This year marks the  500th anniversary of the birth of Vincenzo Galilei. His name is unknown to the average music lover, but his work laid the foundation both for the early Baroque style of music and modern experimental science.

He taught his much more famous son Galileo Galilei both music and an interest in carrying out experiments.

Vincenzo Galilei was apparently born in 1520 in the Tuscan village of Santa Maria a Monte. (Some scholars believe he was born later in the decade.) At a very young age, his musical talent became apparent. He became a well-respected lutenist. Sometime before 1562 he moved to Pisa and married a woman from a Pisan noble family.

The couple had seven children. Galileo was the eldest. Despite his claim to nobility, Vincenzo never acquired wealth. He made his living as a cloth merchant. Music, however, remained his passion. He published a textbook on playing and composing for the lute and two influential works on music theory.

Music theory before Galilei

Medieval education was dominated by Aristotle and Plato. Aristotle’s theories guided scientific inquiry. Plato’s, heavily influenced by Pygthagoras, guided music theory. Music, along with arithmetic, geometry, and astronomy, comprised the quadrivium or mathematical disciplines as taught in medieval universities.

Pythagoras taught that all things are numbers. He based his teaching largely on his discovery of musical ratios. The ratio for an octave is 2:1, for a fifth 3:2, and a fourth 4:3. Medieval theorists taught that these three intervals were the only consonances. They backed up this claim with the numerological significance of the number four. They also stressed the importance of “superparticular ratios,” those whose numbers differ by one.

Musical practice owed nothing to musical theory. In the early fifteenth century, composers started treating thirds and sixths as consonant. Meanwhile, any theorist who challenged  Pythagorean orthodoxy felt the fury of traditionalists.

Eventually, though, the gap between theory and practice became intolerable. In 1558, Gioseffo Zarlino published a treatise that championed the number six over the number four. In that way, he could claim consonance for the major third (5:4) and minor third (6:5).

He had trouble explaining major and minor sixths (5:3 and 8:5). The major sixth doesn’t have a superparticular ratio. The minor sixth requires a number higher than six.

Looking back over Latin translations of ancient Greek theorists, Zarlino found several tuning systems. One of them, now known as just intonation, had used these ratios. So Zarlino insisted that this system was the ideal tuning system, the one singers actually used.

Vincenzo Galilei’s place in music history

In 1574, Galilei moved to Florence, where he attracted the attention of Count Giovanni Bardi, who became his patron, and joined Bardi’s Camerata, a group of men gathered to discuss poetry and music.

Greek philosophers had vividly described the emotional effects of music. The polyphonic music then current didn’t produce any similar effect. Bardi’s group concluded that modern music was, therefore, inferior to ancient music.

Although Galilei was a noted lutenist, singer, and composer, he had little knowledge of music theory. Bardi sent him to study with Zarlino.

Galilei as theorist

After absorbing Zarlino’s teachings, Galilei started to write a treatise based on them. But he decided to enrich it with ideas from the ancient Greek thinkers Ptolemy, Plutarch, and Aristoxenus. It proved impossible for him to reconcile these authors with Zarlino’s strict Platonism. Aristoxenus in particular actively opposed Pythagoras’ ideas.

Eventually, Galilei turned to the Florentine historian Girolomo Mei, a music lover who could read Greek. He had no formal training in music, but like members of the Camerata, he thought modern music deficient. He strove to understand Greek thought without reference to modern musical practice. A fiercely independent thinker, he had moved from Florence to Rome so he could safely dispute traditional stories of Florence’s founding.

Five letters from Mei to Galilei are extant. In them, Mei ridiculed Pythagorean number theory. He also pointed out that the human ear is not sensitive enough to distinguish between intervals in a superparticular ratio and those slightly off.

Although Galilei never came to agree with Mei totally, he did come to prefer his ideas to Zarlino’s. In 1581 he published an influential treatise sharply critical of Zarlino’s teachings. (The full titles of his works, which are very long, appear later in this post.)

Galiliei condemned modern contrapuntal music for not being able to achieve the same effects as the Greeks described. It used more than one melody simultaneously setting the same text. With the different melodies going in different directions, how could any of them capture the affect? (Effect and affect amount to four different words with two spellings. If you don’t know the meaning of affect as a noun, which is a technical term in psychology and music theory, follow the link.)

The ancient Greeks, he insisted, sang only one melody at a time. It had a narrow range. It was set high or low in the singer’s voice according to the feelings it conveyed. The rhythm of the poetry determined the rhythm of the music.

As for accompaniment, Galilei championed the simple chordal style of the simplest of contemporary songs, a style called monody.

Galilei and monody

Galilei’s extant works include a variety of forms and styles. He composed monodic works for meetings of the Camerata, including a setting of Count Ugolino’s lament from Dante’s Inferno. Unfortunately, they do not survive.

We do have monodic works by Emilio Cavalieri, Giulio Caccini (a fellow associate of Bardi) and Jacopo Peri. They were all composed after Galilei’s break with Zarlino. Galilei’s ideas, and possibly his own monodic compositions, must have influenced the development of monody. In turn, these composers influenced the dramatic works of Claudio Monteverdi, the first important composer of opera.

