# Questions tagged [music-theory]

The tag has no usage guidance.

76 questions
Filter by
Sorted by
Tagged with
34 views

### Audio - Compute samples for a given length with a start and end tempo

I'm working on some audio analysis code and I'm currently trying to determine the number of audio samples that would be needed in a segment of audio in which the tempo changes linearly. I know start ...
57 views

### Question about 12-tone musical scale and rational approximations

On a modern tuned instrument, an octave has twelve notes with a common frequency ratio of $2^{\frac{1}{12}}$ Of course, twelve is a very good choice for the number of notes, as $2^\frac{12}{12}=1$ ...
29 views

### Rational Roots Theorem corollary and piano tuning: $\big(\frac{a}{b}\big)^n \neq 2$ [duplicate]

I'm trying to understand why pianos "can't be tuned" and am looking for a proof of a corollary of the rational roots theorem found here (looking for proof not by contradiction): https://youtu.be/...
19 views

### Are the roots of Bessel functions closed under multiplication?

In terms of eigenfunctions, a circular drum vibrates in angular velocity of $\lambda _{mn}$, the nth positive root of the Bessel function $J_m(x)$, $m = 0, 1, \cdots$. If they are closed under ...
70 views

### Wedge Product: Vectors wedged with Multivectors? (Disclaimer: Music theory ahead)

The Xenharmonic Wiki is a great resource to start understanding and, if enough determination is available, constructing temperaments as well as scales. As some of you may know, this Wiki is not ...
110 views

### Determine the shift in tonal center of a piece of music.

Starting with a sampled audio signal of acapella vocals, I am interested in determining the shift in the tonal center of the music through the performance. As a choir progresses through a ...
37 views

### Mathematical theory for the stability of notes in a musical scale

Most mathematical theories for music consider the issue of consonance/dissonance, but in music, we actually care more about the stability of notes in a scale. For example, the subdominant is unstable ...
105 views

### Mathematical music theory concerning melodic intervals and chord progressions

There are many books exploring musical theory with maths. However, so far I have only seen discussions about the consonance/dissonance of two notes played simultaneously (intervals) -- this is the ...
43 views

### Integer sequence that “fills a range in a balanced way”

I am writing a piece of software to generate musical sequences, and I would like a way to slowly introduce notes in a chord in a balanced way across the range of the chord. I want it to be more ...
44 views

### Why is the prime of the Forte number 5-20?

See Forte number in Wikipedia. First of all, let me say that I know very little about music set theory... I am just curious why a set containing an obvious non-prime (8) is considered prime? Also, ...
80 views

### “Fragmentation” of a distribution (from paper)

I've been reading a paper by Robert Morris ("Sets, Scales and Rhythmic Cycles; A Classification of Talas in Indian Music") and came across a formula that I've found a bit tricky. He is referring to ...
86 views

### Finding the envelope frequency of a sinusoid (From a musical major triad) [closed]

[Editor 2’s introduction intended to address votes to close because the question wasn’t mathematical.] The trigonometric formula $\sin{(at)}+\sin{(bt)}=2\cos({a-b\over2}t)\sin({a+b\over2}t)$ can be ...
470 views

### The Complexity of “The Baby Shark Song”.

This question is just for fun. I hope it's received in the same goofy spirit in which I wrote it. I just had the pleasure of reading Knuth's "The Complexity of Songs" and I thought it'd be hilarious ...
27 views

### How many ways can you generate 12 who's pairwise modulus difference is also a unique rank?

I want to generate a special 12-tone row starting with zero, with the remaining 11 columns being allowed any number from 1-11. I'll call this the original row. So rule one is every number must be ...
166 views

### (Music) List of all possible “types of set” of 12 musical notes

I have looked into trying to figure what are all the possible "types" of note set combinations there are and how I would go by listing them if possible. It turns out this is harder than I thought. The ...
126 views

### Fourier Transform on Musical Notes

I am trying to apply the Fourier transform analysis on music. So far, I am aware that the Fourier transform is essentially the breaking down of superposed sine waves, into its individual frequencies. ...
94 views

24 views

### Acoustical properties of a rectangular prism with one open end

I'm studying musical instrument design as a hobby, and could not find the answer to a question regarding instruments with a square-cross sectional bore. After seeing a design for a Paetzold square ...
220 views

### How many ways can 6 pairs of 2 pegs be arranged in 12 holes… discarding duplicates read in opposite direction (re: music theory)

I hope it’s OK for a non-mathematician (a musician) to ask a question here. My question is actually about music, but I’ve dressed it in plain clothes. Suppose you have a line of 12 equally-spaced ...
75 views

### Process of Elimination With Musical Keys

This comes from a discussion I was having with my music teacher regarding the quickest method to confirm that you are playing in the right key starting from a given note. This is complicated by ...
144 views

### Advanced mathematics in stringed instrument industry

This is a soft question. I play classical guitar and I find stringed instrument industry a very fascinating art. I know that, at least for classical guitar, this industry is still developing and ...
40 views

### What are the largest pairs of $p$-smooth integers with a difference of one?

This is an interesting question because for very small $p$, we already know the answer: for $p = 2, 3, 5, 7$, the answers are $1$ and $2$, $8$ and $9$, $80$ and $81$, and $4374$ and $4375$, ...
50 views

### Analogous Mathematical term for extending beyond the elements in a set?

This question relates to projecting pitches in the context of music theory. However, I'm looking for the appropriate mathematical term for this particular concept. Here's the musical context: ...
130 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 ...
5k views

### 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 ...
1k views

### 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 ...
99 views

### 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 ...
1k views

### 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 amplitude ...
929 views

### 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 $$f \times 2^\left( X / 12 \right)$$...
595 views

### 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 ...
188 views

### 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 ...
62 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 ...
142 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 ...
197 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 ...
214 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 ...
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/...