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GEGENSTREBIGE HARMONIK IN THE MUSIC OF HANS ZENDER ROBERT HASEGAWA HE GERMAN COMPOSER and conductor Hans Zender is a prominent figure in the world of contemporary European music. His music is played by orchestras and ensembles across Europe and, as a conductor, he has been a strong advocate for other composers, including Giacinto Scelsi and Helmut Lachenmann. Like many composers born in the 1930s, he was strongly influenced by the post-Webernian serialism of the fifties and sixties; later, though, he developed a strong interest in stylistic pluralism (inspired in part by one of his compositional heroes, Bernd-Alois Zimmermann), including a dialogue with music of the past, as evidenced in works like Dialog mit Haydn (1982), Schuberts Winterreise: Eine komponierte Interpretation (1993), and SchumannFantasie (1997). Other major influences on his music include East Asian music—Muji no Kyo (1975), Lo-Shu I–VII (1977–97)—and the poetry of Friedrich Hölderlin: Hölderlin lesen I–IV (1979–2001). T 208 Perspectives of New Music Since the late 1990s, Zender has been increasingly concerned with the possibility of combining the standard equal-tempered pitch gamut with the pure sounds of just intonation intervals (intervals with simple whole-number ratios between their frequencies). As Zender notes, For many music lovers it is a revelation to discover that intervals like the just major third or natural seventh have a luminosity, which compared to the color of a tempered interval is like a radiant red compared to a muddy red-brown.1 This revival of interest in pure intonation is inspired by the combination of a number of influences: Zender specifically mentions the role of the period performance movement in familiarizing listeners with just intonation, but one might also consider the work of American just intonation pioneers like Harry Partch and Ben Johnston, or the exploration of higher overtones by French spectralist composers.2 Zender used just ratios in works as early as the 1976 Litanei for three cellos, but they began to take a more central role in Shir hashirim, a 1996 setting of the Biblical Song of Songs.3 According to Zender, the work’s harmonic language is based on “the experience of the difference between equally tempered and ‘natural’ intervals of the spectrum.”4 Shir hashirim does not offer a synthesis of the two approaches to interval, but seeks rather to emphasize their uneasy coexistence. As Zender writes, The logically unsolvable problem of mediating between the overtone series and the equidistant scale, between the perception of qualities and linear, quantitative thinking appears in the harmony of Shir hashirim as a paradox: a gegenstrebige Harmonik (a harmony of opposing tensions).5 Zender expanded upon the theoretical underpinnings of this new approach in his 2000 lecture “Gegenstrebige Harmonik,” delivered at the Darmstadt International Summer Courses for New Music. The concept of gegenstrebige Harmonik is inspired by Heraclitus’s Fragment 51: “They do not understand how that which differs with itself is in agreement: harmony consists of opposing tensions, like that of the bow and the lyre.”6 The physical harmony of the bow and lyre is based on the tension inherent in their construction. The bent bow pulls the bowstring in opposite directions, keeping it taut; similarly, the strings of the lyre are kept tight, allowing them to sound. Gegenstrebige Harmonik in the Music of Hans Zender 209 Heraclitus underlines the way that contrary forces, rather than destroying harmony by their conflict, can instead produce harmony when they balance one another. In Shir hashirim, as in later works, these “opposing tensions” arise from two fundamentally different ways of conceiving intervals between pitches. One is the equal-tempered, quantitative world of symmetrical, equal octave subdivisions; the other is the just-intonation, qualitative world of frequency ratios. Thinking in terms of temperament is useful in conceptualizing abstract geometries (epitomized by twelve-tone music or pitch-class set theory), while thinking in terms of frequency draws our attention to an interval’s sonic quality: for example, the specific acoustical consonance of a just 5:4 major third. Zender writes: In principle, no mediation is possible between these two manifestations of the interval; hearing pure (perfect) intervals is an experience of quality, while hearing tempered...