Questions tagged [music-theory]
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32
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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 ...
5
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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 ...
5
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2
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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 ...
5
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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?
5
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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 ...
4
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48
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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 ...
4
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229
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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 ...
2
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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 ...
2
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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 ...
2
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194
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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/...
2
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0
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107
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"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 ...
2
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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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63
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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}...
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70
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(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,...
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41
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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 ...
1
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0
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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
$P(C-major) = c-minor,$
$L(C-major) = e-minor,$ ...
1
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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}...
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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 ...
1
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1
answer
76
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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 ...
1
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48
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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 ...
1
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0
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201
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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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0
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122
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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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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 ...
1
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1
answer
94
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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 ...
1
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0
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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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63
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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/...
1
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1
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230
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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 ...
1
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0
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79
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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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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, ...
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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, ...
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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 ...
0
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1
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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 $...