6 ms·

Chord Transformations and Beethoven (2011) [pdf]

57 points by miobrien 7y ago

josquindesprez 7y ago
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. 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. There are far better places to start, if you're interested, covering much of the same (plagiarized!) material: https://www.math.drexel.edu/~dp399/musicmath/algebraicmusictheory.html https://www.math.drexel.edu/~dp399/musicmath/algebraicmusict... https://sites.math.washington.edu/~morrow/336_09/papers/Ada.pdf https://sites.math.washington.edu/~morrow/336_09/papers/Ada.... https://alpof.wordpress.com/category/music/math-music/neo-riemannian-theory/ https://alpof.wordpress.com/category/music/math-music/neo-ri... http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloquiumslides.pdf http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloq... https://www.maa.org/sites/default/files/pdf/upload_library/22/Hasse/Crans2011.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2... Or, of course, follow the citation chains on Wikipedia: https://en.wikipedia.org/wiki/Neo-Riemannian_theory https://en.wikipedia.org/wiki/Neo-Riemannian_theory https://en.wikipedia.org/wiki/Transformational_theory https://en.wikipedia.org/wiki/Transformational_theory
- kmill 7y ago
  I know you've been in the music business for a few hundred years, Josquin, but there's no need to be so harsh about this undergrad poster! From what I could figure, it's something like a final project for a class on Mathematics and Music at UW Eau Claire. The background material on transformations of sets of pitch classes is in the course textbook. (This doesn't take away from all the citations you helpfully provided, though.)
  - ska 7y ago
    If it's an undergrad project, it absolutely should cite properly; so that is at least worth pointing out. To be fair though, posters are often a bit sloppy this way, and in context supposed to be supported other ways.
    - tim333 7y ago
      It's a one page summary with pictures rather than a research paper or such like. There's quite likely some article with sources elsewhere.
      - ska 7y ago
        It's a scientific poster layout, very standard. They typically have some citation, but only major ones.
- deleted 7y ago
  [deleted]
- mnemonicsloth 7y ago
  I'm trying to decide if I should go down this rabbit hole. The math looks easy enough, but I know nothing about music. Nothing. And I'd love to learn, of course, but I can see myself buying a keyboard and plinking out some of these transformations and that seems like a long time to go without a payoff. What's your musical background?
  - sigstoat 7y ago
    > The math looks easy enough, but I know nothing about music. Nothing. And I'd love to learn, of course, but I can see myself buying a keyboard and plinking out some of these transformations read musictheory.net, get musescore, and then you can start experimenting with some of this. don't need a keyboard. if you do decide to spend some money on hardware, the r/piano folks have some information on the terminology of such things https://www.reddit.com/r/piano/wiki/faq#wiki_choosing_a_keyboard https://www.reddit.com/r/piano/wiki/faq#wiki_choosing_a_keyb... > without a payoff no problem, just redefine payoff and you're all set
  - WalterSear 7y ago
    You may be interested in the twelve tone you tube channel, fwiw - particularly the earlier ones where he discusses the fundamentals.
  - fenomas 7y ago
