C, E-flat, and G go into a bar. The bartender says, "Sorry, but we don't serve minors." So E-flat leaves, and C and G have an open fifth between them. After a few drinks, the fifth is diminished, and G is out flat. F comes in and tries to augment the situation, but is not sharp enough. D comes in and heads for the bathroom, saying, "Excuse me; I'll just be a second." Then A comes in, but the bartender is not convinced that this relative of C is not a minor. Then the bartender notices B-flat hiding at the end of the bar and says, "Get out! You're the seventh minor I've found in this bar tonight." E-flat comes back the next night in a three-piece suit with nicely shined shoes. The bartender says, "You're looking sharp tonight. Come on in, this could be a major development." Sure enough, E-flat soon takes off his suit and everything else, and is au natural. Eventually C sobers up and realizes in horror that he's under a rest. C is brought to trial, found guilty of contributing to the diminution of a minor, and is sentenced to 10 years of D.S. without Coda at an upscale correctional facility.
Another good book in the same vein is Dave Benson's 'Music: a Mathematical Offering'.<p><a href="https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html" rel="nofollow">https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...</a>
Musimathics is great [1].<p>If you want a more interactive source you can play with python notebooks from the music information retrieval site [2]. I've found it helpful, as you try some of the described music theory concepts in a programming environment.<p>Shameless plug, I've also written about how audio fingerprinting works [3], which touches on some of the topics regarding music theory.<p>[1] <a href="http://www.musimathics.com" rel="nofollow">http://www.musimathics.com</a><p>[2] <a href="https://musicinformationretrieval.com" rel="nofollow">https://musicinformationretrieval.com</a><p>[3] <a href="https://emysound.com/blog/open-source/2020/06/12/how-audio-fingerprinting-works.html" rel="nofollow">https://emysound.com/blog/open-source/2020/06/12/how-audio-f...</a>
Recommended:<p>A Geometry of Music by Dmitri Tymoczko - <a href="http://dmitri.mycpanel.princeton.edu/geometry-of-music.html" rel="nofollow">http://dmitri.mycpanel.princeton.edu/geometry-of-music.html</a><p>The Geometry of Musical Rhythm by Godfried Toussaint<p>- Original paper - <a href="http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-rhythm.pdf" rel="nofollow">http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r...</a> (PDF)<p>- Book - Review <a href="https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php" rel="nofollow">https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php</a>
In a similar vein, there's the Topos of Music book[0], which, according to Wikipedia, has been somewhat controversial among mathematicians and musicians alike.<p>[0] <a href="https://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312" rel="nofollow">https://www.amazon.com/Topos-Music-Geometric-Concepts-Perfor...</a>
Have posted this link before, but so relevant to the discussion: <a href="https://softwareengineering.stackexchange.com/questions/136085/is-musical-notation-turing-complete" rel="nofollow">https://softwareengineering.stackexchange.com/questions/1360...</a><p>If music were Turing complete, it could imply we've been developing the ability to derive theorems in it as a species forever, which has some speculatively interesting philosophical implications as well. :)
the software can be found here, <a href="https://imaginary.org/programs" rel="nofollow">https://imaginary.org/programs</a>
I started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for music theory
Absolutely fascinating section on Lissajous figures. I had only been exposed to the concept through orbits.[1]<p>[1] - <a href="https://en.wikipedia.org/wiki/Lissajous_orbit" rel="nofollow">https://en.wikipedia.org/wiki/Lissajous_orbit</a>
I'm not sure whom this is aimed at. The name "La La Lab" and the interactivity suggests kids, but there's a Fourier integral on Page 7 which immediately suggests undergraduates.
I highly recommend Drew Nobile's book or papers on functional circuits as an adjunct to this on how to recursively generate songs from an initial seed progression.