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Oettingen, Arthur (Joachim) von

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Oettingen, Arthur (Joachim) von

(b Dorpat, Livonia [now Tartu, Estonia], 28 March 1836; d Leipzig, 6 Sept 1920). German scientist and musical theorist. After reading sciences at the University of Dorpat (1853–8), he continued his study of physics, physiology and mathematics in Paris and Berlin (1859–62) and completed his Habilitation (1863) in Dorpat. In 1865 he was appointed associate professor and in 1866 professor of physics; from 1869 to 1874 he was secretary of the Natural Science Academy in Dorpat, and, from 1877, corresponding member of the St Petersburg Academy of Science. In 1894, after the russification of the University of Dorpat (Yuriev), he took his pension and settled in Leipzig, where he was honorary professor at the university until 1919.

In Dorpat, Oettingen was president of a musical association and director of a well-trained amateur orchestra; he wrote many important articles in the field of natural science, and also won recognition as a musical theorist by the publication of his Harmoniesystem in dualer Entwickelung (1866). He developed the idea that major and minor triads and key systems are mirror inversions of each other: that the major triad C–E–G, designated c+, is mirrored by the minor triad C–A–F (reading downward), designated c°. The tonic major scale C–D–E–F–G–A–B–C is mirrored by the phonic scale E–D–C–B–A–G–F–E (reading downward), which is the common A minor scale descending from the dominant. In this arrangement the intervals of the two scales are the same and every triad in the tonic scale is mirrored by a triad of the opposite mode in the phonic scale. If the triads repeat their roots, the phonic chords will all be second inversions in the major-minor system.

Oettingen's principle of organization might be summarized by saying that tonality is the property of intervals or chords having a common fundamental tone called the ‘tonica’, while phonality is the property of intervals or chords possessing a common overtone called the ‘phonica’. In the major chord c'–e'–g' all the sounds find a focus in the difference tone or fundamental tone, C, and in the minor chord c'–e'–g', the fundamental tone is the first common partial tone, g'''. The two fundamentals are each two octaves distant from the roots of their respective chords.

Oettingen designed his dual system as the antithesis to Helmholtz's Lehre von den Tonempfindungen (1863). He believed that Helmholtz was wrong in his concept of consonance and dissonance. Because even a single tone has beats caused by the higher harmonics approaching each other in pitch, he believed that Helmholtz was measuring merely a greater or lesser dissonance. He thought that Helmholtz's approach was negative, and he advocated simply considering dissonance as a positive meeting of two or more different chords, major and minor chords thus being of equal value. As a proponent of just intonation he used in his figuration system a line over the letter name to indicate a tonic major 3rd and a line under the letter name of the phonic major 3rd, making clear his reference to 3rds of 5/4 ratio rather than to the major 3rds of 81/64 ratio used in Pythagorean intonation.


Harmoniesystem in dualer Entwickelung: Studien zur Theorie der Musik (Dorpat and Leipzig, 1866, enlarged 2/1913 as Das duale Harmoniesystem)

‘Die Grundlagen der Musikwissenschaft und das duale Reininstrument’, Abhandlungen der königlichen sächsischen Gesellschaft der Wissenschaften, xxxiv/2 (Leipzig, 1916)


R. Münnich: ‘Von [der] Entwicklung der Riemannschen Harmonielehre und ihrem Verhältnis zu Oettingen und Stumpf’, Riemann-Festschrift (Leipzig, 1909/R), 60–76

M. Vogel: ‘Arthur von Oettingen und der harmonische Dualismus’, Beiträge zur Musiktheorie des 19. Jahrhunderts (Regensburg, 1966), 103–32

P. Rummenhöller: Musiktheoretisches Denken im 19. Jahrhundert (Regensburg, 1967), esp. 83–93

G. Schubert: ‘Zur Kritik der Musiktheorie’, Zeitschrift für Musiktheorie, ii/1 (1971), 35–7

W. Keller: ‘Die Modulationen in Mozarts Fantasie KV 475’, Festschrift Erich Valentin, ed. G. Weiss (Regensburg, 1976), 79–88

R. Devore: ‘Nineteenth-Century Harmonic Dualism in the United States’, Theoria, ii (1987), 85–100




See Opus (i).

Oevering, Rynoldus Popma van.

See Popma van oevering rynoldus.

