Beautiful music is supported by beautiful mathematics

Aug 2011
85
1
“Music is the pleasure the human mind experiences from counting without being aware that it is counting.”
-Leibniz

I am myself a musician and been stunned by the interconnectedness between music and mathematics (or science of patterns).

I present here some interesting facts of the deep relationship.

Did you know?

-The harmonic scale (thus the name!) explains the different timbre of instruments.

-Each new note, if we start on 1, on the standard 12-note scale exists thanks to a prime or prime power(e.g. 9).

-All music is beats. The lowest we call rhythm and the highest and more intricate harmony. This is precisely the same as arithmetic and natural numbers. It is interesting to note the universal appraise of melody, very likely as the critical connecting point without which music can feel "empty".

-The great Fourier through his discovery found an infinite number of differently tuned tuning forks can play what an orchestra can play. Today we see this with audio speakers. Fast Fourier Transforms are at the heart of electronic music.

-If the Riemann hypothesis is right, the primes form a metamodern orchestra where no instrument (prime) plays any louder than any other.

-In the west, due to equal temperament, we hear "irrational music" because we tune are pianos with equal steps to foster transposition. This yields exact frequencies as logarithms of 2, from the octave. It is an irony of fate the European civilization most renowned for its harmony is in fact more out of tune than others such as the Chinese which tune their instruments using rational fractions instead.

-Music has a darker side. Ad music, slot machines and so called "muzak", or store music, manipulate people to spend more. Although this is also supported by elegant mathematics, for sure Hardy is whirling in his grave.

-It is astounding how the deep relationship between music and mathematics has come full circle from Pythagoras and his music of the spheres to modern String Theory. Sound harmonics have gone from the violin to the possible component of nature, the one-dimensional String.


Even when mathematics becomes the rigorous, austere and difficult companion, a sweet melody can remind those of ous fallen in love with it how good it sounds to the ears of the soul.
 
Mar 2012
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Music is the best friend whenever we practice mathematics.It creates a positive impact on mind and we easily solves the mathematics sums.
 

mathbalarka

Math Team
Mar 2012
3,871
86
India, West Bengal
suresh123 said:
Music is the best friend whenever we practice mathematics.It creates a positive impact on mind and we easily solves the mathematics sums.
I dont know about others, but for me, music is music and mathematics is mathematics. When I think about something, music (usualy jazz and blues) disturbes me and i cannot concentrate :(

Eureka, the facts in your post are amazing!!! :)
 
Jul 2012
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nice post,
i think its a great relationship among math and music :)
 
Jun 2011
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Eureka said:
-The harmonic scale (thus the name!) explains the different timbre of instruments.

-
The harmonic scale is man made; the timbre of instruments isn't. When a car crashed it has a different timbre than shattering of a plastic cup.
The harmonic scale has nothing to do with the different timbre of instruments. Don't just believe what you hear or read.
 
Jan 2011
106
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Math Dreamer is right! Harmonic scales describe the relations between FREQUENCIES of notes, while timbre of an instrument is the characteristic of functions whose sums determine the "shape" of an instrument's wave function.
 
Sep 2012
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Eureka said:
-Each new note, if we start on 1, on the standard 12-note scale exists thanks to a prime or prime power(e.g. 9).
Could you explain it a little more? I wonder why there is the division in 12 intervals... So what you are saying is that it is on purpose and it has do do with primes???
 
Nov 2015
152
0
usa
The relationship is amazing. Also improvisation of structured music, leads the mind into other forms of creativity in many forms. Both related to this beautiful world and the sounds we are lucky to hear. The math involved I feel is secondary and the math is directly related music is related to this music. I find they are both important and related, but I would rather hear music, than see it. I do not mean to offend, this is only my opinion. It is very hard to put feelings or emotion into numbers, only sounds.
Math and music is still related in this beautiful form of art.