A Little History

In light of its numerous virtues, why isn't Just Intonation currently in general use? Like so many of our peculiar customs, this is largely an accident of history. A detailed history of tuning in the West would require a book of considerable length in its own right, and is thus far beyond the scope of the current work. No one has, as yet, written a comprehensive study of this subject. Until such becomes available, the reader is advised to consult Harry Partch's Genesis of a Music (Second Edition, New York: Da Capo Press, 1974), especially Chapter Fifteen, "A Thumbnail Sketch of the History of Intonation," and J. Murray Barbour's Tuning and Temperament (Da Capo Press, 1972). The following short sketch is intended only to describe, in general terms, how musical intonation in the West achieved its current, peculiar state.


Just Intonation is not a new phenomenon. Indeed, the basic discovery that the most powerful musical intervals are associated with ratios of whole numbers is lost in antiquity. Perhaps it was first discovered by the priestly musicians of Egypt or Mesopotamia in the second or third millennium B.C.E. Some scholars, most notably Ernest G. McClain, regard this discovery as of vital importance to the development of both mathematics and religion in these ancient societies. The semi-mythical Greek philosopher Pythagoras of Samos is generally credited with introducing whole-number-ratio tunings for the octave, perfect fourth, and perfect fifth into Greek music theory in the sixth century B.C.E. In the generations following Pythagoras, a great many Greek thinkers devoted a portion of their energies to musical studies, and especially to scale construction and tuning. These musical philosophers, known collectively as the Harmonists, created a host of different tunings of the various Greek scales, which they expressed in the form of whole-number ratios. The discoveries of the Greek harmonists constitute one of the richest sources of tuning lore in the world, and continue to this day to exercise a significant influence on Western musical thought. Although most of the original writings of the Harmonists have been lost, much of their work was summarized by the second century C.E. Alexandrian, Claudius Ptolemy in his Harmonics. Ptolemy made significant contributions in his own right to the field of music theory, as well as to astronomy and geography.

The Middle Ages and the Renaissance

Since the time of the Greek harmonists, the idea of simple ratios as the determinants of musical consonance has never been wholly absent from Western musical thought. Although much Greek music theory was lost to the West with the fall of the Roman Empire, some was retained and passed on to medieval Europe, primarily through the musical writings of the late Roman philosopher Boethius. (Greek music theory was also preserved and further developed in the Islamic sphere, but this does not appear to have had much influence on musical developments in the West.) Throughout the middle ages, Western music was theoretically based on what is called Pythagorean intonation, a subset of Just Intonation based on ratios composed only of multiples of two and three, which will be described in detail in Chapter Three. Pythagorean tuning is characterized by consonant octaves, perfect fourths, and perfect fifths, based on ratios of the numbers one, two, three, and four. All other intervals in Pythagorean tuning are dissonant. This property is consistent with the musical practice of the middle ages, in which polyphony was based on fourths, fifths, and octaves, with all other intervals, including thirds and sixths, being treated as dissonances.

In the later middle ages and early Renaissance, thirds and sixths were increasingly admitted into polyphonic music as consonances, and music theory was gradually modified to account for the existence of these consonant intervals, although it appears to have lagged considerably behind musical practice. Eventually, theorists were forced to partially abandon the Pythagorean framework of the middle ages in order to explain the existence of consonant thirds and sixths, because the most consonant possible thirds and sixths are based on ratios involving five. The association of consonant thirds and sixths with ratios involving five was first mentioned by the English monk Walter Odington (c. 1300), but it took a long time for this idea to penetrate the mainstream of musical thought and displace the Pythagorean intonational doctrines—indeed, it can be argued that it never wholly succeeded in doing so. In the sixteenth century, the rediscovery of Greek writings on music, especially the writings of Ptolemy, gave considerable added ammunition to the advocates of consonant thirds and sixths based on ratios involving five. In general, music theorists of the Italian Renaissance came to agree with the proposition of the Venetian Gioseffe Zarlino (1517–1590) that consonance was the product of ratios of the integers one through six (the so-called senario). The ratios that define the major and minor triads were discovered in the senario, and were acclaimed as the most perfect concords, thereby setting the stage for the development of chordal, harmonic music in the subsequent "common-practice" period.