(fl 1298–1316). English musical theorist and scientist. His treatise on music, the Summa de speculatione musice, is the most systematic and comprehensive English work of its period. It exists in a complete version, GB-Ccc 410, and a recently discovered major fragment, Lbl Add.56486(A). The Summa was a significant source for later English theory including the Regule of Robert de Handlo, the Breviarium of Willelmus and the Quatuor principalia of John of Tewkesbury, and it continued to be copied into the 15th century. Odington further explored the Quadrivium in treatises on arithmetic, geometry and astronomy. His alchemical treatise, the Ycocedron, seems to have been the most widely disseminated of his works.
The scarcity of direct biographical evidence has led to misattribution and misdating of Odington's work. Bishop Bale, writing in 1557, assigned the scientific works to ‘Odingtonus’, whom he dated c1280, and the musical treatise to ‘Gualterus de Evesham’, dated c1240. As a result, Burney, Fétis, Coussemaker and Eitner variously placed the Summa between 1217 and 1240. A ‘Walter de Evesham’ documented between c1331 and 1346 as a Fellow of Merton College, Oxford, has also been wrongly identified with Odington. (It is possible, however, that he may have been the author of the works ascribed to ‘Walter Evesham’.) On the evidence of Odington’s own words we know that he was a monk of Evesham, a Benedictine abbey near Worcester. In the minutes of a Benedictine chapter general in 1298 he is named as a member of a committee for the administration of Gloucester College, a Benedictine college at Oxford for monks of the Canterbury province. It may have been here that ‘Walter Evesham … made his deliberations at Oxford c1316ad’, as William of Worcester noted in 1463.
The Summa de speculatione musice, as its title suggests, is a comprehensive work, logically organized and firmly based upon recognized authorities. As a work of ‘speculation’ upon music it treats the mathematical bases of the art as prerequisites for the exposition of practical music. Like Hieronymus de Moravia, whose compilation resembles Odington's treatise in scope, Odington drew freely on the standard medieval sources: Boethius (De institutione arithmetica, De institutione musica), Isidore of Seville (Etymologiarum) and Cassiodorus. Of more recent writers, Adelard of Bath and Ibn Sīnā are cited, and an important passage seems to derive from the earlier 13th-century Johannes de Garlandia, perhaps through Hieronymus de Moravia. Unlike Hieronymus, Odington assimilated his borrowings into the logical framework of the Summa.
Part i of the treatise deals with arithmetic, the study of numbers in itself. Following Boethius's Arithmetica, it explains the possible relationships between unequal numbers (multiple, superparticular, superpartient) and the possible means between numbers (arithmetic, geometric and harmonic). Part ii, based on the Musica of Boethius, considers music as understood in the classical sense of number related to sound, or what we would term harmonics. Intervals, consonances and the comma are considered in terms of their mathematical demonstration. In the course of this discussion it is observed that the major and minor 3rds, since they approach the ratios of 5:4 and 6:5, are sometimes considered consonances, and are in performance altered to mathematically perfect consonances.
Part iii, ‘On the construction of musical instruments’, is not a handbook for the craftsman but a demonstration of the harmonic relationships presented in the previous chapter in the proportions of the monochord, organ pipes and bells. Part iv, based on Isidore's discussion of poetic metres, employs the same numerical relations outlined in the first part to enumerate the proportional relationships between the two parts of a metrical foot.
While these four sections of the treatise serve the musicus or theorist, the last two chapters are designed for the practising musician, and their models are closer to hand. Part v is a chant treatise and tonary – a genre stretching from Aurelian of Réôme through Guido to the Lucidarium of Marchetto da Padova. There are tables of notes and ligatures and an explanation of the hexachord system. The tonary, apparently derived from the Sarum Tonale, which forms the bulk of the chapter, describes and illustrates each of the eight ecclesiastical modes.
Part vi is a discant treatise on the lines of the treatises of Johannes de Garlandia and Franco. The opening section on notation falls in the late Ars Antiqua tradition, reflecting English developments just prior to the innovations of the early 14th-century Johannes de Garlandia reported by Handlo in the Regule. It describes the duplex longa, longa, brevis, semibrevis (divisible into three minute … quasi minime seu velocissime), plicas, the rules of perfection and alteration, ligatures and the notation of the rhythmic modes. In discussing modal notation it is stated that ‘among the early composers of organum the long had only two beats as in meters, but afterward it was brought to perfection, to consist of three tempora’. Some writers have interpreted this to mean that binary modes preceded ternary ones. In fact, it merely refers to the earliest rhythmic modes, I and II, both ternary modes in which a two-beat long alternated with a one-beat breve. In more modern rhythmic notation, the dot has not replaced the short stroke as a signum divisionis between brevis values; rather, a small circle (parvulus circulus) replaces the stroke where the brevis is divided into more than three semibreves and in hockets of semibreves and their rests (dividing the brevis in three), where the stroke might be mistaken for a rest.
The chapter concludes with a description of the categories of polyphonic composition: organum purum, rondellus, conductus, copula, motet and hoquetus. This section is also illustrated by numerous musical examples, some of them occurring in continental motet collections, others presumably original. The triplum of one motet on the tenor Agmina is found elsewhere only in Handlo's Regule. The rondellus technique described and illustrated by a unique three-voice setting, Ave mater domini, is not that of the polyphonic rondeau but rather a distinctive constructivist device of later 13th-century English polyphony.
F.F. Hammond, ed.: W. Odington: Summa de speculatione musicae, CSM, xiv (1970)
J. Huff: [a translation of part vi], MSD, xxx (1973)
FREDERICK HAMMOND/PETER M. LEFFERTS