The Mechanics of Music: Scales and Treatises

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The Mechanics of Music: Scales and Treatises

The Medieval Scales.

The medieval musical scales were called modes, which were described by their ranges, the location of the half-steps, the important pitches used at the beginning and end of the composition, and the "reciting tone"—the pitch used for recitation in psalms (see Plainchant, Psalms). During the Middle Ages there were eight modes, grouped into four pairs (this was enlarged to six pairs in the sixteenth century, and reduced to two—the major and minor scales presently in use—in the eighteenth century). Each mode was known by its number and by a Greek name. The names chosen were those of ancient Greek tribes that were believed to have exemplified the emotional character of that mode. Although the system of modes was originally invented to describe and control monophonic music, it was also applied to the polyphonic repertory. In both techniques, modal considerations dictated many decisions concerning choices of notes and harmonies to be put in important structural places in the compositions. The importance of understanding the modes to a medieval composer and performer can be seen in that a detailed discussion of modes constituted a major portion of most theory treatises of the period.


introduction: The love song "Se la face ay pale" ("If my face is pale …") was originally written by Guillaume Dufay for the Savoy court in 1434–1435. Later he used the tenor line of the same song as the basis for an entire mass. The examples below show the opening section of the love song or chanson, followed by an excerpt from Gloria where the tenor line of the mass (third line down) is borrowed from the tenor line of the chanson (the line on the bottom).

Theoretical Treatises.

Much of our understanding of the thinking of medieval musicians, especially composers, comes from the theoretical treatises, books of instruction that provide details about the practice of writing music. The treatises are by and large retrospective in that they usually report or explain current practice, rather than propose anything new. The theorists, many of them university professors and/or monks, observed the changes taking place as practices evolved over the centuries and attempted to explain them (or in some cases, condemn the changes). By looking at what issues absorbed their attention, we can follow the revisions in technique that underlay the various compositional practices.

Practical versus Intellectual Theory.

When people in the Middle Ages discussed music in learned writings, they made a clear separation between the intellectual consideration of the art and the practical, with the practical (that is, music itself) left mostly to practitioners, and usually thought to be unworthy of intellectual discussion. Throughout the period, music was included as one of the seven liberal arts, placed in the quadrivium (four ways) alongside the mathematical arts of arithmetic, geometry, and astronomy, rather than in the trivium (three ways) with the verbal arts of grammar, rhetoric, and logic. Its placement indicates the way in which music was addressed: number, ratio, and proportion were actually what was considered under the subject-heading, based on the study of vibrating bodies (for example, by dividing a vibrating string in the middle, it would vibrate at twice the speed, the ratio of 2:1). Later, these ratios influenced the consideration of perfect and imperfect intervals. Another, more philosophical or theological consideration of music was to divide it into three areas: musica mundana, musica humana, and musica instrumentalis. Musica mundana (music of the Spheres) referred to the harmony caused by the motion of heavenly bodies. Musica humana (music of humans) was the harmony within the human body, having to do with the balance of physical elements. Musica instrumentalis (instrumental music) referred to actual sounds, either sung or made by instruments. This division of music was discussed to some extent in most medieval treatises, ending in the late thirteenth century, when mundana and humana were finally dropped from the discussion following their rejection by Johannes Grocheio in his De musica (c. 1300), one of the earliest treatises to concentrate on the practical detail of music and the first to consider secular music, including dance.

Harmony and Intervals.

Practical theorists during the Carolingian era (eighth to tenth centuries) were frequently concerned with the modes (see next page), attempting to regularize the practice and to explain


The medieval method of describing a melody was to classify it according to the scale used—its distribution of steps and half steps, its final, and its reciting tone. None of the medieval modes corresponds exactly to any of the major and minor scales used today. The sequence of steps and half-steps that differentiate the modes can be most easily described by relating them to the white notes of the piano keyboard.

certain chants that did not exactly fit the system. By the late ninth century, treatises begin to discuss polyphony—explaining the way in which different notes can be sounded together in harmony, classifying intervals (the distance between the pitch of two notes) as more or less harmonious according to the mathematical ratios of their vibration speeds. Those intervals whose ratios could be expressed in simple numbers were referred to as "perfect" (octave [a distance of eight notes on the diatonic scale, as in C to C], 2:1; fifth [a distance of five notes, as in C to G], 3:2; and fourth [a distance of four notes, as in C to F] 4:3); all other combinations of notes were considered dissonant to varying degrees. The classifications continued to undergo revisions throughout the remainder of the Middle Ages, with the fourth losing its status as a preferred interval, while the imperfect third became more and more accepted. Throughout the period the treatises explored the ways in which harmonies can be used to shape and control compositions.

Theories of Notation.

Once polyphony was well established in the twelfth century, the next new issue to appear in the treatises was notation, a topic that continues to occupy theorists down to the present day. The earliest notation recognized only three actual values: short, long, and a long that was the value of both the other two notes combined. The system allowed some freedom in the assignment of values to these notes, causing certain situations to be somewhat ambiguous. One of the earliest theorists to tackle the problem of ambiguity was Franco of Cologne, who in 1260 wrote Ars cantus mensurabilis ("The Art of Measured Song"), which assigns specific duration to each of the note shapes. The next step along this line was to add new flexibility to the system by subdividing the existing notes, which is the major subject of three different treatises written in Paris at the beginning of the fourteenth century: Ars nova ("The New Art") once credited to Philippe de Vitry, Ars novae musicae ("The New Musical Art") by Johannes de Muris, and Speculum musicae ("Musical Reflection") by Jacques de Liège. The systems they describe are highly sophisticated, allowing accurate notation of minute rhythmic variations and complicated combinations. At the same time as these changes were occurring in French music, Marchettus of Padua was explaining an Italian system that was quite different. In his two treatises from approximately 1320—Lucidarium in arte musicae planae ("Explanation of the Art of Unmeasured Music") and Pomerium artis musicae mensuratae ("Orchard-Garden of the Art of Measured Music")—Marchettus described a system of notation as well as a group of harmonic practices that set Italian notation and harmonies apart from the French. By the mid-fifteenth century, however, the Italian composers had abandoned their own notation and adopted that of the French. Treatises from the end of the fifteenth century, such as those by Johannes Tinctoris, demonstrate that a single system of notation and harmonic practices was in use throughout Europe.


Hugo Riemann, History of Music Theory. Trans. Raymond Haggh (Lincoln: University of Nebraska Press, 1962).

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The Mechanics of Music: Scales and Treatises

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