    I've been down this rabbit hole for a few years, except making procedural music with code rather than physically playing an instrument. No musical background at all (I started by googling "chord" etc). My take is, the basics - the math behind chords and chord changes, summarized on the left page of the PDF - are embarrassingly simple; you can know everything there seems to be to know in a weekend or two. However for the application - using those basics to create or understand music - I'm still not entirely sure there's anything to know. That is, one can find scads of sources online similar to the right-hand page of the PDF, which analyze the structure of some phrase or composition. But it all seems to pretty much boil down to giving names to things; there don't seem to be any generally applicable principles. The closest thing we have seems to be voice leading rules, but they're very much "doing X sounds good except when it doesn't" sorts of things.
- deleted 7y ago
  [deleted]
memset 7y ago
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 :) [1] https://en.wikipedia.org/wiki/Set_theory_(music) https://en.wikipedia.org/wiki/Set_theory_(music) [2] https://en.wikipedia.org/wiki/Twelve-tone_technique https://en.wikipedia.org/wiki/Twelve-tone_technique
nick-garfield 7y ago
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. https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-Pedler-ebook/dp/B003NX6KSM https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-P...
- yesenadam 7y ago
  Sounded interesting, so I started reading it.. (jazz pianist here, I learnt basic harmony in large part from playing Beatles songs as a kid) Hmm yeah, it's entertainingly written. I'd never heard the term "Three Chord Trick" (i.e. songs using just I,IV,V.) In "The power of I - the one-chord trick", Tomorrow Never Knows is described as "paradoxically structured around a single, simply embellished G chord, around which hypnotic modal melodies work their textural magic". Uh, no. It's in C, and there's distinctly a Bb/C chord in bars 5 and 6 of an 8 bar pattern - kind of like the IV chord in the first 8 bars of a blues. (Also, come to think of it, like the standard pattern in North Indian classical of not playing open tabla sounds in bars 5 & 6 of each 8 bars) Then "The Chuck Berry rhythm", "a rock'n'roll guitar pattern popularised most famously by Chuck Berry"..turns out to be the boogie-woogie piano left hand pattern, "a two-note diad...a basic root-and-fifth perfect interval...From there, a brief extension from the fifth to the sixth degree (and sometimes on to b7) can be made"–he makes it sound like rock guitarists invented it. Anyway, Rosetta Tharpe invented most of what Chuck Berry "invented", decades before he did it, the rock-n-roll guitar and the dance moves. Check her out! (on youtube) She's amazing.
  - anentropic 7y ago
    to be fair the quote you quoted says "popularised most famously by Chuck Berry" which is pretty uncontroversial I think, no one claims he invented it Sister Rosetta Tharpe is awesome but T-Bone Walker is probably the more direct antecedent for Chuck Berry's guitar style and stage moves
motohagiography 7y ago
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. (see linked papers mystical treatment of a for loop.) People talk about his Tintinnabuli 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. https://www.researchgate.net/publication/271513800_Mathematical_Bases_of_the_Form_Construction_in_Arvo_Part%27s_Music https://www.researchgate.net/publication/271513800_Mathemati... or if link is down: http://žurnalai.lmta.lt/wp-content/uploads/2014/11lietuvos-muzikologija15-8.pdf http://xn--urnalai-cxb.lmta.lt/wp-content/uploads/2014/11lie... 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.

