For a more comprehensive treatment of these works and their authors please refer to the New Grove Dictionary of Music and Musicians, ed. Stanley Sadie (New York 2001).

For the complete texts of the treatises, see Thesaurus Musicarum Latinarum

Breviarium de musica by Frutolfus of Michelsberg (12th century)

Late twelfth-century German theorist and compiler Frutolfus was a monk and priest at the Benedictine Abbey of Michelsberg in Bamberg. Taking advantage of the rich library collection of his monastery, Frutolfus compiled works not only on music theory but also on liturgy. His treatise Brevarium is heavily influenced by Boethius and Berno of Reichenau. Frutolfus discusses the origins and names of pitches, the monochord, proportions, modes, intervals and names of notes.

Ars cantus mensurabilis by Franco of Cologne (13th century)

When compared to Jacobus of Liege's Speculum Musicae, this mid-thirteenth century treatise is very practically oriented, its emphasis being on the major issues and genres of contemporary part-music rather than speculative music. The work contains the first major statement of an idea that different durations should be expressed by different note shapes, rather than different contexts alone. The notational system proposed in the treatise endured, with some modifications, for the next two centuries. Franco of Cologne, the author of the treatise, quite possibly studied and worked for some time at the University of Paris. His influence on the Parisian school is shown not only in music manuscripts from the period, which start to follow his notational style, but also in other medieval music theorists's works. Anonymous IV mentions Franco twice, Jacobus of Liege suggests that he was also a composer, though no evidence remains.

De mensurabili musica by Johannes de Garlandia (13th century)

This enormously influential treatise from the second part of the thirteenth century was the first to provide a full treatment of the rhythmic element of music together with its notation. It also treats the polyphony of the Notre Dame school, in which rhythm played an important part. Practical issues of music are here presented fully methodically. About half of the treatise is devoted to rhythmic matters, the rest deals with three species of polyphony. The French theorist Johannes de Garlandia, Magister in Paris at the end of the thirteenth century probably used an earlier anonymous treatise as the foundation of his work. Most later treatments of mensural theory in the thirteenth century, including De mensuris et discantu by Anonymous 4 and the Anonymous of St Emmeram, are heavily influenced by Johannes' work. With regard to notation, the work treats the form of single notes and ligatures. It also defines pauses and their notation.

De mensuris et discantu by Anonymous IV (13th century)

The author of the treatise De mensuris et dicantu (c. 1270) is commonly known as Anonymous IV, a title given by the first editor of the text. If he was not native to England, he was certainly familiar with its music and masters. Possibly he was a monk at the Benedictine abbey of Bury St. Edmund's where both manuscripts of his work are likely to have come. In this case he may have composed his treatise as part of a study visit to Paris, as his text alludes to both the English and the Parisian music circles. Anonymous IV describes the musical techniques of the Notre Dame school in great detail, concerning himself for the most part with mensural notation of polyphonic music. He also mentions and critiques contemporary composers and theorists, including the likes of Leonius, Perotinus, and Franco of Cologne, as well as certain masters who are only known through this treatise.

Regulae super discantum by Dietricus (13th century)

The short mid-thirteenth-century work (with a full title Regule super discantum et ad discernendum ipsas notas discantus) by the German compiler Dietricus treats mensural rhythmic notation. In his discussion of note shapes and ligatures, the author clearly distinguishes symbols with plicae, introducing for these an oblique form of the square punctum.

Scientia artis musicae by Elias Salomo (13th century)

Salomo's only surviving work dates from the second half of the thirteenth century. It consists of thirty one chapters and covers the fundamentals of chant theory and practice. The author treats such traditional topics as the letter names of the notes and their hexachord syllables, the system of claves, the musical hand, the eight modes, staff notation, falsa musica, etc. The work differs somewhat from other contemporary treatises, for it does not obviously borrow from earlier theorists. The work is filled with digressions that give evidence both of Salomo's personal manner of teaching and of the qualities that a practical musician of the thirteenth century found desirable in performance. An inscription in the treatise implies that the author had some connections with the papal court, then in residence at Lyons for a council.

Breviarium regulare musice by Willelmus (14th century)

This fourteenth-century treatise is thought to have been compiled by a certain writer called Willelmus. Several theorists of the previous generation are cited in the work, such as Franco of Cologne and Johannes Torkesey. Following scholastic tradition, the treatise discusses the early notation of Boethius' De musica institutione, but concentrates mainly on notation issues of mensural music, such as the naming of various note values.

