Principles and Categories
Hindemith's Unterweisung im Tonsatz: Theoretischer Teil teaches material, not composition. It does not originate in any particular compositional style and then make theoretical generalisations about that style, but instead starts with the natural quality of the tones. It investigates the musically usable tones in terms of acoustics and physics and attempts to theoretically comprehend the fundamental relationships between tones. Hindemith then examines the pre-compositional material, the «working material» with which a composer «builds» his work.
Hindemith proceeds from two acoustic phenomenon: the overtone series, which is contained and characteristically coloured in each sounding tone, and the combination tones which arise as soon as two tones sound together. From the overtone series, Hindemith derives a melodic sequence of relationships between the twelve tones of the chromatic scale which he calls «Series 1.» It has the following diminishing relational sequence:
He derives a sequence of increasing tension of the intervals called «Series 2:»
The melodic and harmonic phenomena systematised and evaluated as «Series 1» and «Series 2» are repeatedly found in all corresponding dimensions of music, described by Hindemith with several novel categories:
– The sequence of tensions of the intervals in «Series 2» substantiates a «Phenomenology of all Sounds.» Hindemith sets up a table for determining chords, arranged into two main groups (A: without the tritone; B: with the tritone), according to the intervallic components (with the second, with the seventh, etc.) and subdivided according to the position of the root.
– «Harmonic fluctuation» is what Hindemith calls the differences in quality and tension that result from a sequence of chords.
– «Degree progression» is what Hindemith calls the succession of roots which carry a larger harmonic context.
– «Step progression» is, according to Hindemith, a main rule of melodic construction; it states that the main tones of a melody must be related to each in steps of seconds.
– The principle of «two-voice framework» states that, in a polyphonic work, the bass voice must form a readily comprehensible two-voice texture with the next most important upper voices.