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5
votes
2answers
120 views

Sound of $\sin(x \cdot \sin(x))$ without accumulation

Playing around with the sine function, I noticed that when you plug the formula $y = \sin(x \cdot \sin(x))$ into your speakers, you can hear nice sequences of overtones. Especially if you add a ...
5
votes
1answer
88 views

How is it possible to change the pitch and the tempo of an audio track independently of each other?

If you slow down a turntable or cassette-player, both pitch and tempo are decreased. How is it possible to change one without affecting the other?
0
votes
1answer
30 views

Number of series of this form whose product is 2

$I_n$ is the $n^\text{th}$ member of the series $I$ of length $k$. The first member of the series is of the form $2^\frac{m}{12}\mid m\in\Bbb Z\text{ and } 0\le m\le12$. If $k$ is larger than $1$ and $...
0
votes
1answer
93 views

Music of primes

In http://plus.maths.org/content/music-primes DuSatoy describes the relation between the prime number staircase and harmonics from music. So in the article he uses music as an analogy. But I wonder ...
5
votes
0answers
92 views

Different mathematical models for Audio? Their dimensions and limitations?

Stephen Hazel suggested some dimensions such as time, pitch, velocity of note down event, current root note of chord, chord type(major/minor/7th/etc), pan of the mix, volume of the mix and holding ...
4
votes
0answers
126 views

Is this the chord G Major I am hearing as base tones from interference of zeta zeros times eigenvalues of the von Mangoldt function matrix?

Mathematica knows that the logarithm of $n$ is: $$\log(n) = \lim\limits_{s \rightarrow 1} \zeta(s)\left(1 - \frac{1}{n^{(s - 1)}}\right)$$ The von Mangoldt function should then be: $$\Lambda(n)=\...
2
votes
0answers
63 views

Equation of the ellipse for musical notation (the quarter note/crotchet and shorter)

Note heads are often represented with a slightly rotated ellipse, as shown here for instance (first image). Does anyone happen to know the equation of the ellipsis, and the rotation that's applied to ...
1
vote
0answers
36 views

Fourier Transform: Musical Instruments cotd.

Upon analysing the Fourier Transform of a musical sound, are there any other applications of the Fourier Transform so obtained? Any ideas would be appreciated. Edit 1: To clarify the situation, I ...
1
vote
0answers
46 views

Standard form for partitions of $Z_n$

Let $A$ and $B$ be partitions of $Z_n$. Let's say that $A$ and $B$ are equivalent if $A=Bx+y$ for some $x\in{1,−1}$ and $y\in Z_n$. In other words, two partitions are equivalent if one can be obtained ...
0
votes
0answers
18 views

Tuning schemes for additional valves on a brass instrument

So this question is very much about music, but it's entirely about a mathematical part of music, and that part is tuning and how it relates to pipe length in a brass instrument. Background: I am ...
0
votes
0answers
39 views

What mathematical property does equal temperament have that lets it form keys?

Suppose I have the frequency $f$. According to just intonation, $\frac{3}{2} f$ is a perfect fifth. Now compare the following: $$ \left(\frac{3}{2}\right)^n \neq 2^m$$ for any integer $n,m$ But $$...
0
votes
0answers
32 views

Help needed for statistical analysis of pitch class sets

Within Music Analysis, there is a quite mathematical type of analysis which looks at pitch class sets ($pcs$), not surprisingly known as pitch class set analysis. See http://en.wikipedia.org/wiki/...