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science of string vibration

Discussion in 'Miscellaneous [BG]' started by evilbrian9, Dec 17, 2002.


  1. i was just reading the thread on harmonics and all and i remember reading somewhere that if you play a note and with a half step apart the vibration that you hear is in the ratio of exactly 9:10 does anyone know any other facts like this, i have been looking for other things like this but i have had no luck. the science of the string vibration is very interesting, please help with any knowledge.

    b
     
  2. rustyshakelford

    rustyshakelford

    Jul 9, 2002
    You can actually see the wave if you hold the vibrating string in front of a strobe.

    Florescent lights and your television will work (I think the TV works better because of the refresh rate).

    Anyhow, strike an open string, hold the bass flat so the string is struck by the light from the television. Then tune down. You can actually see the waves on your string.

    Try harmonics. You can see the multiple nodes.

    RS
     
  3. thank you dale, i will try that.
     
  4. moley

    moley

    Sep 5, 2002
    Hampshire, UK
    If you're talking about frequency, then the ratio is the 12th root of 2, or 2 to the power 1/12 - i.e. the number you must raise to the power 12 to get 2. If you multiply a frequency by this number, you get the frequency of the note a semitone higher. But that's not so much to do with string vibration as it is to do with the properties of sound waves - regardless of whether it's a string or whatever that's vibrating.
     
  5. Molloy

    Molloy

    Dec 6, 2002
    Paris, France
    As moley said - in the equal tempered scale, the notes are evenly spaced along the octave : between say frequency F and frequency 2*F, you'll find :

    F ; 2^(1/12)*F ; 2^(2/12)*F ; ... ; 2^(11/12)*F ; 2*F

    With F=220Hz, that would be : A ; A# ; B ; ... ; G# ; A

    Going downward between F and F/2=2^(-1)*F you'll have :

    F ; 2^(-1/12)*F ; 2^(-2/12)*F ; ... ; 2^(-11/12)*F ; F/2

    Stuff becomes interesting when you take into account the natural frequency vibrations multiple of a string, even with ratios as simple as 3/2 (a perfect fifth) and 4/3 (a perfect fourth) : these ratio sound very "true" to the ears but are not exactly matched in the equal tempered scale (that's why a piano is not tuned strictly according along an equal scale.) It's been quite a complex subject and heated debate a few centuries ago, when various tempered scales were competiting for wide usuage. Bach's "well tempered keyboard" in particular are studies that systematically explore a particular tempered scale (the one that would become today's standard.)

    A very rich and very interesting college course about this (and much more) :
    http://www.math.uga.edu/~djb/html/math-music.html

    Depending on your math and music theory background, you may or may not be quickly overwhelmed (there are some tricky stuff, an appendix is easily math-degree level and clearly included for the sake of completeness), but it's easy to browse and pilfer general conepts here and there even if you don't get the equation. A very good start is appendix M.
     
  6. ........Moley's a genius........

    You listen to him good.

    Hi moley.:D :D

    John
     
  7. moley

    moley

    Sep 5, 2002
    Hampshire, UK
    lol, hi there John, and thanks! But, credit where it's due, Molloy gave more details than I did.