57 points by miobrien 7y ago

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. 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. There are far better places to start, if you're interested, covering much of the same (plagiarized!) material: https://www.math.drexel.edu/~dp399/musicmath/algebraicmusictheory.html https://www.math.drexel.edu/~dp399/musicmath/algebraicmusict... https://sites.math.washington.edu/~morrow/336_09/papers/Ada.pdf https://sites.math.washington.edu/~morrow/336_09/papers/Ada.... https://alpof.wordpress.com/category/music/math-music/neo-riemannian-theory/ https://alpof.wordpress.com/category/music/math-music/neo-ri... http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloquiumslides.pdf http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloq... https://www.maa.org/sites/default/files/pdf/upload_library/22/Hasse/Crans2011.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2... Or, of course, follow the citation chains on Wikipedia: https://en.wikipedia.org/wiki/Neo-Riemannian_theory https://en.wikipedia.org/wiki/Neo-Riemannian_theory https://en.wikipedia.org/wiki/Transformational_theory https://en.wikipedia.org/wiki/Transformational_theory

kmill 7y ago
I know you've been in the music business for a few hundred years, Josquin, but there's no need to be so harsh about this undergrad poster! From what I could figure, it's something like a final project for a class on Mathematics and Music at UW Eau Claire. The background material on transformations of sets of pitch classes is in the course textbook. (This doesn't take away from all the citations you helpfully provided, though.)
- ska 7y ago
  If it's an undergrad project, it absolutely should cite properly; so that is at least worth pointing out. To be fair though, posters are often a bit sloppy this way, and in context supposed to be supported other ways.
  - tim333 7y ago
    It's a one page summary with pictures rather than a research paper or such like. There's quite likely some article with sources elsewhere.
    - ska 7y ago
      It's a scientific poster layout, very standard. They typically have some citation, but only major ones.
deleted 7y ago
[deleted]
mnemonicsloth 7y ago
I'm trying to decide if I should go down this rabbit hole. The math looks easy enough, but I know nothing about music. Nothing. And I'd love to learn, of course, but I can see myself buying a keyboard and plinking out some of these transformations and that seems like a long time to go without a payoff. What's your musical background?
- sigstoat 7y ago
  > The math looks easy enough, but I know nothing about music. Nothing. And I'd love to learn, of course, but I can see myself buying a keyboard and plinking out some of these transformations read musictheory.net, get musescore, and then you can start experimenting with some of this. don't need a keyboard. if you do decide to spend some money on hardware, the r/piano folks have some information on the terminology of such things https://www.reddit.com/r/piano/wiki/faq#wiki_choosing_a_keyboard https://www.reddit.com/r/piano/wiki/faq#wiki_choosing_a_keyb... > without a payoff no problem, just redefine payoff and you're all set
- WalterSear 7y ago
  You may be interested in the twelve tone you tube channel, fwiw - particularly the earlier ones where he discusses the fundamentals.
- fenomas 7y ago
  I've been down this rabbit hole for a few years, except making procedural music with code rather than physically playing an instrument. No musical background at all (I started by googling "chord" etc). My take is, the basics - the math behind chords and chord changes, summarized on the left page of the PDF - are embarrassingly simple; you can know everything there seems to be to know in a weekend or two. However for the application - using those basics to create or understand music - I'm still not entirely sure there's anything to know. That is, one can find scads of sources online similar to the right-hand page of the PDF, which analyze the structure of some phrase or composition. But it all seems to pretty much boil down to giving names to things; there don't seem to be any generally applicable principles. The closest thing we have seems to be voice leading rules, but they're very much "doing X sounds good except when it doesn't" sorts of things.
deleted 7y ago
[deleted]

memset 7y ago

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 :) [1] https://en.wikipedia.org/wiki/Set_theory_(music) https://en.wikipedia.org/wiki/Set_theory_(music) [2] https://en.wikipedia.org/wiki/Twelve-tone_technique https://en.wikipedia.org/wiki/Twelve-tone_technique

nick-garfield 7y ago

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. https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-Pedler-ebook/dp/B003NX6KSM https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-P...

yesenadam 7y ago
Sounded interesting, so I started reading it.. (jazz pianist here, I learnt basic harmony in large part from playing Beatles songs as a kid) Hmm yeah, it's entertainingly written. I'd never heard the term "Three Chord Trick" (i.e. songs using just I,IV,V.) In "The power of I - the one-chord trick", Tomorrow Never Knows is described as "paradoxically structured around a single, simply embellished G chord, around which hypnotic modal melodies work their textural magic". Uh, no. It's in C, and there's distinctly a Bb/C chord in bars 5 and 6 of an 8 bar pattern - kind of like the IV chord in the first 8 bars of a blues. (Also, come to think of it, like the standard pattern in North Indian classical of not playing open tabla sounds in bars 5 & 6 of each 8 bars) Then "The Chuck Berry rhythm", "a rock'n'roll guitar pattern popularised most famously by Chuck Berry"..turns out to be the boogie-woogie piano left hand pattern, "a two-note diad...a basic root-and-fifth perfect interval...From there, a brief extension from the fifth to the sixth degree (and sometimes on to b7) can be made"–he makes it sound like rock guitarists invented it. Anyway, Rosetta Tharpe invented most of what Chuck Berry "invented", decades before he did it, the rock-n-roll guitar and the dance moves. Check her out! (on youtube) She's amazing.
- anentropic 7y ago
  to be fair the quote you quoted says "popularised most famously by Chuck Berry" which is pretty uncontroversial I think, no one claims he invented it Sister Rosetta Tharpe is awesome but T-Bone Walker is probably the more direct antecedent for Chuck Berry's guitar style and stage moves

motohagiography 7y ago

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. (see linked papers mystical treatment of a for loop.) People talk about his Tintinnabuli 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. https://www.researchgate.net/publication/271513800_Mathematical_Bases_of_the_Form_Construction_in_Arvo_Part%27s_Music https://www.researchgate.net/publication/271513800_Mathemati... or if link is down: http://žurnalai.lmta.lt/wp-content/uploads/2014/11lietuvos-muzikologija15-8.pdf http://xn--urnalai-cxb.lmta.lt/wp-content/uploads/2014/11lie... 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.