that truly integrates freely-imagined music with material of a more speculative and generative nature. Its composition closely follows Hindemith’s 4-stage approach as described here:
After an initial ‘imagined’ introductory statement (shown above) a number of tonality patterns were devised and
chosen from a 3-note figure: a combination of 4 ascending minor triads (in arpeggio), 4 ascending dominant seventh chords (in arpeggio), and two positions of the octotonic scale acting as a binding mechanism. The whole rhythmic and instrumental design was then drafted on graph paper followed by a tonal layout. Then, finally, specific thematic material was created.

Several sections in the music make extensive use of palindromes, a devise that can be most elegantly explored using simple computer algorithms. Here, it is not only the melodic and rhythmic material that often mirrors itself but the tonality structure too. Notice in the example above that in creating a mirror image of the pitch collections the content is not reversed, just their order, so – using symbolic notation here – (a b c) (d e f) (g a) would become (a b c) (d e f) (g a) (d e f) (a b c). Also, in the example above, the musical material swaps either side of the pivot bar from violin to cello and vice versa.

As the sections progress the complexity of the harmonic rhythm and content is gradually reduced. In each instrumental part a kind of feedback loop is created with a device that simulates an evolutionary process. Short fragments of melodic material are generated from a white noise algorithm, assembled together and fed back into the evolving device; the outcome being that eventually all but one element is discarded. In the final section, as the harmonic material simplifies still further, articulation, bowing and timbre come under the direct control and organization of computer algorithms to create a web of new sound combinations and textures.

Downloads

Study score [pdf]

Instrumental Parts [zip] (4mb)

Reference Recording [mp3]

Annotated SCOM Code [pdf]