Questions tagged [music-theory]
110 questions
589
votes
21 answers
Mathematical difference between white and black notes in a piano
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 black) are always separated by a semitone. Why…
egarcia
- 5,777
4
votes
1 answer
Quality and degree of a musical interval as linear combinations: Is this a known construction?
At some point I discovered that the 'degree' of an interval (unison, sixth, ...) is simply determined by writing it as $\;t\text{ major seconds} + s\text{ sharps}\;$ (both $\;t\;$ and $\;s\;$ can be negative, for example$\;-2\text{ sharps} = 2\text{…
2
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1 answer
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 $4375$, respectively. Is there a formula for these kind of numbers…
bootmii
- 21
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vote
1 answer
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?
Aviv Cohn
- 449
1
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1 answer
Question Math of a Non Linear Semi Whole Tone of a Musical Scale Intervals as Rationals
Peculiar Question Irregular semi-tone of scale. Hi folks, am hoping to achieve a formula
or function that can be applied to the general following problem - any feedback appreciated ;
Given two values that are known ;
(A) Fundamental = 1.07
(B) Some…
AstroD
- 11
1
vote
1 answer
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 and tends to resolve to the mediant. This has…
Ma Joad
- 7,420
1
vote
3 answers
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, is there a formula for calculating those numbers of…
kpopguy
- 145
- 5
1
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1 answer
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 enharmonic notes (e.g. G# = Ab) but, given their…
Alan Cash
- 21
0
votes
1 answer
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?
mydoghasworms
- 113
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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 from $f$. In music, these notes are usually…
Stan Shunpike
- 4,921
0
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1 answer
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 $$ \left(2^{\frac{7}{12}}\right)^{12} = 2^7…
Stan Shunpike
- 4,921