6. Work in music theory.

During the period in which Hindemith’s music was outlawed, he had no performing engagements and did no teaching. He concentrated instead on composition and underpinned his creative endeavours with theoretical studies. He began work on Unterweisung im Tonsatz (translated into English as The Craft of Musical Composition) in 1935 and finished and published the first part (Theoretischer Teil) in 1937 (see also Analysis, §II, 4). A second, revised edition appeared in 1940 and a fundamentally revised third edition was planned for the 1950s, but never appeared.

As a theory of musical material, Unterweisung im Tonsatz investigates aspects of pitch from an acoustic perspective and sets out theoretical principles governing the melodic and harmonic relationships of pitches. Hindemith takes two acoustic phenomena as his starting-point: the harmonic series and combination tones. From the harmonic series he derives a melodic series consisting of the 12 notes of the chromatic scale, arranged in the order of their diminishing degree of relationship to the first, given note (Series 1). Ex.1 shows this series in relation to C. From the combination tones he derives a series of intervals arranged in an order of increasing tension (Series 2; ex.2). Thus Series 1 and 2 identify and categorize the tonal relationships that occur in musical structures.

Hindemith refers to Series 2 as the basis of a ‘classification of all chords’, which he systematizes in a ‘Table of Chord-Groups’ comprising two main sections: A, chords not containing a tritone, and B, chords containing a tritone. These are further subdivided according to the position of the root and the size of constituent intervals in each specific construction (i.e. containing 2nds or 7ths, or not, and so on). Harmonisches Gefälle (translated as ‘harmonic fluctuation’ in the English edition) accounts for changes in tension values across a sequence of chords. Hindemith calls a succession of roots supporting a harmonic interpretation a ‘degree-progression’. In his view the primary technique of melodic construction is ‘progression in 2nds’, through which the most important notes of a two-dimensional structure achieve ‘a smooth and convincing melodic outline’. Using the principle of ‘the two-voice framework’, Hindemith describes the inner logic of polyphonic composition, maintaining that the bass line and the next most important line form an immediately understandable two-part texture.

Unterweisung im Tonsatz is written as a critique of traditional theories of harmony and counterpoint, regarded by Hindemith as theories of historical style. Among the premises of traditional teaching methods that he criticizes are the primacy of the diatonic scale, the separation of harmony from melody and technical exercises from free composition, construction in 3rds as the exclusive principle of building chords and the concepts of invertibility, a chord’s susceptibility to a variety of interpretations and alteration. The result of his invocation of acoustics and physical principles is an endorsement of the traditional, historically evolved tonal system, even though he did not recognize it as a historical entity liable to further change. He regarded the core elements of music theory – the nature of tonal relationships, for example – to be immutable, regardless of the extent to which they were understood. On the one hand he attempted to avoid writing a historical theory of style by making the fundamental facts of music correspond to the acoustic properties of pitch combinations, while on the other he was concerned with historical masterworks in which these general principles had been worked out. In the end, he demonstrated in an unmistakably apologetic argument that his principles held true for contemporary music as well as for music of earlier periods.

Unterweisung im Tonsatz both grew out of Hindemith’s compositional practices and had an effect on them. In its original version, the book included an appendix in which he listed those of his own works that best illustrated the development of his theoretical views, even identifying some works that he intended to revise. (The appendix was eliminated from the second edition.) In the early stages of planning the book, he gained theoretical insight from his revision and reworking of songs from Das Marienleben. Above all, he rediscovered harmony as a means of musical expression. He had already, in the symphony Mathis der Maler, put harmonic and tonal relationships at the service of the work’s central idea, elaborating them with appropriate clarity, and now he used more conventional types of chords and chordal progressions in harmonic writing governed by 4ths and open 5ths. While this development may have appeared to embody a return to convention, for him it represented a systematic expansion of compositional means. Subsequent works such as the Violin Concerto (1939), the Cello Concerto (1940) and the Symphony in E (1940) have a markedly traditional character. The expansive, relatively conventional cadences in the Violin Concerto sound as fresh and new as if Hindemith had only just invented them (ex.4).

Hindemith’s examination and substantiation of music theory was expressly served by the series of sonatas for virtually every orchestral instrument that he began to compose in 1935, finally amounting to over 25 works. While these works, especially those composed in the 1930s, create the impression of a well-regulated and standardized compositional technique, thanks to the purest possible operation of the principles of the ‘two-voice framework’, ‘harmonic fluctuation’ and ‘progression in 2nds’, Hindemith gave each of them an individual formal structure. In every case, he tailored the music snugly to the character of the solo instrument so that the sonatas became portraits of the instruments themselves, the music being generated by the unique qualities of each individual timbre.

In the late 1930s, while writing the sonatas, Hindemith was also preparing to write another opera, conceived as a companion piece to Mathis der Maler. Centred on the life and work of the astronomer Johannes Kepler, the opera was to be called Die Harmonie der Welt. Although he had already established the theme of the work and the content of several individual scenes, as well as having undertaken thorough historical research, his emigration to the USA forced him to set the project aside.

Hindemith, Paul