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0answers
35 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
23 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
26 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
96 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
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4answers
424 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
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0answers
22 views

Help with The Nature and Perception of Fluctuations in Human Musical Rhythms paper.

I'm a electronic musician. I've found this article about human rhythm. I know some electronic musicians are already using it to humanize electronic drums (e.g. James Holden) but I'm having trouble ...
0
votes
1answer
78 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 ...
0
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0answers
110 views

How many melodies are there?

Clearly if we assume only 12 chromatic notes to the scale, not all of which sound good next to each other, a melody of length $N$ chooses from less than $12^N$ potential melodies. Allowing melodies to ...
1
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1answer
67 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? ...
5
votes
2answers
164 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
640 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
513 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
766 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
votes
1answer
561 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
49 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
81 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
372 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
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3answers
139 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
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4answers
1k 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
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1answer
850 views

“The Music of Pi” [closed]

For anyone interested, see the Oct/Nov MAA Monthly Supplement about The Music of Pi. I originally posted this along with a couple questions, but have since asked for the original question to be ...
14
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1answer
735 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
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2answers
913 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 ...
7
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1answer
1k 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 ...
5
votes
4answers
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
1k 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. ...
19
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9answers
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
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3answers
2k 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 ...
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6answers
2k 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
votes
1answer
435 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 ...
319
votes
20answers
55k 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 ...