(b 5 Nov 1933). Guatemalan composer. He studied at the National Conservatory of Music and was violinist in the National SO for many years. He distinguished himself as an important new composer early in his career. In 1958 El jardín encantado was awarded first prize in the annual Central American Science, Letters and Fine Arts Competition. In 1965 his String Trio was commissioned by the Third Inter-American Music Festival and first performed there in Washington, DC. These earlier works were essentially tonal, the String Trio using pan-diatonicism. In the 1970s he began experimenting with flujos sonoro-sociales, recombinations on tape of ambient sound peculiar to the sonorous landscape of Guatemala. Two of his first and most successful compositions using this approach are Electroacústica and Imposible a la X: historia en redondo (1976), both presented in several international forums. An aleatory approach characterizes Híbrido a presión (1982) for two flutes, several specially created instruments and magnetic tape. He also investigated the sonorous possibilities of the Guatemalan marimba, considered the national instrument, by constructing new instruments from fragments of the marimba grande. These original instruments, which carry such names as ciclo-im, rastra-son and pandemarimbas, reproduce and expand certain aspects of the marimba's timbre, especially its percussive attack. Tzulumanachí (1974) features one of these, a sonarimba. Especially notable among these works is Evocación profunda y traslaciones de una marimba (1984), scored for marimba, narrator, mixed chorus, magnetic tape and several original marimba-derived instruments.
(bNormandy, c1320; d Lisieux, 1382). French philosopher and mathematician. He is recognized as the leading mathematician of his day. He studied at the University of Paris and took the MA in 1356. He served as Grand Master of the College of Navarre in Paris (1356–62) and held a series of ecclesiastical posts leading to his appointment as Bishop of Lisieux in 1377, a post he held until his death. He wrote on a wide range of topics, including theology, physics, magic and economics, frequently drawing from writers such as Plato, Aristotle, Boethius and Cassiodorus.
Oresme’s observations on music arose from his studies of mathematics and physics. Along with the mathematician Gersonides, Oresme expanded Plato’s series of ‘harmonic numbers’ (Timaeus, 35ff) to include two endless series of numbers based on multiples of two or three. He developed Gersonides’s theory, proposing that all proportions between the two series are ‘harmonic ratios’, although he acknowledged that only four proportions produce consonant intervals. In his commentary on Aristotle’s De caelo, written at the request of Charles V of France, Oresme arranged these numbers in a grid pattern (see illustration) and stated that ‘this figure is full of very great mysteries and from it we can draw extremely attractive and marvelous conclusions, for it contains virtually the whole formation of speculative music’ (Le livre du ciel et du monde, ii.18; Menut and Denomy, 478–81). He commented on harmonic numbers in several treatises, including his study of motion Tractatus de configurationibus qualitatum et motuum (ii.17) and his Algorismus proportionum (iii). Oresme wrote on other philosophical issues related to music, such as whether the movements of heavenly bodies produce sounds (Le livre du ciel et du monde, ii.18) and the relationship between sound and magic (Tractatus de configurationibus, ii.25). In his commentary on Aristotle’s Politics (viii.6–14) he set out his ideas of harmonic numbers and expounded on Aristotle’s views with quotations from the scriptures, Pythagoras, Boethius and other sources. The term ‘harmonic number’ is also found in Johannes Boen’s Musica. Oresme was in contact with the leading musical theorists and mathematicians of his day: he dedicated his Algorismus proportionum to Philippe de Vitry and discussed mathematical issues that were also of interest to Johannes de Muris.
Tractatus de commensurabilitate vel incommensurabilitate motuum celi (MS, early 1350s); ed. and trans. E. Grant as Nicole Oresme and the Kinematics of Circular Motion (Madison, WI, 1971)
Tractatus de configurationibus qualitatum et motuum (MS, early 1350s); ed. and trans. M. Clagett as Nicole Oresme and the Medieval Geometry of Qualities and Motions (Madison, WI, 1968)
Le livre de politiques d’Aristote (MS, 1374); ed. A.D. Menut (Philadelphia, 1970)
Le livre du ciel et du monde (MS, 1377); ed. A.D. Menut and A.J. Denomy (Madison, WI, 1968)
E.E.Lowinsky: ‘Music in the Culture of the Renaissance’, Journal of the History of Ideas, xv (1954), 509–53, esp. 543; repr. in Renaissance Essays, ed. P.O. Kristeller and P.P. Wiener (New York, 1968), 337–81
V.P.Zubov: ‘Nicole Oresme et la musique’, Mediaeval and Renaissance Studies, v (1961), 96–107
M.Clagett: ‘Oresme, Nicole’, Dictionary of Scientific Biography, ed. C.C. Gillispie (New York, 1970–80)
F.Della Stella: ‘Scienza e filosofia nella teoria musicale dell’Ars Nova in Francia’, NRMI, x (1976), 357–83
E.Grant: ‘Oresme, Nicole’, Dictionary of the Middle Ages, ed. J. Strayer (New York, 1982–9)
W.Frobenius: ‘Numeri armonici: die Zahlen der Timaios-Skala in der Musiktheorie des 14. Jahrhunderts’, Kontinuität und Transformation der Antike im Mittelalter: Freiburg 1987, ed. W. Erzgräber (Sigmaringen, 1989), 245–60, esp. 256–8
K.Chemla and S.Pahaut: ‘Remarques sur les ouvrages mathématiques de Gersonide’, Studies on Gersonides, ed. G. Freudenthal (Leiden, 1992), 149–91