Instruments of Music Theory

Alexander Rehding

doi:10.30535/mto.22.4.4

Abstract

This article explores musical instruments as a source for the historical study of music theory. The figure of Pythagoras, and his alleged penchant for the monochord, offers a way into this exploration of the theory-bearing dimensions of instruments. Musicians tend to think of instruments primarily in terms of music-making, but in other contexts instruments are, more broadly, tools. In the context of scientific experimentation, specifically, instruments help researchers come to terms with “epistemic things”—objects under scrutiny that carry specific (but as yet unknown) sources of knowledge within them. Aspects of this experimental practice can productively be transferred to the study of music theory and are explored in two test cases from different periods of musical theorizing (and instrument building): Nicola Vicentino’s archicembalo from mid-sixteenth century Italy, and Henry Cowell’s rhythmicon from early twentieth-century America.

Highlights

585 CE) awarded the Greek philosopher the honorific “Pythagoras musicus.”(2) Despite his undeniably strong affinities with arithmetic, Pythagoras was associated with music throughout the Middle Ages and into the early modern period, in ways that parallel the astronomer Ptolemy with his emblematic planetary rulers, or the geometer Euclid with his compass
This image appears in the Theorica musicae (1492) by the North Italian humanist Franchinus Gaffurius (1451–1522), one of the first music theory books to appear in print
This story, which determines the ratios of the consonant intervals of the octave, fifth, and fourth at 2:1 (= 12:6), 3:2 (= 12:8 and 9:6), and 4:3 (= 12:9 and 8:6), was transmitted throughout the Middle Ages and well into the mid-sixteenth century, primarily in Boethius’s influential variant, and need not be further rehearsed here.(4) For all the numerical beauty of the Pythagorean ratios, we know that the account is apocryphal, as the underlying physics is problematic: the relationship between the weight of a hammer and the pitch it produces suggested by the illustration does not hold

Summary

Alexander Rehding

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Conclusions

Works Cited

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