# Tagged Questions

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### 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 ...
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### 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 ...
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### How many 7-note musical scales are possible within the 12-note system?

This combinatorial question has a musical motivation, which I provide below using as little musical jargon as I can. But first, I'll present a purely mathematical formulation for those not interested ...
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### How would I determine all possible rhythmic combinations given certain limitations?

If I have: 1) kick drum 2) hihat 3) snare drum And I can play 1) One measure of 4/4 time 2) any note values between sixteenth and whole EDIT: (excluding tuplets) How many possible drum beats could ...
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### How to determine if this musical exercise is valid: will the pattern complete?

I'm hoping that math has an answer to a question arising out of a musical exercise. In music terms, the exercise is: Choose two arpeggios (sets of notes) of equal (or roughly equal) span (number ...
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### Which equation? Sin, math and music [closed]

I found it inside an italian music book: It represents the music scale. I think it is a series of trigonometry sin equation. With some difference in the ...
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### Plotting points of Musical Note frequencies linearly on a Graph

I am trying to plot the frequencies of musical notes on a graph so that they are equally spaced apart. I have researched that the relationship between each note is $$f \times 2^\left( X / 12 \right)$$...
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### Months and notes. Pure coincidence? [closed]

There are $12$ months in a year and $12$ notes in the chromatic scale. Moreover, there are $7$ long and $5$ short months and there are $7$ white and $5$ black keys in each octave on the piano ...
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### In 12TET, is there a maximum number of musical scales possible?

For those who don't know, 12 Tone Equal Temperament (12TET) simply means that, for a given frequency $f$, each step between $f$ and $2f$ can be written as $2^{k/12}f$, where $k$ denotes the $k$th step ...
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### 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 ...
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### 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 ...
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### 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? $N_1=A_4(440Hz)$...
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### 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 that?...
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### 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 ...
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### 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 :-)
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### 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 ...
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### 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?
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### 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 =...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### “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 ...
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### 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 $\frac {\log \left( c \right)}{\log \left( \text{rad} \left( abc \right) \right)}>1+\varepsilon$, ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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. ...
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### 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 ...
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### 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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### 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 ...
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 ...
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 ...