October 15th, 2008, 02:14 PM  #1 
Newbie Joined: Oct 2008 Posts: 8 Thanks: 1  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 
October 15th, 2008, 05:05 PM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 2  Re: Math and Music
Interesting. I've always wanted to take a settheoretic 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.) 
October 16th, 2008, 12:13 AM  #3 
Newbie Joined: Oct 2008 Posts: 8 Thanks: 1  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. 
November 21st, 2008, 12:11 PM  #4 
Newbie Joined: Nov 2008 From: Germany Posts: 9 Thanks: 0  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 12tone series, or to check if students series are correct. I also wrote a simple program to teach hearingskills, 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 musictheory question, you may ask freely. Regards, Andreas 
November 22nd, 2008, 08:59 PM  #5 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  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 WWHWWWH (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). 
October 26th, 2011, 12:23 PM  #6 
Member Joined: Aug 2011 Posts: 85 Thanks: 1  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.

April 2nd, 2014, 09:12 AM  #7  
Member Joined: Feb 2014 Posts: 32 Thanks: 0  Quote:
Hi Andreas, I am also a musician plus I do math. I agree you totally..  
April 2nd, 2014, 10:44 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 932 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
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 Last edited by CRGreathouse; April 2nd, 2014 at 10:48 AM.  
April 2nd, 2014, 01:13 PM  #9  
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra  Quote:
The wholetone 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 wholetone scales: namely, {C, D, E, Fâ™¯, Gâ™¯, Aâ™¯} and {Câ™¯, Dâ™¯, F, G, A, B}. Group theory rocks!  
April 9th, 2014, 10:36 AM  #10 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 406  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: "BaliHai" 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: DAdada, DAdada, DAdada, DAdada. Now in the last two triplets, accent every other note: DAdada, DAdada, DAdaDAdaDAda. 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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