
Chord Transformations and Beethoven (2011) [pdf] - miobrien
https://minds.wisconsin.edu/bitstream/handle/1793/55613/KnaufSpr11.pdf?sequence=1
======
josquindesprez
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/algebraicmusict...](https://www.math.drexel.edu/~dp399/musicmath/algebraicmusictheory.html)

[https://sites.math.washington.edu/~morrow/336_09/papers/Ada....](https://sites.math.washington.edu/~morrow/336_09/papers/Ada.pdf)

[https://alpof.wordpress.com/category/music/math-music/neo-
ri...](https://alpof.wordpress.com/category/music/math-music/neo-riemannian-
theory/)

[http://www-personal.umd.umich.edu/~tmfiore/1/mathmusiccolloq...](http://www-
personal.umd.umich.edu/~tmfiore/1/mathmusiccolloquiumslides.pdf)

[https://www.maa.org/sites/default/files/pdf/upload_library/2...](https://www.maa.org/sites/default/files/pdf/upload_library/22/Hasse/Crans2011.pdf)

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)

~~~
mnemonicsloth
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?

~~~
fenomas
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.

~~~
mnemonicsloth
Can you recommend any sources?

What kind of setup do you use to do your development?

~~~
fenomas
No particular sources, but topic-wise what made things click for me was roman
numeral notation and secondary chords. Or rather, implementing the math behind
those things made me feel like I understood what was going on, and that's the
nomenclature/data structure I stuck with. But the notation in the PDF is
equivalent - it all boils down to having an array of numbers and then either
reindexing the array or adding to the elements modulo 12; everything beyond
that is just nomenclature.

The only thing difficult about it is finding sources that just explain the
(extremely simple) math without tons of opaque terminology. E.g. here's the
second sentence of wikipedia's definition for "secondary chord":

> Because tonic triads are either major or minor, you would not expect to find
> diminished chords (either the viio in major or the iio in minor) tonicized
> by a secondary dominant.

Blech. For years I've meant to write a bare-bones "music for programmers"
article but haven't done it yet. There are other such articles around but I
never saw one I was enthusiastic enough about to bookmark.

For dev setup, if you're a browser/JS person I recommend Tone.js, which is a
very short path from zero to "here's an array of integers, play quarter notes
for their midi values". I outgrew it at some point and now roll everything by
hand, but I probably shouldn't have.

------
motohagiography
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_Mathemati...](https://www.researchgate.net/publication/271513800_Mathematical_Bases_of_the_Form_Construction_in_Arvo_Part%27s_Music)

or if link is down:

[http://xn--urnalai-cxb.lmta.lt/wp-
content/uploads/2014/11lie...](http://žurnalai.lmta.lt/wp-
content/uploads/2014/11lietuvos-muzikologija15-8.pdf)

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.

------
nick-garfield
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-P...](https://www.amazon.com/Songwriting-Secrets-Beatles-Dominic-
Pedler-ebook/dp/B003NX6KSM)

~~~
yesenadam
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
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

------
memset
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)

