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Questions tagged [music-theory]

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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, ...
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0answers
69 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 ...
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63 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 ...
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37 views

Informations about Fourier Transform for a Python project (sound manipulation)

I have a project in Python with a friend where we want to manipulate music sound, and we'll need Fourier Transforms, so I made research online and wanted to know if I understand correctly the concepts....
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384 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 ...
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1answer
22 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 ...
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3answers
140 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 ...
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0answers
97 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. ...
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29 views

What knowledge is needed for developing a Music Processing Application like Audacity?

What knowledge is needed if I want to develop a Music Processing Application like Audacity? As a master student of Information Technology, I want to take a research about Music processing. For ...
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1answer
83 views

Is there an arithmetic mean limit on the symmetrical items of the harmonic series?

Is it possible to determine what is the arithmetic mean of the harmonic series where $n$ and $-n$ are added and divided by two in this manner: $$f(n) = \frac{ (\frac{3}{4})^n \times 2^{⌈-n \times ...
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2answers
32 views

What is the solution of normalized harmonic series based on $4/3$ between one and two?

In music theory notes generated by the consequencing interval of $4/3$ generates harmonic series. Series can be normalized by multiplicating the fraction with a $2$ in power $n$. What is a formula ...
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2answers
56 views

Find three points on a scale using golden ratio

My question came from my musicial part: The note A4 on a piano is 440hz and the note A5 (one octave higher) is 880hz. On the piano there are 12 notes between A4 and A5 (include). Im trying to find ...
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115 views

Algorithm for converting complex sine wave to constituent simple sine waves

Since any real sound is by nature a complex sine wave based on the harmonic series, every sound is made up of many simple sine waves. Since a sound is constructed via the combination of these waves, ...
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2answers
208 views

Musical and combinatorial proof

How many distinct rhythms can a musical measure have? Obviously the answer is not "$\infty$", so to answer this question we set a minimum rhythm $\frac{1}{4}$. We will consider both notes and rests ...
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0answers
39 views

Is there a name for this exponential analog to modular arithmetic? (octave equivalency)

In music theory, there is a concept called octave equivalency: two pitches are said to have the same pitch class if the quotient of their frequencies is a power of 2, i.e. if they are an integer ...
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2answers
33 views

Constraining the results of a division between two “poles”

I often have to do calculations that pertain to musical intervals, i.e. the ratios between two pitches. E.g., the interval that commonly we call a "major third" (c-e...
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53 views

Maths of chords

I have a few naive questions on music theory. Let us assume that I have two pitches A and C with certain frequencies. Then the corresponding sound waves are pure sinusoidal waves. But what happens if ...
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1answer
113 views

Could Collatz rules $3x+b$ hold every possible song melody in existance?

Since Modulo seems to have a significant role in the Collatz Conjecture for one reason or another, I wondered what would happen if the Conjecture was put to music (I was inspired by this interesting ...
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3answers
118 views

Example of a power of 3 which is close to a power of 2

I'm looking for a power of 3 close to a power of 2. Let's say, what is $(n,m)$ such that $$\left|\frac{2^n}{3^m}-1\right| = \min\left \{\left|\frac{2^i}{3^j}-1 \right|, 1\leq i,j\leq 20\right\} \...
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0answers
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 ...
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1answer
204 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 ...
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1answer
73 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 ...
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1answer
132 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 ...
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1answer
38 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 $4375$, ...
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0answers
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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: ...
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0answers
124 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 ...
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7answers
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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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2answers
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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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2answers
96 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 ...
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2answers
907 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 ...
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2answers
793 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 $$f \times 2^\left( X / 12 \right)$$...
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472 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 ...
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3answers
161 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 ...
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0answers
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 $$...
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128 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 ...
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186 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 ...
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1answer
182 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 ...
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0answers
57 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/...
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1answer
35 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 $...
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1answer
152 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?
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1answer
144 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 ...
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1answer
689 views

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

This question What is Mazzola's "Topos of Music" about? has already been asked, but I am dissatisfied with the response for several reasons and would like Math SE to revisit it. For ...
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1answer
179 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), (...
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0answers
66 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 ...
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1answer
73 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 $f(...
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1answer
550 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?
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4answers
501 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 ...
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1answer
315 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 ...
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1answer
102 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? $N_1=A_4(440Hz)$ ...
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268 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 that?...