MHB How is Group Theory Applied in Music?

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Group theory is applied in music through the mathematical relationships that define pitch and rhythm. Music notation utilizes a staff system where notes represent specific pitches and durations, correlating to fractions of measures. The structure of scales and chords can be analyzed using group theory, highlighting symmetries and transformations in musical compositions. Understanding these mathematical concepts can enhance the analysis and creation of music. This application of mathematics in music provides a foundation for projects exploring the intersection of these fields.
Pratibha
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Is there any application of maths in music, which topic is directly used. I've heard group theory is used, but how it is used. Plz help..i m going to work on a project that will show how maths works in music or sound system.
 
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Pratibha said:
Is there any application of maths in music, which topic is directly used. I've heard group theory is used, but how it is used. Plz help..i m going to work on a project that will show how maths works in music or sound system.

If you know a bit about how to read music, the mathematics of music becomes obvious.

Music is written on a "staff" (five horizontal lines). If you create a simple tempo (amount of time), you can mark this with equally spaced vertical lines, called "measures" or "bars".

A note has two important features, its PITCH (how high or low it is) and its DURATION. So when you see notes drawn on the staff inside each bar, it's telling you WHAT FRACTION OF THE BAR (i.e. how many beats) that each note goes for.

Pitch is also determined by mathematical relationships. I suggest you read this article.
 
Pratibha said:
Is there any application of maths in music, which topic is directly used. I've heard group theory is used, but how it is used. Plz help..i m going to work on a project that will show how maths works in music or sound system.

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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