(b Liège, c1260; d Liège, after 1330). Franco-Flemish theorist. His principal work, the Speculum musice, is the largest surviving medieval treatise on music, containing 521 chapters arranged in seven books. The first five books deal with speculative music, the sixth with ecclesiastical chant and the seventh with discant in refutation of Ars Nova teaching on rhythm and notation. The Speculum is thus an encyclopedic work in the tradition of Hieronymus de Moravia and Walter Odington. It is without parallel, however, in its scope and cogency as a statement of the theory and practice of the Ars Antiqua.
Information and conjecture about Jacobus of Liège have accumulated piecemeal. The Speculum was originally attributed to Johannes de Muris. Coussemaker based this conclusion on a 16th-century inscription and the proximity of the two authors in a Paris manuscript, ignoring the direct contradiction between the teachings of the two treatises. The author of the Speculum stated, moreover, that his name could be discovered from the initial chapter of each book; this gives the acrostic ‘Iacobus’. Smits van Waesberghe proposed the identification of ‘Iacobus’ with a Iacobus de Oudenaerde, canon of Liège and professor at the University of Paris in 1313. Another possible identification may be found in the Berkeley Manuscript of 1375 (US-BE 744), whose anonymous author refers to a certain ‘Iacobus de Montibus’ in connection with Boethian theory, a major concern of the Speculum musice. The surname ‘de Montibus’ could refer to an unspecified mountainous region or, possibly, to the city of Mons in Belgium. Bragard conjectured that he was born in or near Liège in about 1260 and spent his early years there, receiving a musical training imbued with the theories of Franco of Cologne. Bragard identified the treatise on the consonances (Tractatus de consonantiis musicalibus) printed by Coussemaker as Anonymus 1 (CoussemakerS, i, 296–302) and a companion work on psalm tones (Tractatus de intonatione tonorum) cited in books 1 and 6 of the Speculum as early works of Jacobus. (Both works are attributed to Jacobus in the edition by Smits van Waesberghe, Vetter and Visser, 1988, together with a third treatise, Compendium de musica, also ascribed to him). From several remarks in the treatise it appears that he studied in Paris, where he laid the foundation of his later work by mastering the first two books of Boethius's De institutione musica. The Speculum may have been among the ‘many things’ which Jacobus said he had begun in Paris, especially since the voluminous quotations in books 1–5 suggest ready access to an extensive library. Books 6 and 7 may have been composed at Liège, since book 6 draws upon the Questiones in musica (c1100) found in two Liègeois manuscripts, while book 7 cites two motets of Petrus de Cruce according to another Liège source.
In the preface to book 1 Jacobus described the general plan of his work and justified its vast scope by the assertion in chapter 1 that music ‘taken in a general sense, objectively extends to almost everything, God and created beings, corporeal and incorporeal, heavenly and human, theoretical and practical knowledge’. His principal sources were Boethius for speculative music, Guido of Arezzo and his followers for chant theory and Franco ‘the German’ for discant.
The first book deals with material necessary for understanding musical consonances (i.e. intervals). The preliminary materials – definitions of music and the musicus, the inventors of music – draw not only upon standard authorities (Boethius, Isidore of Seville, Plato), but also upon Aristotle, Robert Kilwardby (d 1279) and Petrus Comestor. After discussing the various ways in which the four mathematical sciences of the Quadrivium treat measures and proportions, Jacobus passed to the divisions of music: mundana, humana and instrumentalis (Boethius); harmonic, rhythmic and metric (Isidore); modest and lascivious (Boethius); practical and theoretical. This preliminary material is marked off by a chapter summarizing the matters to be treated. There follow basic definitions: sound, tone, motion, time. Necessary mathematical concepts are introduced: unity; number and the division of number; proportions (multiple, superparticular, superpartient), their compounds and properties; the numerical means (arithmetic, geometric, harmonic) and a collocation of the three. After an account of the Pythagorean harmony (6:8:9:12), book 1 closes with examples of continuous superparticular proportions and their multiplication.
Book 2 deals with musical consonances, especially as related to the monochord. It opens with a résumé of the classical doctrine of consonance and dissonance, including the thesis that consonances are found in the multiple and superparticular proportions. This axiom is later used to determine the consonance of specific intervals. The discussion of whether the unison is a consonance exemplifies the scholastic method of the treatise as a whole. Varying authorities are marshalled and judgment rendered in a long responsio. The various intervals, their names, division and so on are discussed, together with compounds of the 5th, octave, octave and 5th, and double octave. Jacobus refused to admit chants having a range of more than an octave but cited the motet Non pepercit deus (Anonymus 1, CoussemakerS, i, 307a) to show that this did not apply to measured music. In discussing the 4th he compared the genera of the ancients (diatonic, chromatic, enharmonic) with the species of the moderns (tone, tone, semitone; T ST T; ST T T). In addition to the usual consonances and their compounds Jacobus also treated the comma, diesis, apotomē and intervals such as the tetratone, the pentatone (which had no place in the gamut except for ‘false mutations’) and the hexatone (six 9:8 whole tones rather than the 2:1 ratio of the octave). Book 2 concludes with a complex monochord partition.
The third book, according to the general preface, ‘speaks of those consonances which Boethius treats more expressly’. The entire book is in fact taken up with the numerical discussion of proportions and intervals and their division in terms of those proportions.
