
Math and Music: The Deeper Links (1982) - nek28
https://www.nytimes.com/1982/08/29/arts/math-and-music-the-deeper-links.html
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adamnemecek
I’m working on this software for writing music that uses some cool math to
make you more productive. I’m close to being done. Check it out
[http://ngrid.io](http://ngrid.io)

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emptybits
Also recommended: two-volume set "Musimathics" by Gareth Loy.[1]

The work's topics are, mostly, independent so I find it enjoyable to pick up
and read a chapter from time to time. He tries to cover the math of everything
musical from scales and composition to synthesis and signal processing to
acoustics and physics.

[1] [http://musimathics.com](http://musimathics.com)

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alok-g
Is there something in the books about the mathematics of chords and chord
progressions?

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emptybits
IMO, the books are great but they don't go very deeply into the math of chords
or relationships between chords, no. Certainly there is math coverage of
intonation (JI, 12TET, etc.), which leads to "why" chords might sound the way
they do as stacked intervals with more or less pure dissonance or consonance.
But the "why" of progressions are a level above that yet again. So I'm sure
there are better works on chords. From a guitar (but also keyboard)
perspective a fascinating book is Werner Pohlert's "Basic Harmony" \-- it's
thick and analytical of chords and progressions. It's comprehensive though I
suppose not particularly mathematical. And you probably know there is some
great writing on Just Intonation which is rooted in the ratio math of
"correct" intervals and chords. "The JI Primer" by David Doty is a nice short
starting point on JI with references, with emphasis on the math of intervals,
obviously, but it does have some coverage of stacking these into triads and
beyond. If you find a pleasing rabbit hole for chord and progression math, let
us know!

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alok-g
Thanks for a detailed response. I'll check the references out.

I am a lot less knowledgeable than you have imagined here. :-) Well, I know
practically all the physics and electronics part, but have not found much that
connects to music theory. I could figure the mathematical why's of scales and
chords ("stacked intervals with more or less pure dissonance or consonance")
by myself. But ever since have been struggling to find about which
chords/progressions would fit which melody. Most musicians are doing this
naturally, "by the ear" as they say. :-) And music theory books I have looked
at so far (including the thick ones) do not talk about mathematics at all. :-(
:-)

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emptybits
I hear you. My $0.25 ... I bet the expert authors of many music theory books
would be capable of thinking in mathematical terms but (now I'm guessing)
there is likely some undeserved "ew, yuck, math!" culture in the arts so
rather than turn off their audience, they avoid talking about the quantitative
underpinnings of why things sound the way they do.

Two more enjoyable books on the math and physics of music (though, again,
probably not far enough up the tree of abstraction for chords):

"The Science of Musical Sound" by Pierce (lovely little book, not too deep
though, quite coffee tableable)

"Fundamentals of Musical Acoustics" by Benade (old book, considered a classic,
reads like a science text)

Good luck!

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alok-g
Thanks a lot! :-)

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gtycomb
The last paragraph has something lovely to take home:

"Stravinsky, in discussing ''the art of combination which is composition''
quoted the mathematician Marston Morse: ''Mathematics are the result of
mysterious powers which no one understands, and in which the unconscious
recognition of beauty must play an important part. Out of an infinity of
designs a mathematician chooses one pattern for beauty's sake and pulls it
down to earth.'' Morse, Stravinsky says, could as well have been talking about
music. It is not only in the clarity of things, but in their beauty and
mystery that the two arts join."

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the_cat_kittles
there is infinite complexity in both, i think this is part of the allure of
music for me. i keep realizing the “true” nature of something only to later
discover an even deeper truth. repeat forever

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TheOtherHobbes
Very true. People who try to reduce music to math rarely succeed.

It looks like it's a simple problem, then you realise there are edge cases,
then you realise the edge cases are where all the interesting detail is, then
you realise your models are braindead and actually kind of useless, and then
maybe you start again with a better model.

Repeat forever.

