Questions tagged [music-theory]

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Months and notes. Pure coincidence?

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 ...
Alexander Belopolsky's user avatar
5 votes
0 answers
145 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 ...
rossmcm's user avatar
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5 votes
2 answers
299 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 ...
Lucas's user avatar
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5 votes
1 answer
279 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?
isomorphismes's user avatar
5 votes
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154 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 ...
hhh's user avatar
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4 votes
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Curvature of "music-scale"

Lately I am thinking about music from a mathematical point of view. Let us consider $\mathbb{H} =\mathcal{L}^2([0,T])$ as the Hilbert space of functions that represents the time-intensity plot of a ...
Andrea Marino's user avatar
4 votes
0 answers
229 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 ...
user avatar
2 votes
0 answers
54 views

Resonance/Acoustics equations.

I have a bit of a conundrum I'm trying to figure out. I have some spare time on my hands and I decided I wanted to custom make a set of wind chimes for my parents, and have been doing some research on ...
JaXm's user avatar
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2 votes
0 answers
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Quantitative measure of a good (musical) temperament

Is there actually a quantitative measure to know if a temperament is "good" or not? The motivation for my question is that there are quite a few temperament for the 12-tone systems (which ...
ARG's user avatar
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2 votes
0 answers
194 views

Twelfth root of two?

I have been experimenting in mathematically analysing and combining two melodies based on the twelfth root of two. Here is a mix of two known melodies: https://drive.google.com/file/d/...
mathoverflowUser's user avatar
2 votes
0 answers
107 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 ...
Luke Poeppel's user avatar
2 votes
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623 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, ...
Free Url's user avatar
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1 vote
0 answers
63 views

Possible links between class 1 numbers, Lucas numbers, and 12-tone octave

Definitions Class 1 numbers: 1, 2, 3, 7, 11, 19, 43, 67, 163 Lucas numbers: …2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199... 12-tone octave ratios: $\frac{16}{15}, \frac{9}{8}, \frac{6}{5}, \frac{5}{4}...
mattrdowney's user avatar
1 vote
0 answers
70 views

(weird) Explanations in Xenakis' Formalized Music

First time posting on MSE, very nervous. Been lurking for a long time. I've been looking through Formalized Music (Xenakis) and building software around the ideas in the book. Upon thorough inspection,...
passaway1337's user avatar
1 vote
0 answers
41 views

How to find a successive frequency from a series of frequencies

I am building a new instrument, and I need to find the sixth sequence in the given series, {659.25, 440.00, 293.66, 196.00, 130.81} that would be around 80 Hz. An exponential regression at wa, gives ...
Luthier415Hz's user avatar
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1 vote
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66 views

How to identify the two copies of $D_{24}$ in the homomorphisms of the 2 musical actions?

Let $S$ be the set of minor and major triads. Two sets of actions are defined on the set: 1) Musical transposition and inversion 2) P, L, R actions $P(C-major) = c-minor,$ $L(C-major) = e-minor,$ ...
Zara's user avatar
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Is there a standard name for "signed distance to the nearest integer" that's reasonably succinct?

Notation. Write $\mathbb{R}_\mathbb{Z}$ for the set of all real numbers for which there exists a unique nearest integer. Explicitly: $$\mathbb{R}_\mathbb{Z} = \mathbb{R} \setminus(0.5 + \mathbb{Z}...
goblin GONE's user avatar
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1 vote
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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 ...
Dannyu NDos's user avatar
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1 vote
1 answer
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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 ...
Ma Joad's user avatar
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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 ...
Andy Mac's user avatar
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1 vote
0 answers
201 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. ...
Wilson Ivandy's user avatar
1 vote
0 answers
122 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 ...
splornths's user avatar
1 vote
0 answers
27 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 ...
John Dill's user avatar
1 vote
1 answer
94 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 ...
Alan Cash's user avatar
1 vote
0 answers
55 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: ...
MarkOates's user avatar
1 vote
0 answers
63 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/...
Charles Gaskell's user avatar
1 vote
1 answer
230 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 ...
TKM's user avatar
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1 vote
0 answers
79 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 ...
Jeremy K's user avatar
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0 answers
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FOURIER TRANSFORM: How can I find the index of data points

I am a senior in high school and am currently trying to conduct an exploration on Fourier Analysis, specifically using the Discrete Fourier Transform to analyze a chord played on my piano. Basically, ...
Ralph Khouri's user avatar
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0 answers
41 views

How many musical notes does a scale need such that any integer intervals can be found in this scale?

We know that in the 12-tone equal temperament musical system, each octave is equally divided into 12 semitones. In a major scale, for example the C major scale, the notes are C, D, E, F, G, A, and B, ...
Pectin on Guitar's user avatar
0 votes
0 answers
99 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 ...
zoli's user avatar
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0 votes
1 answer
39 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 $...
Dan D's user avatar
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