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Can you explain where the mathematics are in music?

  1. Oct 18, 2012 #1
    I am a musician, i've been playing guitar form 8 years now. And piano and drums as well for under 3. People tell me music is mathematical same with artwork, something i am also very proficient at. Is it purely from the patterns of the notes and timing of the pitches that make it mathematical? Or the organization of notes into chords derived from scales and intervals. I understand how there are mathematical principals but the application doesn't seem like it, to me. I don't perceive it as mathematical, i am not a math wiz at all so i find it funny how something that people say is composed of math comes naturally for me. Can anyone illuminate this?

    Thank you
  2. jcsd
  3. Oct 18, 2012 #2


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    Oh where to begin...

    The most fundamental aspect of modern western music is equal temperament. This comes from observing that if you raise by an octave you double the frequency. The chromatic notes arise from dividing this interval by 12 logarithmically.

    A 12 note scale has relations with abelian groups. IIRC there is a connection between the subgroups and triads (i.e. all chords are mathematical). Some subgroups are "better" and these correspond to consonance. There's also some mathematical reason as to why the harmonic seventh is "sweeter" than the standard minor seventh.

    Counterpoint. Oh counterpoint. There are entire books that use math to teach students how to compose counterpunctual music.

    I remember glancing through a math paper which looked at chord progressions. The very complicated progressions in orchestral music seem to have deep underlying structure. I don't remember much from the paper though.
  4. Oct 19, 2012 #3

    Stephen Tashi

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    It's correct to say that that mathematics can be used to explain certain aspects of music but, as traditional music is practiced, playing or composing music does not use mathematical methods. The rules of harmony and counterpoint have their own jargon and rules of thumb. (Such as "b to f and f to b is the devil in music".) These rules are somewhat systematic but they are not a form of mathematics that it is taught in math courses.

    I think a few peoplel do apply mathematics and computer science to analyze, composea and genrate music. Such people must know mathematical methods as they are taught in math courses. That type of education isn't gained by natural instinct.
  5. Oct 19, 2012 #4


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  6. Oct 19, 2012 #5


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    Equal temperament, though, is a compromise to make the practice of music simpler; no need to retune keyboard and fretted instruments at every key change. It is only an approximation to 'perfect' temperament. There's a good discussion of temperaments and history at http://www.pyxidium.u-net.com/Acoustics/MusicMaths/MusicMaths.html.
  7. Oct 20, 2012 #6
    As a pianist and mathematician, it's my opinion that there is no clear relationship between music and math, in the sense that math is directly applicable to actually playing music or vice versa. Yes, there's the obvious use of counting beats, but that is not exactly deep mathematics, just a little counting and ratios.

    However, in the brain, there could be relationships where we don't see them on the surface. There are studies showing that music correlates with better performance in math. Mathematicians, engineers, and physicists are overwhelmingly more likely to play musical instruments than the general population. I was once in a big lecture room where someone asked who played an instrument and only a few hands went up. However, among mathematicians, the proportion of people who play instruments, at least casually, is noticeably higher.
  8. Oct 20, 2012 #7
    Take a look at the interactive application at this site HERE.

    See if that helps.
  9. Oct 20, 2012 #8
    Pythagoras was the first to have discovered the relationship between music and mathematics when he observed a pattern between the thwang of tongs at a blacksmith shop. Try searching about that thing.
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