Book 4 considers the comparison of consonances (chapter 1) ‘with respect to their general conformity and differences, height and depth, order, whether they are simple or compound, with respect to whole and part, intervals, species, perfection and imperfection, and some other proportions’. In comparing consonances according to their use Jacobus cited ecclesiastical chants using intervals other than the six (up to the perfect 5th) approved by Guido. Species of 4th, 5th and octave are given correctly (descending) according to Boethius. The extension of the concept of species to other intervals is in fact the work of Johannes Cotto rather than, as Jacobus stated, of Guido. After proving that the octave was the prime consonance Jacobus cited several historical orderings of consonances. Concord is divided into perfect, imperfect and intermediate, with the sensible proviso that ‘this is not sufficient for concord unless the mixture of such sounds be pleasing and grateful to the ear’. The ensuing discussion of concord and the complementary exposition of discord, also divided into perfect, imperfect and intermediate, draws not only upon Boethius but also upon more recent authorities: Johannes de Garlandia, Franco, Anonymus 1 (i.e. ?Jacobus) and Anonymus 2. The chapter comparing concords with respect to a cadence is of particular interest. Cadence is defined as ‘a certain order or natural inclination of a more imperfect concord toward a more perfect one’ (iv, 1). A 2nd above or below and a minor 3rd resolve to the unison; the major 3rd seeks the 5th, the 4th either the unison or the 5th. The 5th itself is stable but is perfected by the unison or octave. The major 6th resolves to the 5th or to the octave, as does the minor 7th. (Neither the minor 6th nor the major 7th is mentioned.) The unison and octave are thus the most common endings for discant and organum, although the 5th is often used for one discanting voice above a tenor.
Jacobus summarized the contents of book 5 as the three genera of the tetrachord, their properties, the tetrachords of the Greater and Lesser Perfect Systems, the division of the monochord and various descriptions of its partition according to the three genera. The principal sources of this book are Boethius (books 1, 4, 5) and Guido of Arezzo. The three genera are compared to (but not equated with) the three hexachords, natural, hard and soft. The monochord, according to the moderns, contains two octaves and a 6th, gamma–e, one note more than Odington’s system. After describing Guidonian and other monochord divisions Jacobus posited the addition of a sixth tetrachord (for his monochord diagram, see Theory, theorists, fig.4).
In the prologue to book 6 Jacobus announced a shift of emphasis, from speculative music as represented by Boethius to practical music: the modes or tones both ancient and modern; their differentie; psalm tones; music and the many things necessary for performing skilfully. Since Boethius derived the modes from octave species Jacobus began with an account of the species of octaves, 5ths and 4ths. To the classical account of eight modes he appended Guido's description of the 1st, 2nd, 3rd and 4th modes of medieval chant. This treatise on the modes or tones according to Boethius concludes with an account of the Greater Perfect System, Greek note names and the 8th (Hypermixolydian) mode added by Ptolemy.
The
treatise on ecclesiastical modes opens with a monochord description and an
account of tetrachords and species according to Guido and his followers. A
curious chapter compares these to metrical feet (T = long, ST = short, thus
e.g. T ST represents a trochee). An explanation of the terms modus, tropus
and tonus as applied to intervallic constructions is extended to a
parallel between music and rhetoric. The eight church modes are described with
their regular and irregular finals. In the chapter on affinities (by 4th, 5th
and octave) Jacobus twice referred to Liègeois practice. The structure and
range of each of the eight modes is described in detail according to Guido,
after which the modes are compared by their species construction and their use
of B/B
. Hexachords are
described with natural and irregular mutations. The final portion of book 6 is
largely concerned with notation and chant repertory: systems of letter
notation; modal structure and chants ending in C or A. A tonary gives examples
of differentie, psalm tones, antiphons and mass chants according to the
ecclesiastical modes. Characteristic opening formulae are provided as indexes
of the modes.
Speculum musice, ed. R. Bragard, CSM, iii (1955–73)
Tractatus de consonantiis musicalibus; Tractatus de intonatione tonorum; Compendium de musica, ed. J. Smits vab Waesberghe, E. Vetter and E. Visser (Buren, 1988)
StrunkSR1
R. Steglich: Die Quaestiones in musica (Leipzig, 1911/R)
W. Grossmann: Die einleitenden Kapitel des Speculum musicae von Johannes de Muris (Leipzig, 1924/R)
J. Smits van Waesberghe: ‘Some Music Treatises and their Interrelation: a School of Liège (c. 1050–1200)?’, MD, iii (1949), 25–31, 95–118
J. Smits van Waesberghe, ed.: Johannes Afflighemensis: De musica cum tonario, CSM, i (1950)
R. Bragard: ‘Le “Speculum musicae” du compilateur Jacques de Liège’, MD, vii (1953), 59–104; viii (1954), 1–17
M. Huglo: Les tonaires (Paris, 1971), 429ff
J. Ballke: Untersuchungen zum sechsten Buch des Speculum musicae des Jacobus von Lüttich unter besonderer Berücksichtigung der Tetrachord- und Moduslehre (Frankfurt, 1982)
O. Ellsworth, ed.: The Berkeley Manuscript (Lincoln, NE, 1984), 9–10
K. Slocum: ‘Speculum musicae: Jacques de Liège and the Art of Musical Number’, Medieval Numerology, ed. R.L. Surles (New York, 1993), 11–37
FREDERICK HAMMOND/OLIVER B. ELLSWORTH