Math Question

Discussion in 'Ballroom Dance' started by suburbaknght, Jun 3, 2009.

  1. suburbaknght

    suburbaknght Well-Known Member

    Having completed algebra with flying colors lo these many moons ago, I'd have thought this would be an easy question, but for some reason it's eluding me.

    Where:
    Bn is the unaltered speed of a song expressed as beats per minute.
    Bd is the desired speed of a song expressed as beats per minute.
    Pn = 100% is the length of a song expressed as a percentage of the unaltered overall length.
    Pd is the length of a song to achieve the new Bd expressed as the percentage of the unaltered overall length.

    Create an expression describing Pd as a simple function of the other variables where all other variables are known.
  2. etp777

    etp777 Active Member

    Pd = (Bn*Pn)/Bd

    As rough notation, as some units dropped out. Bn in my equation is no longer bars per minute, just bars (aka 30 bars, instead of 30 BPM), Pn is just an integer (that's where you cancel out the minutes in BPM), and BD is just in Bars too. Hrmm, which means I've lost the Minute unit on right hand side. But whatever, believe that should work, roughed it out on paper, going to actually try it with a song now.

    And of course, don't forget proper order of operations there (though I doubt it matters in this case ;) ). Please Excuse My Dear Aunt Sally, to quote the old mnemonic.

    Can recheck my work and do some more test "time warps", but went from 28.9 BPM to 32 BPM right on the dot (which is what I was aiming for) using that math. Normally I just guesstimate it, so that's going to be useful in the future. Thanks.
  3. Me

    Me New Member

    *head explodes*
  4. bluebereft

    bluebereft Member

    Is P a percentage?

    Pd/Pn = Bd/Bn ?
  5. etp777

    etp777 Active Member

    Test file was 2:15(Pn), current BPM was 28.9(Bn). Target BPM was 32(Bd), so using my equation (least, way it works in my head, my notation might not work for anyone else :) ), multiplied 2.25 (converted 2:15 to decimal so I could use calculator) times 28.9, getting 65.025, then divided by 32 to get 2.03. Converting that back, get 2:01.9535 mniutes

    Another way to do the math (to skip the first multiplying step), is to figure out the total number of bars in the song, then just divide by the tempo you want in BPM. That will give you the target lenght (and in fact is all my equation is doing)
  6. suburbaknght

    suburbaknght Well-Known Member

    Thank you etp! You are a life saver.
  7. j_alexandra

    j_alexandra Well-Known Member

    mine, too
  8. etp777

    etp777 Active Member

    lol @ me and j.

    and you're welcome SK. Happy to help, esp. when it's somethign I shoudl have done a while ago, and can use now. :)
  9. suburbaknght

    suburbaknght Well-Known Member

    Ah, I just figured out where I was going wrong. I was getting the same formula, then plugging in the numbers for slowing a 60 MPM international Viennese to 54 MPM American and getting 111%. Then I'd say to myself, "Self, this can't be right. Why would the number be higher if the song got slower?" forgetting that this was the percentage to <i>stretch</i>, not compress. Thanks for stepping me through the math.
  10. DL

    DL Well-Known Member

    I think that's inverted.

    Writing etp's result another way and expressing the number of beats as N, we could say:

    BdPd = BnPn = N

    or, with units:

    Bd beats/min * Pd min = Bn beats/min * Pn min = N beats

    That is, the number of beats is the same regardless of the rate at which they are played or how long it takes to play them.
  11. etp777

    etp777 Active Member

    Too late for me to do the math on your equation (not doubting, just way I was raised, DL :) ), but i can guarantee my dad would agree with you that my equation needs rewriting. The joys of a dad who's a math teacher. SO I guess that's 2 to 1, even if I want to disagree. :D
  12. DL

    DL Well-Known Member

    I just multiplied both sides of your equation by Bd, which incidentally puts the equation in a form other than OP requested. So I think you got it right just the way you had it.

    BlueBereft's version / question isn't the same as yours. I added the dimensional analysis in the hopes that it made things more clear and would minimize head explosions. Maybe I just added confusion, though. Oh, well.
  13. etp777

    etp777 Active Member

    ah yeah, see what you did. Makes sense to me. Course, won't say you didn't add confusion to people. Math, even algebra (I avoid calculus and higher, even though profs and dad all say I understand it), is defenitely an acquired skill. And to really think that way, I think yhou ahve to be born with it. Otherwise you're thinkin in one "language" and converting in your head. Just like I do with Spanish.

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