This appears to be a mediocre piece of undergrad "research", which is to say, the theoretical material is entirely plagiarized without citation. Even the applied analysis (Beethoven's 9th, 2nd mvt. mm. 143-172) is directly lifted from another work.<p>The application of group-theoretical ideas to music theory (in particular, the rules underpinning voice leading) is quite interesting, however! People have been interested in the link between symmetry and musical beauty since the time of the Pythagoreans. Looking through the modern lens of group theory shows a delightful simplicity: if you look at the world of musical operations in this way, the ones that sound best are often small deviations away from maximum symmetry.<p>There are far better places to start, if you're interested, covering much of the same (plagiarized!) material:<p><a href="https://www.math.drexel.edu/~dp399/musicmath/algebraicmusictheory.html" rel="nofollow">https://www.math.drexel.edu/~dp399/musicmath/algebraicmusict...</a><p><a href="https://sites.math.washington.edu/~morrow/336_09/papers/Ada.pdf" rel="nofollow">https://sites.math.washington.edu/~morrow/336_09/papers/Ada....</a><p><a href="https://alpof.wordpress.com/category/music/math-music/neo-riemannian-theory/" rel="nofollow">https://alpof.wordpress.com/category/music/math-music/neo-ri...</a><p><a href="http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloquiumslides.pdf" rel="nofollow">http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloq...</a><p><a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Hasse/Crans2011.pdf" rel="nofollow">https://www.maa.org/sites/default/files/pdf/upload_library/2...</a><p>Or, of course, follow the citation chains on Wikipedia:<p><a href="https://en.wikipedia.org/wiki/Neo-Riemannian_theory" rel="nofollow">https://en.wikipedia.org/wiki/Neo-Riemannian_theory</a>
<a href="https://en.wikipedia.org/wiki/Transformational_theory" rel="nofollow">https://en.wikipedia.org/wiki/Transformational_theory</a>
Was just reading on this topic while learning Arvo Pärt's Spiegel im Spiegel, and couldn't help interpret it as being heavy on critical-woo and light on functional analysis.<p>(see linked papers mystical treatment of a <i>for</i> loop.)<p>People talk about his <i>Tintinnabuli</i> style as being algorithmic and generated, but this particular paper wasn't persuasive, and reading the score while listening to it, I don't think it is. There are probably some symmetries encoded in his work, given how demanding they are on your attention, but the idea of discovering hidden meaning is itself superstitious.<p><a href="https://www.researchgate.net/publication/271513800_Mathematical_Bases_of_the_Form_Construction_in_Arvo_Part%27s_Music" rel="nofollow">https://www.researchgate.net/publication/271513800_Mathemati...</a><p>or if link is down:<p><a href="http://žurnalai.lmta.lt/wp-content/uploads/2014/11lietuvos-muzikologija15-8.pdf" rel="nofollow">http://xn--urnalai-cxb.lmta.lt/wp-content/uploads/2014/11lie...</a><p>However, the idea of reasoning about relationships and intent in music could have some applications to reasoning about code, and machine language and behaviour in particular. So I'm not entirely dismissive of the poster, just a bit wary of some of the baggage the ideas may have collected along the way.
The "complex" math in this poster disguises the simplicity of these chords and transitions.. If you're really interested in music theory (and why those transitions sound the way they do), "The Songwriting Secrets of The Beatles" is one of the best sources available today.<p><a href="https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-Pedler-ebook/dp/B003NX6KSM" rel="nofollow">https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-P...</a>
It looks like the author is applying Set Theory [1] and concepts from 12-Tone [2] to tonal music. It is an interesting exercise - though I would expect that this music essentially boils down to "Tonic -> Domainant" relationships. Schenker would be proud :)<p>[1] <a href="https://en.wikipedia.org/wiki/Set_theory_(music)" rel="nofollow">https://en.wikipedia.org/wiki/Set_theory_(music)</a>
[2] <a href="https://en.wikipedia.org/wiki/Twelve-tone_technique" rel="nofollow">https://en.wikipedia.org/wiki/Twelve-tone_technique</a>