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1
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0answers
30 views

Equation of the ellipsis for musical notation

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 ...
4
votes
2answers
100 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 ...
0
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1answer
43 views

How does a number correspond to a sound when listening to an OEIS sequence?

I noticed that the OEIS allows you to listen to a sequence. It converts a sequence of integers to sounds somehow, but I can't find any information on which numbers correspond to which sounds. The OEIS ...
0
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0answers
17 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 ...
0
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1answer
28 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 ...
5
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1answer
50 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
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1answer
74 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 ...
0
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0answers
41 views

formula to get combinations of notes that can be played over chords.

I was experimenting with chord tones,and asked myself-if i'm allowed to play only one note everytime the chord changes,i would come up with a situation in which there are some fixed positions,the ...
17
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1answer
259 views

Revisiting “What is Mazzola's ”Topos of Music“ about?”

This question has been asked here: What is Mazzola's "Topos of Music" about? But I am dissatisfied with the response for several reasons and would like Math SE to revisit this ...
1
vote
1answer
81 views

wave equation on a square domain

I'm stuck on the following problem. Let $u(x, y, t)$ denote a solution to the linear wave equation $k^2(u_{xx}+u_{yy}) = u_{tt}$ with $k = 2$ on a square domain with corners at (0, 0), (0, 1), ...
1
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0answers
40 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
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1answer
33 views

Normal modes of a drum and Kac's question: Can one hear the shape of a drum?

I consider a vibrating membrane $D\subset {\mathbb{R}}^2 $, fixed on $\partial D$. The vertical displacement $f=f(x,y,t)$ of the membrane satisfies the wave equation. I search solutions of the form ...
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1answer
66 views

How to find the number of semitones between two frequencies?

Given two frequencies in HZ, how can I find the number of semitones between the notes they represent?
3
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0answers
118 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: ...
5
votes
4answers
451 views

Is the reasoning/algebra for my proof correct? (musical tuning theory proof)

This isn't for a class, I was just wondering if I would be able to work out a proof for something like this myself for fun, and wanted to verify that my methods are correct. Basically, what I'm trying ...
0
votes
1answer
117 views

Creating coexistent patterns, with several pattern-less systems

I'm a young musician, as well as a computer programmer. My understanding of math is formed well to my needs, but I am by no means a mathematician, but the field is very interesting to me. I have come ...
1
vote
1answer
83 views

dividing an octave to $7$ instead of $12$

Usually an octave is divided into $12$ parts based on the harmonic series(basic zeta function). how can I calculate the frequency of a note if I divide the octave into $7$ parts? ...
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3answers
215 views

Is it still possible for mathematicians to contribute to the theory of music?

Is it still possible that mathematicians contribute to the theory of music? Is the mathematical foundation of music still an area of research? If yes, what new researches have been done regarding ...
2
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3answers
950 views

What relation does music have to math?

A lot of people claim that music is just math and I don't understand why. Is there any facts behind this claim? It angers me when people make this claim and when I ask them to explain, even when they ...
9
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3answers
771 views

Is the Pi melody real or fake?

Having seen this video I can't stop wondering whether it is real (which is amazing) or fake. A mathematician-musician polymath opinion needed :-)
25
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1answer
1k views

Possible Playable Chords on a Guitar

Fingerstyle Guitar Chord Diversity Check Considering a $20$-fret $6$-string acoustic guitar and supposing that the fretting range (inclusive of the fingered notes) for an average hand is $4$ frets in ...
0
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1answer
1k views

How to calculate the ratio between Semitones in the diatonic scale?

There are twelve semitones in the diatonic scale, so the frequency doubles every twelve steps. Knowing this, how do you calculate the ratio between the frequency of one semitone and the next?
0
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1answer
54 views

Minimizing error in user-entered series of timestamps representing musical beats

I've got an app in which the user taps a key to the beat of a music to mark out measures. If a song has a tempo of 120, for example (500ms / beat), the human-entered values might look like this: $$u ...
5
votes
0answers
88 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 ...
5
votes
2answers
458 views

Is there a branch of math studying music algorithms?

I have found 2-3 search engines for scientific studies, things like algorithms, thesis, piece of researches and stuff like that; I'm really surprised to see a lot of applications for the math ...
1
vote
3answers
157 views

How to find a formula for a sequence of slightly inaccurate numbers

I'm in the process of reverse engineering a music file format from an old computer game. It uses numbers from 0 to 127 to represent note frequencies, however I need to convert these numbers to a ...
4
votes
4answers
2k views

What is Octave Equivalence?

This is an updated copy of a question I asked on Physics Stack Exchange not too long ago. Since I work primarily in mathematics, I thought it would be a good idea to ask it here as well (especially ...
8
votes
1answer
967 views

“The Music of Pi” [closed]

I'm curious about this piece in the oct/nov MAA Monthly Supplement about The Music of Pi, and have wanted to share it here. I'm curious for many reasons, including the composer's choice to represent ...
14
votes
1answer
780 views

A Weaker Version of the ABC Conjecture

The ABC conjecture states that there are a finite number of integer triples (a,b,c) such that $\frac {\log \left( c \right)}{\log \left( \text{rad} \left( abc \right) \right)}>1+\varepsilon $, ...
6
votes
2answers
1k views

How do you determine the closest whole number ratio for a given real number?

I've been messing around with formulas for musical notes (trying not to read anything that would help me unless I get stuck) and currently I'm at a point where I'm trying to get a function that ...
9
votes
2answers
2k views

What is Mazzola's “Topos of Music” about?

Disclaimers: I am neither a musician, nor I want to discredit Mazzola's work. Corollary of the first point: please use a plain style, without technical terms in the area of Music Theory. Corollary of ...
6
votes
5answers
2k views

Music — Is the diatonic scale optimal in some sense?

I have recently found a mathematically-sound "proof" that the twelve-tone musical scale is optimal. I am looking for a similar explanation proving that the diatonic scale is optimal in some sense. ...
19
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4answers
2k views

Why isn't a harp in a logarithmic shape?

I was watching a harp, yesterday, and thought about the mathematics involved. I know that music is closely related to logarithms, because having a string or pipe twice as long produces the same note. ...
23
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10answers
2k views

Mathematics and Music

I have heard that, in recent years, many mathematicians as well as music theorists have applied different branches of mathematics to music. I would like to know about some books/resources relating to ...
10
votes
3answers
3k views

The mathematics of music - why sine waves?

Of course, the Fourier transform is an extremely elegant mathematical method of overwhelming simplicity, and this straight away puts sine waves (or complex exponentials) on a high pedestal. But what ...
20
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7answers
3k views

Math and Music theory books

Are there any good books on musical theory from a mathematical standpoint? Is "Music theory and mathematics : chords, collections, and transformations", edited by Jack Douthett, Martha M. Hyde, and ...
4
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1answer
478 views

What constants do I need to create this specific logarithmic spiral?

please bear with me as I'm not a mathematician and this is difficult to word properly. :] I need the equation for a logarithmic spiral (let's call it $S(\theta)$) that meets certain constraints for a ...
361
votes
20answers
60k views

Mathematical difference between white and black notes in a piano

The division of the chromatic scale in $7$ natural notes (white keys in a piano) and $5$ accidental ones (black) seems a bit arbitrary to me. Apparently, adjacent notes in a piano (including white or ...