
Combinatorial Music Theory (1991) - adamnemecek
http://andrewduncan.net/cmt/
======
acjohnson55
Fascinating paper! Somehow, this escaped my attention when I was researching
this topic. I was interested in the question of how the heck we evolved such a
crazy system of 7 white notes + 5 black notes (i.e. the diatonic (and
pentatonic) scale overlaid on the 12-tone equal temperament), as well as the
origin of the Western concepts of major and minor scales and chords.

Long story short, it seems the answer is that our scales and chords derive
from a combination of what makes for interesting voice leading and what notes
sound good together in a given timbre. The choice of approximating ideal
chords and scales using 12 equally spaced notes derives from a instrumental
playability concerns and the desire to be able to freely transpose and to
modulate between distant keys.

It's a deep topic, but if anyone's interested, I recommend two books:

\- Timbre, Tuning, Spectrum, Scale by William Sethares \- A Geometry of Music
by Dmitri Tymoczko

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leephillips
I saw a presentation by Tymoczko at the recent AAAS meeting in DC. A kind of
review of this, and two other presentations about the intersections of
mathematics and music, are at
[http://arstechnica.com/science/2016/03/mathematics-meets-
mus...](http://arstechnica.com/science/2016/03/mathematics-meets-music/)

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sbuttgereit
Worth noting that this use of the word "combinatorial" in this article is not
the same "combinatorial" as used by Milton Babbitt describing a row set
characteristic in twelve tone music composition. For further reading on that,
[https://en.wikipedia.org/wiki/Combinatoriality](https://en.wikipedia.org/wiki/Combinatoriality)
is as good a start as any.

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yellowstuff
Tangential, but the quote saying that musicians don't think about counting is
wrong. For example, Chuck Berry said "My biggest influence was my mathematics
teacher. Music is so much mathematics that it’s pathetic."

[http://www.guitarplayer.com/artists/1013/chuck-
berry-1971/21...](http://www.guitarplayer.com/artists/1013/chuck-
berry-1971/21212)

~~~
jameshart
Musicians do a lot of counting, just that they stop at four. On the subject of
which, music would make a lot more sense if the normal count went 'oh and one
and two and three and'.

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eggy
Just what the doctor ordered for me!

I've been playing with music and mathematics for a while, and I had a thought
that someone far more mathematical and musical than myself could correlate
tried and true mathematical constructs to music other than defining patterns
via Markov processes, neural or evolutionary algorithms, or simply generating
random melodies. Pulling these patterns into 12 point space is really
interesting.

~~~
adamnemecek
You should check out music set theory
[https://en.wikipedia.org/wiki/Set_theory_(music)](https://en.wikipedia.org/wiki/Set_theory_\(music\))
and also diatonic set theory, they are pretty fascinating
[https://en.wikipedia.org/wiki/Diatonic_set_theory](https://en.wikipedia.org/wiki/Diatonic_set_theory)
.

~~~
eggy
Thanks!

I was just turned on to SYZYGYS's music based on Harry Partch's 43-microtone
scale. It is hard to stop listening to it today, but maybe because it's novel
for me.

Mathematics is all about patterns and relationships, so music is an aural
expression of mathematics as has been said by so many others, yet I never tire
of seeing (and hearing) examples of this.

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dharma1
Thanks! Will have a read through. I often wonder if we could develop software
to make chord/harmony discovery easier when arranging a melody. At the moment
it's down to a combination of knowledge of music theory, intuition and trial
and error.

I'm talking about more advanced harmony constructions like Jacob Colliers work
(check him out if you haven't heard)-

[https://youtu.be/SM2nhLSeJXg](https://youtu.be/SM2nhLSeJXg)

[http://brightonjazzschool.com/jacob-collier-
masterclass/](http://brightonjazzschool.com/jacob-collier-masterclass/)

Harmony (and it's relation to melody) is a time based problem, you can't just
join random chords together that match the current melody note. LSTM works for
time series learning but I am not convinced it "gets" concepts of music
theory, so maybe some kind of hybrid of engineered music theory features +
LSTM with good training material could work

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llvihearsevil
Man that page loaded fast! It must have been using the new Google AMP
javascript framework!!

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rhizome
(1991)

~~~
adamnemecek
Fixed, thanks.