Ofenbauer, Christian

(b Graz, 24 March 1961). Austrian composer and organist. He studied at the Klagenfurt Conservatory, at the Vienna Musikhochschule with Uhl (1979–82) and Cerha (1982–7), and in Paris (1986) where he was in touch with Boulez. From 1982 to 1987 he worked as an organist at the Votivkirche, Vienna, and as a composer for the experimental drama group TheaterAngelusNovus. He has also performed with the Viennese ensemble Die Reihe. He began working as a freelance editor for Universal Edition in 1985. His teaching appointments have included positions at the Graz Musikhochschule (1986, 1987–91), the University of Giessen (1988, 1991), the Vienna Musikhochschule (from 1989, visiting professor 1991–2) and the Musikhochschule of the Salzburg Mozarteum (visiting professor 1994–7).

Contrasts in Ofenbauer’s work, such as the harsh tonality of the Streichquartettsatz 1997 in comparison to the much gentler music of unordentliche inseln/de la motte fouqué-vertonung (1995), indicate his reluctance to adopt a consistent style. The issue of identity has been a theme in a number of compositions; in Medea (1990–94), for example, the role of the heroine is shared by seven soloists. Later works, such as the violin concerto fancies/fancy papers (1997), show an increasing tendency towards tranquillity and subtle transitions.


Dramatic: Tod des Hektor (Musiktheater, Homer, J.H. Voss, J.W. von Goethe and H. Müller), 1987–; Medea (op, H. Müller), 1990–94; Septet (Hektors Tod), spkr, chbr ens, silent film; SzenePenthesileaEinTraum (op, H. von Kleist), 3 female vv, 3 male vv, spkr, actors, 27 insts, 1999–

Orch: … wie eine Nachtmusik, 1986; Sospir – fragmenté par polyphonie, 1988; Odysseus/Abbruch/Sirenen, pf conc., 1989; 2 int, chbr orch, 1991 [from Medea]; BruchStück 6, 1996; fancies/fancy papers, vn conc., 1997; 2 Frankfurter Preludes, 1997–8

Vocal: Ich bin der Franz (K. Bayer, Ofenbauer), 3 female spkrs, fl, ob, cl, bn, perc, pf, str qt, 1983; 3 Lieder (G. Meyrink), S, fl, cl, perc, pf + cel, vn, vc, 1983; Der Engel ist geschlachtet (A. Gerk), Mez, 3 cl, 3 trbn, perc, cel, pf, str qt, 1995; Kommt, Sirenen Klagt, S, cl, vn, Hammondorg, pf, 1999

Chbr and solo inst: 5 Stücke, org, 1984; Katalog 1, pf, 1985; 2 Stücke, vc, pf, 1985; Katalog 2, pf, 1986; BruchStück 1, vc, 1987; BruchStück 2, pf, 1988; Albumblatt für J.M., pf, 1990; BruchStück 3, va d’amore, vc, Hammond org, pf, 1990; Pf Trio, 1990; Bruchstück 4, 3 vn, prep pf, 1992 [commentary on Medea]; Mechanische Bagatelle, vn, pf, 1993; BruchStück 5, 3 cl, 3 trbn, perc, cel, pf, str qt, 1995; Klavierstück 1995, 1995; unordentliche inseln/de la motte fouqué-vertonung, ens, 1995; Streichquartettsatz 1997, 1997

El-ac: Fatzer Material Frag., 6–10 tapes, 1985; … durchsichtig bewegt … , chbr ens, tape, 1987; Hektors Tod, 16 tapes, 1987 [based on Tod des Hektor]; Katalog 3, 1–20 pf + tape/elecs, 1988; Simultan, pf, telephone message, 1988; Argonautenstudie (Studio per un Argonauta), elec enhanced prep db, 1993; Prolog und Epilog, orch, tape, 1993 [from Medea]; Klage der Persephone bin ich: Sirene, 6 female vv, 12 channel elecs, 1995

Arrs.: A. Berg: Sonata op.1, 1984

Principal publisher: Doblinger



R. Westphal: ‘Christian Ofenbauer – Aufbauen und Abbrechen … das … widersprüchliche komponieren … Widersprüchliche Komponieren’, Wien modern IV: Vienna 1991 (Vienna, 1991), 113ff

R. Busch: ‘Christian Ofenbauer, “Klavierstück 1995” und “Bruchstück IV”: ein fingiertes Gespräch’, Musikprotokoll im steirischen herbst ’96 (Graz, 1996)


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