Mathematicians act and think like artists.
Throughout history, music has been considered an expression of the universe.
Pythagoras, who believed that the universe was built according to numbers and the relationships between them, also addressed music from this aspect and wrote down its mathematical mystery; He demonstrated that music could be reduced to mathematical proportions, discovered the diatonic scale and proposed the "Harmony of the Spheres" proposition. Euclid, known as the father of geometry, is also a follower of Pythagoras in music.
Greek traces are also seen in the works of mathematical scholars Kindi and Farabi and in the music-related treatises of the Brotherhood of Safa (10th century). In his work titled İhsâ'ü'l-'Ulûm, in which he classified the sciences, Farabi also included music in the mathematics chapter and, like Pythagoras, accepted music as one of the 'higher sciences'. Kindi's work named Risâle fî Hubri Te'lîfi'l-Elhân is the first work to include the abjad note.
Ibn Sina, who allocates a section called "Cevâmi'u İlmi'l-Mûsika" for music in Kitâbu'ş-Şifâ, includes the definition of music, note information, intervals, genera and types, groups and types, transmission, rhythm information, rhythm types . He discussed the subjects of poetry, composition, musical instruments and expressed his views on music. Ibn Sina benefited from Farabi in sections such as 'interval' and 'series' and emphasized the need to look at Euclid's works for detailed information about music.
Ibn Khaldun, who said, "Music examines the proportion and quantity of scientific sounds and melodies," counts music among the mental sciences such as astronomy, arithmetic and engineering in his classification of sciences.
Kutbüddin-i Şirazî, who was also a scholar of geometry and arithmetic , used circular expression in his musical treatise, which he included in his work titled Dürretü't-Tâc li Gurreti'd-Dîbâc, in which he discussed many sciences .
Reza Sarhangi , who worked on geometric patterns in Islamic art and focused on the relationship between music and mathematics , was also a musician. He founded The Bridges in 1998 to promote research, practice and interest in the mathematical connections of art, music, architecture, education and culture. Sarhangi, who believes that mathematics and art, which may seem unconnected most of the time, can inform and enrich each other, emphasizes that music was not kept away from mathematics in the medieval Islamic understanding of science.
The principles of geometric surface coating formation in Islamic art are similar to music. In geometric designs that start from a single point to a circle, then to a unit, and with these units to infinity, the background lines and circle used to form the pattern do not appear to exist. The resulting unit cell multiplies and expands to infinity, just like the flowering of a seed. In the body-particle relationship, each line is a sound that forms the orchestra, and all sounds flow to infinity in harmony with each other.
It is possible to associate the image of the four directions in Islamic art in the form of a circle with the circle and the circle with the universe. Biruni states that the words circle and fate are synonymous, but the word fate is used more to describe the circle or sphere in motion. Books about Turkish music are called 'edvâr' (circles, cycles). In this context, it can be thought that the codes of geometry are similar to the maqams.
Anthony Burgess, in his book Mozart and the Deyyus, says, “A person who is a born musician must also be a born mathematician. These two abilities undoubtedly arise from an instinctive numericality, for a reason Pythagoras explained somewhere. In fact, notes are vibrations that obey strict mathematical rules.” he said.
Mathematician J. Fourier, who examined the quality of musical sounds in the 19th century, proved that all these sounds can be described with mathematical expressions such as periodic sine functions.
Questions about the diversity, similarity, counting and classification of musical structures have interested mathematicians as well as musicians. Mathematical models have been found, from theoretical analysis to actual composition or sound production. In the last few decades, there has been a focus on studies that incorporate the modern mathematical content of music. Examples include the application of methods from algebraic combinatorics or topology and graph theory to the classification of different musical objects. Mariana Montiel and Robert Peck brought together studies on this subject in their work titled Mathematical Music Theory . The book titled Musimathics , which deals with musicians who bring art and science together , contains basic information on the subject. In his work A Geometry of Music , Tymoczko takes a revolutionary geometric approach to music theory and shows how to create simple diagrams that represent relationships between familiar chords and scales. Geometry of Musical Rhythm offers a systematic and accessible computational geometric analysis of musical rhythms.
In 1780, physicist-musician Ernst Chladni examined the visual equivalent of sounds with his experiment. He vibrated a metal plate covered with sand with a spring, and observed that as the frequency increased, the geometric patterns on the plate became more complex. This approach, based on a scientific methodology by physicist and naturalist Hans Jenny, is called 'cymatics'. The process is based on the principle that some of the areas on the plate vibrate while others do not. Substances resist gravity with frequency. Each substance has its own geometric behavior and these behaviors vary according to frequency.
Number, proportion and geometry found in nature have been used consciously or unconsciously by artists in their works. For example, the ratio ¢=1.618034…, which consists of the Fibonacci sequence, is featured in the works of musicians such as Mozart.
Akio Hizume used the continuous interconnected structure of the golden ratio for musical scale and rhythm. Hizume stated that his music, which he calls "Fibonacci Kecak", is an initiative focusing on rhythm based on the Fibonacci series, and generalized poly-rhythm music to real numbers by using continued fractions. He states that there are Turkish music works with 5, 7, 9, and 11 beats, which can be considered parallel to the frequent use of pentagonal, heptagonal, and ninagonal geometric patterns in Islamic art, and mentions that there may be songs with 13 beats.
It is possible to see in the works of scientists and artists nourished by nature their efforts to understand the world around them. The knowledge of the universe is related to each other, and studies carried out by realizing this relationship strive to reach the "Whole". As physicist Richard Feynman said, “Nature uses only the longest threads to weave its tapestry, so that a single piece of thread reveals the structure of the entire tapestry.”
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