(b. Santa Maria a Monte, Italy, ca. 1520; d. Florence, Italy, July [?] 1591)
music theory, acoustics.
Vincenzio, father of Galileo Galilei, was of a Florentine patrician family originally surnamed Bonajuti, renamed in the fourteenth century. The son of Michelangelo Galilei and Maddalena di Bergo, he began the study of music at Florence about 1540. After establishing his reputation as a lutenist, he studied at Venice under Gioseffo Zarlino, the foremost music theorist of the time, probably about 1561–1562. On 5 July 1562 Galilei married Giulia Ammannati of Pescia and settled near Pisa. Galileo was the eldest of their seven children.
Through correspondence with Girolamo Mei at Rome during the 1570’s, Galilei became interested in ancient Greek music and was encouraged to put to direct experimental test the teachings of Zarlino concerning intonation and tuning. The result was a bitter polemic with Zarlino, who in 1580–1581 appears to have used his influence to oppose the publication of Galilei’s principal theoretical work at Venice and its sale there after it was printed at Florence.
Galilei’s Dialogo della musica antica e della moderna (1581) attacked the prevailing basis of musical theory. This was rooted in the Pythagorean doctrine that the cause of consonance lay in the existence of the “sonorous numbers,” two, three, and four, which in their ratios with one another and with unity were considered to produce the only true consonances. A modified tuning given by Ptolemy (the syntonic diatonic) was favored by Zarlino, who rationalized this tuning by extending the sonorous numbers to six. Galilei observed that musical practice did not conform to this (or any other) numerical system based on superparticular ratios (which, expressed as fractions, have numerators exceeding their denominators by unity). He declared that neither the authority of ancient writers nor speculative number theories could be valid against the evidence of the musician’s ear. Although he recommended placing frets on lute and viol in the ratio 18:17, he recognized this as merely approximate in obtaining an equally tempered scale suitable for unrestricted modulation, in the direction of which musical practice was rapidly moving.
Renaissance physicists had already recognized the inadequacy of speculative mathematical acoustics. Giovanni Battista Benedetti had questioned the older tunings in letters to Cipriano da Rore, whom Zarlino succeeded as choirmaster at St. Mark’s in Venice in 1565. Simon Stevin, in an unpublished treatise on music, advocated the outright abandonment of rational numbers and the division of the scale in true equal temperament based on the twelfth root of two. As mathematics matured, modern harmony replaced polyphony.
Zarlino defended his system based on the number six (the senario) in his Sopplementi musicali, published at Venice in 1588. His former pupil Galilei was a principal target of attack in this book, although Zarlino did not name him and although Bernardino Baldi, in a short biography of Zarlino, wrongly identified the adversary as Francisco de Salinas. Galilei replied with a spirited polemic, the Discorso, published in 1589. In this work he stated the law that a given musical interval between similar strings is produced either by different lengths, or by tensions inversely as the squares of those lengths. Thus the perfect fifth, which is produced by lengths related as 3:2, is also given when weights in the ratio of 4:9 are hung from strings of equal length. This is probably the first mathematical law of physics to have been derived by systematic experimentation, or at any rate the first to replace a universally accepted rival law, for a standard illustration in music books showed the Pythagorean sonorous numbers applying to weights on equal strings as well as to lengths of unequal strings (or air columns).
Galilei employed this experimental result to show that the traditional association of numbers with particular musical intervals was capricious. The musical qualities of intervals had to be determined by the ear, he argued, and mathematics had no authority where the senses were concerned.
Galilei’s empirical attitude toward musical theory had an ancient counterpart in Aristoxenus, a prominent pupil of Aristotle’s who shared his distrust of Pythagorean numerology. But in the sixteenth century music was again regarded as a branch of mathematics. Galilei’s Discorso foreshadowed the subordination of mathematics to experience and the discovery of unexpected laws through close observation that was to distinguish science in the seventeenth century from its predecessors. Galilei was driven to experiment in order to refute erroneous entrenched musical theory, as his son Galileo later attacked ancient physical theory. Among the manuscripts inherited by Galileo is Vincenzio Galilei’s untitled treatise beginning with the words “L’arte et la pratica del moderno contrapunto . . .,” of which Claude Palisca has said: “For prophetic vision, originality, and integrity, it has few equals in the history of music theory.”
Galileo gave two separate accounts of his introduction to mathematics, both indicating that his father opposed this introduction. Vincenzio’s mathematical skills seem inconsistent with this attitude. His writings, however, reveal a deep hostility toward specious reasoning in practical matters induced by fascination with numerical relations and geometrical designs. It is understandable if he did not want his eldest son to be so beguiled.
I. Original Works. Galilei’s writings, excluding musical compositions, are Fronimo, Dialogo . . . del intavolare la musica nel liuto (Venice, 1568; 2nd ed., 1584; facs. ed., Bologna, 1969); Dialogo della musica antica e della moderna (Florence, 1581; 2nd ed., 1602 : facs. of Ist ed., Rome, 1934; abr. ed. of 1st ed., Milan, 1947); and Discorso intorno all’opere di messer Gioseffo Zarlino da Chioggia (Florence, 1589; facs. ed., Milan, 1933). MSS of unpublished works are preserved in the Biblioteca Nazionale, Florence, MSS Galileiani.
An excerpt from Galilei’s Dialogo of 1581 is translated in O. Strunk, ed., Source Readings in Music History (New York, 1950; repr. New York, 1965), vol. II, The Renaissance Era, 112–134. The same vol. contains part of a “Discourse on Ancient Music and Good Singing” (pp. 100–111), published as the work of Giovanni Bardi but perhaps written for him by Galilei about 1578.
II. Secondary Literature. The principal biography is Claude Palisca, “V. Galilei,” in F. Blume, ed., Die Musik in Geschichte und Gegenwart, IV (Kassel-Basel, 1955), cols. 1903–1905, with bibliography to 1950. See also C. Palisca, “Vincenzio Galilei’s Counterpoint Treatise: A Code for the Seconda Pratica,” in Journal of the American Musicological Society,9 (1956), 81–96; “Scientific Empiricism in Musical Thought,” in S. Toulmin and D. Bush, eds., Seventeenth Century Science and the Arts (Princeton, 1961), 91–137; “Vincenzio Galilei’s Arrangements for Voice and Lute,” in G. Reese and R. J. Snow, eds., Essays in Musicology in Honor of Dragan Plamenac (Pittsburgh, Pa., 1969), 207–232; and “Ideas of Music and Science,” in P. P. Wiener and C. E. Pettie, eds., Dictionary of the History of Ideas (New York, in press); and S. Drake, “Renaissance Music and Experimental Science,” in Journal of the History of Ideas,31 (1970), 483–500; and “Vincenzio Galilei and Galileo,” in Galileo Studies (Ann Arbor, Mich., 1970), 43–62.
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