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# Calculus in Music

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## Annika Gordon

on 20 May 2016

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#### Transcript of Calculus in Music

Calculus in Music
Derivatives in Music
General form of music notes:
y=sin[f*2pi(t)]
f=interval t=time

Integrals in Music
integral=area under the curve
Derivatives continued
A Music Piece Is A Function.
Conclusion
Music is said to represent the dynamics of human emotion. The dynamics and tension created by music fluctuates, as do human emotions while we are listening. Calculus can be a powerful tool in showing these fluctuations and dynamic changes, as well as showing us how well the volume is balanced.

Music Notes
Periodic function
Creating Chords
A sound wave is the pattern of disturbance caused by the movement of energy traveling through a medium (such as air, water, or any other liquid or solid matter) as it propagates away from the source of the sound.
Higher pitch= faster vibrations
Lower pitch=slower vibrations
derivative= slopes of tangent lines
interesting music=changes in derivative
The slope of any time t will be the derivative of that interval
t=.015
dy/dt =f(2pi)*cos[f(2pi.015)

derivative of a tension curve= the affective velocity
area under curve is too small= drowned out by crowed
area under curve too large= overpowering
balancing act
Calculus Formulas in Music
scale fitness function, midi numbering:

http://www.math.harvard.edu/~knill/teaching/math1a_2012/handouts/43-music.pdf

Bibliography:
http://www.math.harvard.edu/~knill/teaching/math1a_2012/handouts/43-music.pdf
http://smallvenuesurvivalist.com/the-calculus-of-music/
http://people.sju.edu/~rhall/proposal.pdf
http://whatis.techtarget.com/definition/sound-wave
http://www.math.umn.edu/~rogness/math1155/soundwaves/
http://daniellevitin.com/levitinlab/articles/2005-Vines-Music-Perception.pdf

Quick History of Math and Music
Pythagoreans of Ancient Greece first to investigate musical scales in terms of numerical ratios
"all nature consists of harmony arising out of numbers"
Time of Plato harmony branch of physics
Full transcript