Math in Music

Discussion in 'Miscellaneous [BG]' started by TopBillinBass, Nov 21, 2012.


  1. TopBillinBass

    TopBillinBass

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    Hi Everyone!

    So I'm very interested in pursuing an advanced degree (Master's or Doctorate) in something closely related to Mathematics in Music Theory. Unfortunately, I don't know what to search for and I don't know much to about it. Can anybody point me in the right direction for information about this field or graduate schools that have programs in this field? Thank you!
     
  2. Kmonk

    Kmonk

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  3. ntenny

    ntenny

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    Thanks, that looks fascinating. I had no idea it existed.

    To the OP: I'm an actual mathematics Ph.D., and from my experience in grad school I think you'll have more luck approaching the "crossover" topic from the music side than the mathematics side. (For instance, the link above is an interest group within the Society for Music Theory, not the American Mathematical Society.)

    What's your academic background thus far? Already done with an undergrad program, and if so, in what? If you're basically qualified to go into a music theory grad program, it seems like it might make sense to apply to some schools where there are faculty working in this area (which you should be able to find out from that link above).

    Obviously you're talking about a narrow academic field that's going to be challenging to make into a remunerative career and all that, but you probably thought of that already.

    -NT
     
  4. TopBillinBass

    TopBillinBass

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    Thanks you guys!

    I've just completed and undergraduate degree in Physics so I have a fair amount of Mathematics under my belt. I've been playing bass for 8 years or so and have played cello, trombone and guitar. I read music well and know the basics of music theory.

    I found this link on Stanford's web page. It's the program called Computer Based Music Theory and Acoustics. Tell me what you guys think!

    http://exploredegrees.stanford.edu/schoolofhumanitiesandsciences/music/#doctoraltext
     
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  6. placedesjardins

    placedesjardins

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    What are you going to do with a degree in Mathematics in Music Theory?
     
  7. wcnewby

    wcnewby Supporting Member

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    This isn't about what you asked but it is about math and music, sort of. I posted this in the luthiers section a while ago. I saw a pattern on my fretboard and it made me wonder some about who set all this up.

    I made the matrix below by using a scale like you would have on your fretboard. The * frets, the letters are notes. I started with F just because, it doesn't matter, you can make it any size. Read it like a book left to right then down the next line. It is just A*BC*D*EF*G starting on F and repeating over and over. Now read it vertically and you get FCGDEAB***** or bottom up BEADGCF***** (the pattern I noticed) It does it diagonally as well. This pattern is related to the circle of fifths.

    F*G*A*BC*D*EF*G*A*BC*D*EF*G*A*B
    C*D*EF*G*A*BC*D*EF*G*A*BC*D*EF*
    G*A*BC*D*EF*G*A*BC*D*EF*G*A*BC*
    D*EF*G*A*BC*D*EF*G*A*BC*D*EF*G*
    A*BC*D*EF*G*A*BC*D*EF*G*A*BC*D*
    EF*G*A*BC*D*EF*G*A*BC*D*EF*G*A*
    BC*D*EF*G*A*BC*D*EF*G*A*BC*D*EF
    *G*A*BC*D*EF*G*A*BC*D*EF*G*A*BC
    *D*EF*G*A*BC*D*EF*G*A*BC*D*EF*G
    *A*BC*D*EF*G*A*BC*D*EF*G*A*BC*D
    *EF*G*A*BC*D*EF*G*A*BC*D*EF*G*A
    *BC*D*EF*G*A*BC*D*EF*G*A*BC*D*E
    F*G*A*BC*D*EF*G*A*BC*D*EF*G*A*B
    C*D*EF*G*A*BC*D*EF*G*A*BC*D*EF*

    On the left, find G below G you get D,A,E... and B (if you have a five string) These are the strings on your bass and to the right are the notes on your fretboard, (if it had 31 frets)

    Doesn't work on a guitar neck, because it doesn't follow the pattern. The guitar is not logical.

    See, it is kind of mathematical when you look at it like this. I don't understand how it could lay out like this without planning or mathmatics, or some natural pattern like a seashell but with sound... I just thought a person with a math education might have insight the luthiers didn't
    __________________
     
  8. Stilettoprefer

    Stilettoprefer

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    ^^^ and if you read that backwards its the circle of fourths;)

    Standard tuning for a bass is 4ths from E-G (4string). So logically you would have part of the circle of fourths anywhere on your fingerboard if you just go in a straight line across the neck from E string to G string. Go backwards and you have fifths.

    It's pretty basic theory.

    For a cello or violin, you tune to fifths from the lowest string to the highest. same with mandolins.

