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October 15th, 2008, 02:14 PM   #1
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Math and Music

Hey,
I have been doing a little work on finding mathematical structures that represent musical structures. I have started a lot of promising things using groups and group transformations. If you have any ideas on some things I could look into that would be great. Also, if you would like to see some of my work, I am slowly posting it, along with some other stuff, on my blog at
mathandmusicworld.blogspot.com
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October 15th, 2008, 05:05 PM   #2
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Re: Math and Music

Interesting. I've always wanted to take a set-theoretic approach to music structure, but I really don't have the music theory for it. One thing that might be interesting though is serialism. I don't know much about it myself.

Anyway, I'll take a look at your blog and get back to you.

(Also, I think this may be better suited for the "introduce yourself and other topics" forum, let me know if you don't mind me moving it.)
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October 16th, 2008, 12:13 AM   #3
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Re: Math and Music

I don't really know much about serialism, I would have to look into it more, thanks for the link. There are so many examples of sets in music structure, I feel like with a little more music theory, a set theorist could have a hay day with this. If you are interested and need any information on music theory I could let you know, it's a big passion of mine. I would be really interested to see what you could do with this. I was working with a number theorist on this so we started taking that approach. You can move this wherever you think is better for it, I wasn't really sure where to post something like this.
Thanks a lot.
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November 21st, 2008, 12:11 PM   #4
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Re: Math and Music

Hi,

I do teach math and music, and have quite some knowledge of music theory.

I also wrote some software to generate 12-tone series, or to check if students series are correct. I also wrote a simple program to teach hearing-skills, which - of course - requires simple math to do transpositions and so on.

But to be honest, I dont really see the point of a math theory for music. Some things are really simple and obvious (like transposing, mirroring, reversing), while others are incredibly complex (what makes a sonata a good sonata? Can you "proove" that?).

So if you have a music-theory question, you may ask freely.

Regards,

Andreas
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November 22nd, 2008, 08:59 PM   #5
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Re: Math and Music

What's up, mathemusician?

I play some guitar everyday, and I know some interesting music theory involved in it. For example, the formula for the major scale inbetween the scale notes are W-W-H-W-W-W-H (W is whole and H is half). Although this is not really math, I do know some music theory for guitar. Also, the key signatures (if Bb major scale, then the key signature has 2 flats, etc).
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October 26th, 2011, 12:23 PM   #6
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Re: Math and Music

Modular arithmetic seems as a natural system to encode music with given our reckognition of the "same" note across varying octaves. Thus the modulo should be the octave or 12 if we are to analyze western music.
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April 2nd, 2014, 09:12 AM   #7
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Quote:
Originally Posted by Andreas Goebel View Post
Hi,

I do teach math and music, and have quite some knowledge of music theory.

I also wrote some software to generate 12-tone series, or to check if students series are correct. I also wrote a simple program to teach hearing-skills, which - of course - requires simple math to do transpositions and so on.

But to be honest, I don�t really see the point of a math theory for music. Some things are really simple and obvious (like transposing, mirroring, reversing), while others are incredibly complex (what makes a sonata a good sonata? Can you "proove" that?).

So if you have a music-theory question, you may ask freely.

Regards,

Andreas

Hi Andreas,

I am also a musician plus I do math.
I agree you totally..
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April 2nd, 2014, 10:44 AM   #8
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Quote:
Originally Posted by Eureka View Post
Modular arithmetic seems as a natural system to encode music with given our reckognition of the "same" note across varying octaves. Thus the modulo should be the octave or 12 if we are to analyze western music.
Yes, that's a good start. Next would be to look at the best rational approximations to the ratios of the frequencies of two notes. When the denominators of a 'good enough' approximation are small they sound 'good' together. So a note one octave up sounds good (ratio 2/1), but other combinations sound good too (ratios like 3/2). Some sound particularly bad -- most famous in Western music is the wolf interval
Wolf interval
which is (in Pythagorean tuning, for example) at a ratio of 1.47814... which is too close to 3/2 to sound like any other small ratio but too far to sound like it.

The idea of being too close to have other good approximations is mathematical too, see
http://en.wikipedia.org/wiki/Farey_sequence
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Last edited by CRGreathouse; April 2nd, 2014 at 10:48 AM.
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April 2nd, 2014, 01:13 PM   #9
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Quote:
Originally Posted by Eureka View Post
Modular arithmetic seems as a natural system to encode music with given our reckognition of the "same" note across varying octaves. Thus the modulo should be the octave or 12 if we are to analyze western music.
Precisely. For example, the musical theory of the circle of fifths (or fourths) is based on the cyclic group of order 12. Basically, if you start on any note and go up by intervals of a fifth, you will go through all the 12 notes of the chromatic scale. Similarly if you go up by intervals of a fourth. There are two other ways you can do this: go up by intervals of a semitone, or go up by intervals of a major seventh. If you go up by any other intervals, you will not go through all twelve notes, only some of them. Reason? Because 1, 5, 7 and 11 are the generators of the cyclic group of order 12 – they are the only integers from the set {1, 2, …, 11} which are coprime with 12.

The whole-tone scale is based on the subgroup of order 6 (index 2) of the cyclic group of order 12. Since this subgroup has only two cosets, there are precisely two distinct whole-tone scales: namely, {C, D, E, F♯, G♯, A♯} and {C♯, D♯, F, G, A, B}.

Group theory rocks!
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April 9th, 2014, 10:36 AM   #10
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Some music trivia


Many many years ago when I was first studying Music,
we had "Ear Training". We learned to write down the
notes as we heard them.

When we started, we were pretty awful at identifying
intervals. So we had list of songs for most intervals.

Perfect Fourth: "Sailing sailing, over the bounding main".

Perfect Fifth: "Twinkle, twinkle, little star".

Major Sixth: "My Bonnie lies over the ocean:.

Major Seventh: "Bali-Hai"


We didn't have one for the Augmented Fourth.
Some years later, Leonard Bernstein wrote
West Side Story. I'm certain that he wrote
"Maria" just so he could use an Augmented Fourth.

Speaking of West Side Story, consider four
consecutive triplets. Recite this phrase:
DA-da-da, DA-da-da, DA-da-da, DA-da-da.

Now in the last two triplets, accent every other note:
DA-da-da, DA-da-da, DA-da-DA-da-DA-da.

It's a bit unsettling, isn't it?
Practice a bit and you'll get it,

Bernstein used this deliberately:
"I like to be in America!"


Andrew Lloyd Weber has his little joke
in Phantom of the Opera.
In the song "That's All I Ask of You",
the phrase "Say you love me" has
a descending major ninth.
(We were doing "Phantom" in our
community chorus, and I almost
choked on those notes.)
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