Pythagoras: The mathematics of music

Pythagoras: The Mathematics of Music

The connection between music and mathematics dates back thousands of years, with historical figures such as Pythagoras exploring this connection in depth. Pythagoras, primarily known as a mathematician, also had a significant influence on the field of music, discovering the foundations of music theory that relate to mathematics. Here are some points that illustrate how Pythagoras linked mathematics to music:

• The Discovery of Harmonic Relationships: Pythagoras is famous for having discovered that musical intervals pleasing to the human ear corresponded to simple numerical ratios. This revelation was made by observing that, for example, a vibrating stretched string produces a sound, and if this string is divided into exact fractions, such as 1/2 or 2/3, the sounds emitted are harmonically pleasing and musically significant (octave, fifth, etc.).

• The Invention of the Monochord: Pythagoras developed an instrument called the monochord, which allowed him to measure precisely how much length of a vibrating string was needed to produce an octave, a fifth, or other musical intervals. This contributed greatly to the understanding of mathematical relationships in music.

• The Importance of Whole Numbers: Pythagoras emphasized the importance of whole numbers and their properties in music. His observation that ratios of small whole numbers produce the most harmonious sounds has formed the basis of Western music for centuries.

• Influence on the musical scale: The Pythagorean discovery of proportions in music influenced the creation of musical scales, especially through the use of frequency ratios. Pythagorean scales were built with intervals derived from these numerical relationships, which are still studied and used in music theory today.

• The concept of harmony of the heavens: Pythagoras extended his theory of proportions to astronomy, proposing the theory of harmony of the spheres, according to which the celestial bodies move in musical numerical ratios. Although this theory is not scientifically accurate, it further emphasized the connection between music, mathematics, and the natural world.

• Educational Implications: In Pythagorean education, music played a role in cultivating inner harmony and discipline. Musical practice, according to Pythagoras' philosophy, was essential for intellectual and spiritual development, a belief that profoundly influenced education in Western cultures.

• The Pythagorean Scale: The Pythagorean scale is an example of a direct application of Pythagoras' discoveries to the practical field of music. Using the ratios found in the lengths of the strings, it is possible to create a scale with specific intervals based on precise numerical ratios.

• Musical Instruments: Pythagoras' research also influenced the construction of musical instruments. In turn, the precision and standardization in the manufacture of musical instruments allowed for a closer relationship between mathematics and music.

• Theory of Tuning: Tuning, or choosing the exact musical intervals to create different scales, is based fundamentally on the same mathematical principles as Pythagorean. Even today, Pythagorean tuning theories are important in understanding various techniques of tuning instruments.

• Pythagoras' Legacy in Music: Mo