![]() ![]() ![]() This raises the question of what exactly makes traditional harmony so universally understandable, despite the fact that there exist alternate systems that are based on fundamental acoustics. But, audiences often find that traditional harmony is more palatable to their ears than the perceived dissonances in Hindemith’s music. The examination of Hindemith’s formulation of tonality and harmony based on Series 1 yields a valuable insight – “traditional” harmony is not based on natural acoustic phenomena (as Series 1 is) and is thus no more “natural” than Hindemith’s harmony is. Series 1 thus serves as a starting point to build on Hindemith’s own interpretation of the theory of harmony. Chords have a measurable relationship to tonic and therefore a specific purpose within a tonality. It then becomes possible to measure the “closeness” of a certain note or sonority to a given tonic by examining its root’s relative position according to Series 1. If the tones of Series 1 are considered to be not single pitches but rather roots of chords, then the hierarchy applies to harmonic relations. Harmonic and melodic power of the intervalsįrom Series 1 Hindemith also formulates his concept of tonality. With Series 1, the tone Bb occupies a specific hierarchical position in the C series, more related to C than those tones which follow it in the series and less related than those preceding it. For example, the tone Bb, in the key of C major, would in traditional harmonic theory have only an indirect or derived meaning as a “borrowed” sonority or as the seventh of a secondary dominant (dominant in the region of F major). Series 1 gives meaning to tones which would otherwise have no place in the diatonic major/minor system other than as chromatically altered tones. This series of tones should not be considered to show the mutual relationship between any given tones, but rather only the relation of each tone to the fundamental tone. The twelve tones are arranged in a series according to their supposed relationship to a given fundamental tone, in order of diminishing degree of relationship to that tone. From the overtone series, Hindemith derives a melodic sequence of relationships between the twelve tones of the chromatic scale which he calls Series 1. Hindemith began with two acoustic phenomena: the overtone series, which is contained in each sounding tone, and the combination tones which arise as soon as two tones sound together. Ludus Tonalis uses what Hindemith called “Series 1”. In this system, the major–minor duality is meaningless and the practice of modulation is dropped. Hindemith believed that roots are supports of larger harmonic structures, and as such they must exhibit tonal coherence if the chord-successions which take place above them are to be understandable. The affinity of each note with the keynote is directly related to its position on the harmonic scale. ![]() Ludus Tonalis can be thought of as the most direct application of Hindemith’s theory that the twelve tones of the equally tempered scale all relate to a single tone (called a tonic or keynote). Notably, the piece begins with a Praeludium in C, in the style of Bach’s toccatas, and ends with a Postlodium that is an exact retrograde inversion of the Praeludium. Unlike Bach’s work, however, the non-fugal pieces in Ludus Tonalis frequently repeat the work’s main theme. This piece was intended to be a 20th century equivalent to The Well-Tempered Clavier. In 1942, Hindemith composed his work “ Ludus Tonalis – Kontrapunktische, tonale, und Klaviertechnische Übungen “ (Tonal Game – Counterpoint, tonal and technical studies for the piano). One such composer is Paul Hindemith, a prolific German composer perhaps best known for his advocacy of the Neue Sachlichkeit (New Objectivity) style of music in the 1920s, with compositions such as Kammermusik (which is in fact reminiscent of Bach’s famous Brandenburg Concerto), including works with viola as solo instruments in a “neo-Bachian” spirit. It is thus no surprise that The Well-Tempered Clavier served as an inspiration to modern composers, who built on Bach’s model by adding in their distinct flavours. This work influenced a variety of now renowned composers from disparate musical periods – Mozart, Chopin (who was inspired to write his 24 Preludes, Op.28 by this piece) and Shostakovich (his 24 Preludes and Fugues are one of the few works that attempt to come close to Bach’s model). Few works in the Western classical canon carry the unique distinction of influencing a multitude of composers across eras, as Bach’s The Well-Tempered Clavier. ![]()
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