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Calculus in Music
Transcript of Calculus in Music
Derivatives in Music
General form of music notes:
Integrals in Music
integral=area under the curve
A Music Piece Is A Function.
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.
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
derivative of a tension curve= the affective velocity
area under curve is too small= drowned out by crowed
area under curve too large= overpowering
Calculus Formulas in Music
scale fitness function, midi numbering:
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