Among the many elucidations of, or commentaries upon, Guido, that of
Aribo of Freising (d. 1078) is specially valuable because of the nearness
of date.
In the prolix work of Joannes Presbyter (late 11th century) is a vocabulary of terms—the earliest known.
Johannes Cotton, probably of English birth, was a singing-teacher in a monastery near Brussels. His treatise is noteworthy for its painstaking description of the harmonic ideas of his day, especially as to organum and discant. He refers to the hexachord-system, but does not know about measured music.
The other l2th-century writers are not specially important, except that the English Ælrede of Rivaulx (d. 1166) and John of Salisbury (d. c. 1180) imply that rather free part-singing was being attempted, but without system, while the writer known as 'Aristotle' is allied to the later mensuralists in his desire to classify intervals for contrapuntal use, though in his list of dissonances he counts the sixths as best, the thirds as medium, and the tritone and the seconds as worst.
All works after 1200 indicate the advance of thought regarding both the classification of intervals and the time-relations of part-writing. [Three striking cases of identical names are associated with works that are diverse in matter or period. The difficulty is roughly solved by enumerating two Garlandias, two Francos, and two Johannes de Muris.]
The first Garlandia shows a clear insight into systematic counterpoint, including even the principle of imitation between the voices. He, like his successors, reckons the thirds as consonances, is feeling his way towards a time-system, and uses some chromatic tones to soften harsh progressions.
Franco of Cologne (though sadly confused with Franco of Paris) is apparently the first to give full expression to the theories of intervals and of time that were becoming generally accepted by his time. His great treatise on Measured Music is one of the most famous and useful in the whole period before the 15th century.
Hieronymus de Moravia, a Parisian monk, makes clear the opposition between the popular instinct for duple rhythms and the arbitrary ruling of the mensuralists in favor of triple; while Marchetto di Padua, somewhat later, ventures to assert the superiority of duple forms. The latter also argues against the expression musica falsa for chromatic alterations of the modes, claiming them to be legitimate and necessary.
For some reason English musicians and those in touch with them seem to have been more ready than others to give up the Pythagorean tuning of the thirds (major = 81/64 and minor = 32/27) in favor of the modern tuning (major = 5/4, minor = 6/5), with its utility in the forming of triads. Walter Odington (d. after 1330), writing about 1300, argues strongly for this latter view, and was probably the first to emphasize the major triad as a real three-part consonance.
He also is the first to mention the minim (
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minim, stem down ).
The most significant theorists in the 14th century were Johannes de Muris (two writers) and Philippe de Vitry. The first Johannes de Muris, 'the Norman,' trained at Oxford, is now distinguished from the second, 'of France,' who from 1321 was teacher and later rector at the Sorbonne. The
