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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?

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math.stackexchange.com/questions/79885/… possibly related. –  Daniel Rust Sep 16 '13 at 13:43
    
@DanielRust: No, I had read that but that topic is mostly about book suggestions and reference request. On the other hand, this one is about the recent research done in this area, if there's any. –  some1.new4u Sep 16 '13 at 13:46
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@some1.new4u How does that contradict that that link is related to this question? –  Git Gud Sep 16 '13 at 13:49
    
When you ask "new researches", what do you mean by "new"? New since when? –  MJD Sep 16 '13 at 13:49
    
It seems that IRCAM researches on this. –  Vÿska Sep 16 '13 at 14:13

3 Answers 3

I know that a member of Mathoverflow Tobias Schlemmer works in this topic, you can consult with him.

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Yes, specifically in the area of musical tuning theory: the xenharmonic wiki is a good place to read about this. Harmonic entropy and xenharmonic temperament theory are two relatively new topics with a lot of current (albeit somewhat obscure) research going on in them.

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Key reference:

That set theory is useful with digital music, especially MIDI, seems not to be widely known.
Consider a sequence consisting of the following chords: $F^1 , C^2 , G7^4$ .

enter image description here

Changing the chords means that the set of notes $F^1 = \{F,A,C\}$ is replaced by the set of notes $C^2 = \{E,G,C\}$ is replaced by the set of notes $G7^4 = \{F,G,B\}$ . Mind the notes in common; these are joined by bows in the score.
In MIDI, first the notes in $F^1$ are set On (Note On). After a duration of four beats, the notes in $C^2$ should sound. In order to accomplish smooth transition of the chords, this should be done by first hitting the chord $C^2$ before (immediately) releasing the chord $F^1$. More in detail, apply a Note On event to the elements in $\{E,G,C\}$ minus $\{F,A,C\} = \{E,G\}$ immediately followed (timestep $0$) by a Note Off event applied to the elements in $\{F,A,C\}$ minus $\{E,G,C\} = \{F,A\}$ . Note that nothing happens with the note $C$ .
After a duration of four beats again, the notes in $G7^4$ should sound. This should be done by first hitting the chord $G7^4$ before (immediately) releasing the chord $C^2$. More in detail, apply a Note On event to the members of the set $G7^4 \setminus C^2$ immediately followed by a Note Off event applied to the members of the set $C^2 \setminus G7^4$ .
This is in a nutshell how chord transition works - or rather should work - in MIDI. It's implemented in my personal mathematical contribution to music : MidiDoos .

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