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Calculus Of Music

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by

Moises Sains

on 27 May 2014

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Transcript of Calculus Of Music

Calculus Of Music
Derivative
The slope of any time t will be the derivative of that interval.
dy/dt =f(2pi)*cos[f(2pi.015)]
You Try!
In graphs, please put the following frequencies with the general form of sin[f*2pi(t)]
Basic Information
Sound Wave is pressure disturbance that travels through a medium by means of particle-to-particle interaction.
The Calculus Of Music
This project demonstrates how derivatives affect how sound wave produce musical notes and how the trig. function of "sin" is used to calculate the slopes of the function.
Conclusion
Music is beautiful thing nd something that nature gave us. Something people won't think with math, much less calculus so I leave to reason if calculus has much to do with music, then what doesn't? (don't say English)
In addition, how the harmonic series gets its name and how the series applies to music and frequency.
BC Topic
Anti-Derivative
Lastly, because music doesn't use Anti-derivatives, this part would just be about finding the area of the sin function for music
Frequency refers to the number of vibrations that an individual particle makes per unit of time
How Are Musical Notes "made"?
The pitch of a sound is determined by the frequency of its vibrations.
Faster pitch-faster vibrations
Lower pitch-slower vibrations
Musical Notes are sounds that have definite pitch which are called tones.
The vibrations of a tone are regular and reach the ear at equal time intervals
General Form of Musical Notes is y=sin[f*2pi(t)]
Where f is interval and t is time
Example
Musical Note of C4
263.63(2pi)*cos[cos261.63(2pi.015
Slope is 1463.11
However, slopes don't matter because of the sin function intervals of [-1,1]
G chord
G4-392.00
B4-
D5-587.33
493.88
D Chord
D4-293.33
F#4-369.99
A4-440.00
C chord
C4-261.63
E4-329.63
G4-392.00
Guess What Song You just Played?
BC Topic
Harmonic Series
The p-series with p=1 is the harmonic series
So we know that this series is going to diverge
Definitions
The terms in the harmonic series correspond to the nodes on vibrating pitch that produce multiples of fundamental frequency
Fundamental Frequency-the lowest frequency produced by the oscillation of the whole of an object, as distinct from the harmonics of higher frequency.
Fundamental Tone-the tone that represents the fundamental frequency of a vibrating object
Overtones
They are fractional segments of the fundamental tone
Starts off, with 1/2, 1/3,1/4 etc. going to infinite because of the divergence of the series.
The faster they vibrate higher, higher frequency, meaning higher tones(overtones) aka Harmonics
What This All Mean?
The overtones sound together with the fundamental tone to make up the full sound.
So lower notes', overtones can be heard easier meaning they sound more rich in tone.
Lastly, as the series goes on, the overtone become musical interval to the fundamental tone.
Example
Oops!
Sorry music doesn't use anti-derivatives so instead lets just find the area of the musical note function.
Well, what happen?
Because music is nature, the sound has to be equal meaning that the integral well always be zero due to the sin function "behavior"
Let's Try
Full transcript