Vincenzo Galilei’s place in the history of science

The ancient Greeks knew how to conduct experiments, but they seldom used them. Aristotle, in particular, relied on deductive logic. He used neither experiment nor close observation to test his conclusions.

Some medieval thinkers insisted on the importance of mathematics and experimental verification. They even found some of Aristotle’s mistakes. But most medieval scholars continued to rely solely on Greek models.

The following illustration demonstrates the prevailing attitude toward experimentation.

It appears to depict an experiment. Three panels show objects labeled with numbers. Pythagoras points to the numbers 16 and 8. These numbers have the ratio of 2:1. Therefore, according to Pythagorean theory, they should produce an octave.

Gaffurio never actually performed such experiments. After all, everyone knew that 2:1 means octave. Except it doesn’t in most of the situations pictured.

In his third letter (January 18, 1578), Mei challenged Galilei to conduct an experiment: stretch two strings on a large lute. Place frets under one of them according to Pythagorean tuning and the other according to just intonation. He assumed that the experiment would demonstrate the falsity of Zarlino’s advocacy of just intonation. And therefore, he assumed, it would verify Pythagorean tuning.

Galilei performs real experiments

Galilei actually performed the experiment, which did not turn out as Mei expected. Neither system matched anyone’s musical practice. That experiment led to Galilei’s break with Zarlino.

Over the next few years, Galilei performed other experiments, including one similar to the one depicted above.

Although he never described his procedure in any detail, it’s likely that he attached weights to two strings in a ratio of 2:1. They did not produce an octave. He kept adding to the heavier weight until the two strings made an octave. The actual ratio of the weights was 4:1.

Likewise, when comparing tension on a string, 9:4 produces a fifth and 16:9 produces a fourth. The ratios have nothing to do with consonant or dissonant intervals. He published his findings in his Discorso of 1589.

Two unpublished manuscripts describe more experiments. In a comparison of linear measurements, such as the length of a string or pipe, the octave is 2:1. Tension on strings or any surface measurement requires the linear ratios to be squared. A major third, 5:4 in linear measurements, is 25:16, and 2:1 produces a tritone.

In comparing the volume of two organ pipes, the linear ratios must be cubed. An octave is 8:1 and a fifth 27:8.

Regarding two strings, true unison is possible only if both are the same material, length, and thickness. They must also be stretched to the same tension. He tuned a gut string and a steel string to the best possible unison. They did not produce unisons at the frets.

The influence of Galilei’s experiments

Since Galilei never lived to publish most of his findings, one might wonder why they matter. But in 1588, when he started to work on them, his son Galileo helped him out.

Galileo had been enrolled at the University of Pisa until 1585, but he lacked the funds to continue. Legend has it that he noticed how pendulums behave by watching a suspended lamp in Pisa’s cathedral.

Certainly in the experiment with the weights on strings, the weights swung back and forth. It gave him more opportunity to observe the pendulum effect––that the amount of weight does not affect the pendulum’s period.

Comparison of Vincenzo’s and Galileo’s works show two traits in common that were rare at the time. Neither trusted the authority of the ancients. They had that attitude in common with Mei, but hardly anyone else. And both developed rare interest and skill in mathematics.

Galileo’s distrust of authority had him in constant trouble with the University of Pisa, which existed to foster respect for tradition. He eventually became the chair of mathematics there, even though he never finished his degree. For that matter, he had studied medicine and never had any instruction in mathematics there.

When he decided he had to leave Pisa, he won the chair of mathematics at the University of Padua. It had been vacant for four years.

In his published discourse on mathematics (1638), he devoted twelve pages to musical matters. He used the same reasoning found in Vincenzo’s unpublished works. He opened and closed the section describing the behavior of pendulums.

Galileo, of course, played a major role in the scientific revolution. It appears that he learned the foundation of his work at home from his father.

Vincenzo Galilei also influenced Marin Mersenne, who likewise had a tremendous impact on both music theory and science.

Vincenzo Galilei’s published prose works

• Fronimo : dialogo di Vincenzo Galilei nobile fiorentino sopra l’arte del beneintavolare et rettamente sonare la musica negli strumenti artificiali si dicorde come fiato et in particulare nel Liuto  (1568—French-language edition also published in 1568. Second edition, 1584)
• Dialogo di Vincentio Galilei nobile Florentino della musica antica, et della moderna (1581, with a posthumous edition in 1602)
• Discorso di Vincentio Galilei, intorno all’ opere di messer Gioseffo Zarlino da Chioggia, et altri importanti particolari attenenti alla musica (1589)

Sources:

Music and experimental science in sixteenth-century Italy / David M. Guion (Master of Arts thesis, University of California at San Diego, 1973)
The new Grove dictionary of music and musicians, edited by Stanley Sadie. (Macmillan, 1980), s.v. “Galilei, Vincenzo”
This month in physics history: July 2, 1591, the death of Vincenzo Galilei / APS News, 24, no. 7 (July 2015)