What can maths teach us about music? - Telegraph
Similar research can be done for the connection between mathematics and music from other cultures, but this is not the focus of this project. The more I read and. The connection between music and mathematics has fascinated scholars for centuries. Now, three music professors – Clifton Callender at. Who says maths is all cold logic and music all emotion? that I believe the true connection between mathematics and music reveals itself.
I can get a computer to churn out endless true statements about numbers, just as a computer can be programmed to create music. Invention is discernment, choice. The sterile combinations do not even present themselves to the mind of the inventor. Bach's Goldberg Variations depend on games of symmetry to create the progression from theme to variation.
Messiaen is drawn to prime numbers to create a sense of unease and timelessness in his famous Quartet for the End of Time.
Mathematics and Music - Study | Simplifying Theory
Schoenberg's tone systemwhich influenced so many of the major composers of the 20th century, including Webern, Berg and Stravinsky, is underpinned by mathematical structure. The organic sense of growth found in the Fibonacci sequence of numbers 1,2,3,5,8, Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: A note, for example, corresponds to a frequency of Hz.
Mathematics in music And where Mathematics enters in music? It was observed that when a frequency is multiplied by 2, the note still the same.
Music and mathematics
If the goal was to lower one octave, it would be enough just dividing by 2. In that time, there was a man called Pythagoras that made really important discoveries to Mathematics and music. Imagine a stretched string tied in its extremities. When we touch this string, it vibrates look the drawing below: Pythagoras decided to divide this string in two parts and touched each extremity again.
The sound that was produced was the same, but more acute because it was the same note one octave above: He decided to experience how it would be the sound if the string was divided in 3 parts: He noticed that a new sound appeared; different from the previous one. Thus, he continued doing subdivisions and combining the sounds mathematically creating scales that, later, stimulated the creation of musical instruments that could play this scales.
In the course of time, the notes were receiving the names we know today.
Mathematics and music scales Many peoples and cultures created their own music scales. One example is the Chinese people, which began with the idea of Pythagoras using strings.
They played C in a stretched string and then divided this string in 3 parts, like we showed before. The result of this division was the note G. Noticing that these notes had a harmony; they repeated the procedure starting in G, dividing again this string in 3 parts, resulting the note D.
This note had a pleasant harmony with G and also with C.The Geometry of Music
This procedure was then repeated starting in D, resulting in A. After that, starting in A, they got E. Set theory music Musical set theory uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of typically atonal music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such as transposition and inversionone can discover deep structures in the music.
Operations such as transposition and inversion are called isometries because they preserve the intervals between tones in a set. Abstract algebra Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music.
For example, the pitch classes in an equally tempered octave form an abelian group with 12 elements. It is possible to describe just intonation in terms of a free abelian group. The theory allows for great generality because it emphasizes transformations between musical objects, rather than the musical objects themselves.
Theorists have also proposed musical applications of more sophisticated algebraic concepts. The theory of regular temperaments has been extensively developed with a wide range of sophisticated mathematics, for example by associating each regular temperament with a rational point on a Grassmannian.
The chromatic scale has a free and transitive action of the cyclic group Z.