Music and mathematics: how are they related?

In summary, the mathematical difference between dissonance and consonance is that dissonance is created when notes are far apart in frequency, while consonance is created when notes are close together in frequency. Classical music is generally more dissonant because it uses more dissonant combinations.
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my main question: is there some mathematical formula that leads to a great song? be it a beat, melody, etc. what is the mathematical difference between dissonance and connosance? we know that listening to classical music at a young age results in high math scores. but why?
i have listened to compositions by such artists as daniel cummerow.(those who applied mathematical algorithms to making music). and i can say without a doubt that none of these artists will be on the top hits anytime soon. so what mathematical formula creates a great song? what makes a melody catchy?
 
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  • #2
okkvlt said:
my main question: is there some mathematical formula that leads to a great song?

no, there's musical theory which is a set of "rules" that lead to palatable music.

be it a beat, melody, etc. what is the mathematical difference between dissonance and connosance?

A good metric of dissonance and consonance is the distance between the notes involved. The closer they are, the more dissonant. But this isn't an absolute rule. Mainly, the notes need to be integer fractions of each other to be more "connonant". (Google the harmonic series in terms of music).

Examples of consonant combinations are the unison, the octave, the fifth. See how they place in the harmonic series (for instance, an octave is twice the frequency of the fundamental).

we know that listening to classical music at a young age results in high math scores. but why?

I'm pretty sure there's no significant correlation. It may just be a marketing technique for the Baby Mozart people, or correlates found may have just come from the fact that more intelligent people listen to classical music and also happen to pass intelligence genes to their kids.

I play instruments for my baby to show her cause n' effect, but it's interactive (I let her play with the instruments as best she can).

so what mathematical formula creates a great song? what makes a melody catchy?

The most popular set of chords in Western music is the I-IV-V. This is likely because of their integer relationship in frequency. (Also, I is to IV as V is to I so there's a hierarchy there).

Some examples of I-IV-V are:

A, D, E
E, A, B
G, C, D
C, F, G
 
  • #3
http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf

If math is what you want, don't say you didn't ask for it.:smile:

It has much theory on symmetries and consonance as well as general signals and waves.
 
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Negatron said:
http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf

If math is what you want, don't say you didn't ask for it.:smile:

It has much theory on symmetries and consonance as well as general signals and waves.

wow, that is music as only an electrical engineer could love it. kudos.

and that circle of fifths stuff is familiar. i ran into it while googling after seeing the http://boingboing.net/2009/08/01/bobby-mcferrin-hacks.html" [Broken]. the idea i found was that the structure of the cochlea itself has something to do with it, but i got a little lazy about it when confronted with checking the math.
 
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What is the connection between music and mathematics?

The connection between music and mathematics is that both involve patterns, ratios, and proportions. Music is made up of notes, which have specific frequencies and durations, and these can be represented mathematically. Additionally, music follows structures and forms that can be compared to mathematical equations or patterns.

How has mathematics influenced music?

Mathematics has influenced music in various ways, such as the development of musical notation, which uses mathematical symbols and ratios to represent different notes and their durations. Additionally, composers often use mathematical concepts, such as symmetry and Fibonacci numbers, to create harmonious and pleasing compositions.

Can studying mathematics improve musical abilities?

There is some evidence that studying mathematics can improve musical abilities, as both subjects involve similar cognitive skills such as pattern recognition, spatial reasoning, and critical thinking. Some studies have also shown that students who excel in math tend to excel in music as well.

What is the golden ratio and how is it related to music?

The golden ratio is a mathematical concept that represents a ratio of approximately 1.618, which is considered aesthetically pleasing to the human eye. It has been found in various aspects of music, such as the proportions of a violin, the placement of frets on a guitar, and the structure of musical compositions.

Are there any famous musicians who were also mathematicians?

Yes, there are several famous musicians who also had a strong background in mathematics. Some notable examples include Johann Sebastian Bach, who was known for his use of mathematical structures in his compositions, and Pythagoras, the ancient Greek philosopher and mathematician who also studied music and the mathematical relationships between musical notes.

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