Cantuagium by Heinrich Eger von Kalkar (14th century)

This work, written in Cologne in 1380, treats the theory and practice of chant, completely excluding the topics of polyphony and instrumental music. The authors cited include Boethius, Augustine and Jerome of Moravia. Heinrich Eger von Kalkar (1328-1408) was a German Carthusian monk who studied in Cologne and Paris. Later he became an important figure in his order, serving as a prior in a number of its monastic houses. Cantuagium was probably written to instruct fellow members of the Carthusian order. Besides his work on music, Heinrich Eger von Kalkar has also left various mystical writings which are heavily influenced by Bernard of Clairvaux and Hugh of St Victor.

Notitia artis musicae by Johannes de Muris (14th century)

French music theorist, astronomer and mathematician Johannes de Muris was active in the first half of the fourteenth century (born in Normandy about 1295). Some of his most important works, including the music treatises Notitia artis musicae and the Musica speculativa secundum Boetium were written in Paris in the early 1320's where he also attained the academic degree of Magister (1321). Johannes' writings on musical proportions and mensural notation were cited by numerous writers for at least two centuries. The first book of the Notitia, titled Musica theorica is concerned with terms and definitions (of sound in general and musical proportions). The second book, Musica practica deals with musical time, its measurement and notation. Muris especially addressed certain issues of mensural notation. Chapter 5 of Book 2 titled De figuris nominandis (Concerning the naming of musical figures) is of particular interest for its treatment of notation issues.

Speculum Musicae by Jacques de Liège (14th century)

This largest surviving medieval treatise on the theory and practice of the ars antiqua, written c.1330, contains 521 chapters arranged in seven books. The first five books deal with speculative music in the tradition of Boethius, the sixth with ecclesiastical chant and the seventh with discant in refutation of the ars nova teaching on rhythm and notation. Guido of Arezzo and his followers are the main influence for chant theory and Franco of Cologne for discant. For long time the treatise was mistakenly attributed to Johannes de Muris. The true author, however, is Jacques de Liège (c. 1260 - after 1330). Quite possibly he is the same person as Iacobus de Oudenaerde, a canon of Liege and a professor at the University of Paris in 1313. Alternatively he could be a certain 'Iacobus de Montibus' mentioned by an anonymous author in context of speculative music. The most important material on chant notation can be found in Book VI, chapters 72 and 73. Jacobus gives a short survey of the development of notation from its Greek roots, mentioning, among others, the contributions of Boethius and Guido of Arezzo. As part of his overview, Jacobus describes the differences between imperfect and perfect square notation and identifies France as the region where, in contrast with Germany, the use of square notation was very common during his lifetime. The author's fascination with symbolism and numerology throughout the treatise provides insights into various meanings of number four and the square shape in general (see esp. Book VI, ch. 21).

Summa de speculatione musice by Walter Odington (14th century)

Walter Odington was an English theorist active in the first quarter of the fourteenth century. He was a monk of Evesham, a Benedictine abbey near Worcester. Besides music Odington also wrote on the other three subjects of the Quadrivium (arithmetic, geometry and astronomy) and an alchemical treatise, the Ycocedron, which became rather well known. The Summa of Odington is the most comprehensive English work from the early fourteenth century. Several later English theoretical works, such as those of Robert of Handlo and John of Tewkesbury, used it extensively as a source. Among Odington's own sources were many standard authorities including Boethius, Isidore of Seville and Cassiodorus. He also made use of the writings of more recent authors, such as Adelard of Bath and Ibn Sina. The first four sections of the treatise are on speculative theory, the last two deal with the practical side of music. The presentation of notation issues in section VI is in the late ars antiqua tradition. The work describes note values, the rules of perfection and alteration, ligatures and the notation of the rhythmic modes.

Quatuor principalia musicae by John of Tewkesbury (14th century)

The author-compiler of the treatise was a thirteenth-century English friar. He is also the scribe of the earliest extant copy of the work, completed at Oxford in 1351. John of Tewkesbury's other book was an astronomical treatise De situ universorum, completed in 1392. The Quatuor principalia includes lengthy quotations from Boethius, Isidore of Seville, Guido of Arezzo, Magister Lambertus and Franco of Cologne. In addition, the work expounds the principles of the ars nova. The treatise contains an interesting comment about the work of notators and scribes of the time.

Declaratio musicae disciplinae by Ugolino of Orvieto (15th century)

This treatise in five books is a summa of both musica speculativa and musica activa. Aristotelian influence is obvious throughout the work. The first three books are devoted to more practical issues (pitches, properties, modes, musica ficta), the rest expounds theory in Boethian style (intervals, nature of sound, etc.) The author of the work is the Italian theorist and composer Ugolino of Orvieto (c1380-1452), canon at the cathedrals of Forli and Ferrara, later an arch-priest in the latter where he influenced the expansion of the local choir-school. From 1449 until his death Ugolino served as a papal secretary. Only a few of his musical compositions, mostly songs, survive in complete form.