    The guitar tuning system has always stumped me because of the switch from fourths to a third with the B string then back to fourths to reach the high E. Seems like it would have been just as easy to leave it all in fourths. Would certainly make soloing easier....

    And I'm just now realizing how off topic this comment is....
     
  9. wcnewby

    wcnewby Supporting Member

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    I retuned an ec-10 to be logical and then discovered that many chords were very hard to make.

    Now we are in left field together...
     
  10. Stilettoprefer

    Stilettoprefer

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    Yeah I thought about chord shapes after I commented. It would be pretty awkward to barre chords and whatnot. I guess what we're seeing as illogical is actual very incredibly logical haha.
     
  11. Rush-2112

    Rush-2112

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  12. wcnewby

    wcnewby Supporting Member

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    amazing... Pi is a fascinating number, the key to all circles. Music is definitely mathematical. It isn't immediately obvious, but math is there in music so music must also be in math. The question is how.
     
  13. Dubista

    Dubista

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    Don't forget the wave equation now. Just solving it in one spatial dimension really opened up my eyes about overtones. I also find it very fascinating how the overtones are in some kind of "quantised state" which, to me, kind of relates it to Quantum Physics, in a sense.
     
  14. wcnewby

    wcnewby Supporting Member

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    I totally hi-jacked this thread, and I did not mean to. I hope OP got the answer because now that I am a bandito I might as well stick with it.

    What is the wave equation? Are you familiar with the golden ratio? What eats on me is I can see an interconnectedness here... like the pattern of a snowflake... a fractal... or simple design that is used to make a larger design that looks like the small one.

    Are you the one who started "every time someone drop tunes a guitar Jesus kills a puppy" I told my music teacher that when he suggested drop tuning. He almost fell off his chair laughing. He claims to be Jesus and maintains that this is not true.
     
  15. Clef_de_fa

    Clef_de_fa

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    Well ... their is software where math could be handy for the velocity and various degree of everything.

    Otherwise I remember the dodecaphonism and serialism and other more philosophical approach to music of the last century. It is really far and hard to understand or appreciate but it is still music. Maybe you may like it.
     
  16. ntenny

    ntenny

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    For a completely different "math in music" flavor, there's a paper from 1976 studying the generation of music from a particular kind of signal called "1/f noise":

    Voss, Richard F. and John Clarke. " '1/f noise' in Music: Music From 1/f Noise." J. Acoust. Soc. Am. 63(1) (1978): 258-261.

    It's readable for an educated layman (I think I was a junior in college when I encountered it) and has some really interesting results that seem to hint at the kind of properties that make music sound "right". It's a bit orthogonal to music theory---it just treats the music as a signal, without regard to higher-order structures like key and time.

    Fascinating stuff, which was later picked up my Martin Gardner and others in the mathematical world, but I don't know how much it's really been looked at in the musical world.

    -NT
     
  17. Dubista

    Dubista

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    Wave equation is a second order linear PDE that you can use to model waves on something like a string generally looks like:

    u is a function of one time and however many spatial dimensions and c is the wave speed.

    u[SUB]tt[/SUB] = c[SUP]2[/SUP]∇[SUP]2[/SUP]u

    Where grad is the derivative operator takes derivatives in spatial dimensions.

    In one dimension it is:

    u[SUB]tt[/SUB] = c[SUP]2[/SUP]u[SUB]xx[/SUB]

    Where u is a function of x and t

    The general solution in the one dimension case is:

    u(x,t) = Σ sin(nπx/L)[A[SUB]n[/SUB]sin(nπct/L) + B[SUB]n[/SUB]cos(nπct/L)]

    where n is an integer from 1 to infinity, L is the length of the string and A and B are arbitrary constants that you can determine by using fourier series, boundary conditions and the initial conditions.

    TL;DR:

    The "n" part is what I find interesting because each value of n corresponds to the fundamental and the overtones. Of course, this stuff takes place in "Math world" as I like to call it and it is just the one dimensional case but I still think it's pretty rad that overtones come in a sort of "quantised state".
     
  18. wcnewby

    wcnewby Supporting Member

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    It is a rare musician that speaks calculus... I had up to calc one in college, not a music college... no football team and very few girls that were taller than round. We called them gravitationally challenged.

    Most of what you said went over my head, but not by much, I think my hair moved.
     
  19. mark b2

    mark b2

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  20. charliefreak

    charliefreak

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    *If you are happy w/ your current state of mind, DON'T READ THIS THREAD.

    You've been warned
     
  21. fraublugher

    fraublugher

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    The overtone series , one note contains a dominant 7 chord and extensions.
     

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