
Harmony Explained: Progress Towards a Scientific Theory of Music - colund
https://arxiv.org/abs/1202.4212
======
dahart
I love the dissection of harmony from a physics/computation point of view; I'm
going to read this in more detail.

But the wrapping is quite off-putting to me; the author seems to misunderstand
_both_ music theory _and_ science, and rather deeply. I don't see a scientific
theory here at all. To be called science, it needs to have a hypothesis and be
falsifiable, and after that get tested experimentally and proved - I don't see
that, nor even a stab at a metric that is verifiable. What I see here is note
relations described using science terminology instead of music terminology.
That's not science, that's just someone using the terminology they're
comfortable with rather than learn the accepted paradigm.

"The more factored a theory and the more emergent the observed phenomena from
the theory, the more satisfying the theory." \- Feynman.

It's ironic that this better explains existing music theory than the one
presented here, even though Feynman wasn't talking about music theory.

The author accuses music theory of being pseudo-science, when music theory is
not and never was attempting to be science, and yet the author proposes a
theory of music claiming to be science that in fact isn't science.

Unfortunately, this 'theory' here only seems to contend with the first two of
the 32 chapters in my copy of "Harmony and Voice Leading", and this mainly
talks about what makes notes sound good, not what makes music sound good.

Also unfortunately, the author doesn't seem to be aware of what's going on in
modern music theory, which is exploring things like how to compose music out
of the beat frequencies that exist as harmonic dissonances between two or more
notes. A lot of the physics of harmonics is currently already being
incorporated into music theory.

~~~
Bromskloss
> to compose music out of the beat frequencies that exist as harmonic
> dissonances between two or more notes

Do you have any links regarding this?

~~~
dahart
Yeah, I was thinking of "Spectral Music":

[https://en.wikipedia.org/wiki/Spectral_music](https://en.wikipedia.org/wiki/Spectral_music)

Tristan Murail is a well known composer of spectral music.

[http://www.tristanmurail.com/en/outils.html](http://www.tristanmurail.com/en/outils.html)
[https://en.wikipedia.org/wiki/Tristan_Murail](https://en.wikipedia.org/wiki/Tristan_Murail)

Also worth exploring in terms of modern music theory are microtonal music and
atonal music, both of those are playing with incorporating the physics of
notes, overtones and harmonic relationships.

[https://en.wikipedia.org/wiki/Microtonal_music](https://en.wikipedia.org/wiki/Microtonal_music)
[https://en.wikipedia.org/wiki/Atonality](https://en.wikipedia.org/wiki/Atonality)

Apologies for only bringing Wikipedia links, but they are pretty good
launching points for learning more.

~~~
Bromskloss
> Yeah, I was thinking of "Spectral Music"

Oh. It has not been my understanding that spectral music is about beat
frequencies.

Beside the point: My experience of spectral music has been that it's a neat
idea that seems worthy of trying out. Then, when you do it – test the
hypothesis, so to say – it turns out that nope, didn't work, sounds awful.

~~~
dahart
Yes. Spectral is a bit more about composing using overtones than beat
frequencies. I know the latter has been done, but I mixed them up a little, I
would have described it as overtones were I to write my initial comment again.

I agree that it's not producing pleasant music to the masses. It's more of an
academic exercise, but it is influencing modern music theory and bridging
classical music theory with a more recent understanding of harmonics.

------
metaxy2
The best work happening in this area is by a Princeton professor named Dmitri
Tymoczko [1]. He's discovered some pretty fundamental results that tie
together a lot of the previous theories of harmony based on geometry. He was
the first music theorist ever published in Science [2] and he wrote an amazing
book called A Geometry of Music [3] (technical but readable, a must for anyone
trying to really understand why music sounds good).

He also teaches a 2-semester intro level music class at Princeton that is
infused with his ideas, and makes the lecture notes available online [4].
Those notes are so good they're better than any intro music textbook I know
of, especially for us geeks who like to hear the scientific explanation for
everything.

[1]
[http://dmitri.mycpanel.princeton.edu/bio.html](http://dmitri.mycpanel.princeton.edu/bio.html)

[2]
[http://dmitri.tymoczko.com/sciencearticle.html](http://dmitri.tymoczko.com/sciencearticle.html)

[3] [https://www.amazon.com/Geometry-Music-
Counterpoint-](https://www.amazon.com/Geometry-Music-Counterpoint-) Extended-
Practice/dp/0195336674

[4]
[http://dmitri.tymoczko.com/teaching.html](http://dmitri.tymoczko.com/teaching.html)

~~~
acjohnson55
I read that several years ago, when it first came out, and it blew my mind.

I also highly recommend _Tuning, Timbre, Spectrum, Scale_ by William Sethares
[1]. It's a different approach to deriving our familiar harmonic structures,
with a greater emphasis on consonance within a given timbre than voice
leading.

[1] [https://www.amazon.com/Tuning-Timbre-Spectrum-William-
Sethar...](https://www.amazon.com/Tuning-Timbre-Spectrum-William-
Sethares/dp/1852337974)

------
mazelife
Other commenters here have done a good job picking out specific problems with
the author's arguments. It's always frustrating when someone who is capable
and knowledgeable about one subject decides to try their hand in a different
field without having bothered to do any real research or study in it. And it's
doubly so when they proceed to then dismiss, literally, the entire field as
"superstitions," and "unscientific" even as everything they've written betrays
that they haven't bothered to familiarize themselves with basically any of the
work that's been done in music theory or psychoacoustics in the last 100
years.

I usually love it when articles about the intersection of music and
computation show up on HN, but in this case it's really unfortunate. At least
it's sparking some good discussion, I guess.

~~~
gardano
You know -- you're right.

Music is incredibly complex, and I'm so glad to have a conversation about it.
Perhaps I've been too strenuous in my objections to the article, but at the
same time, music to me is an intersection between theory and practice; science
and art, and I just hate to see it simplified on one side or on the other
side.

I look forward to the day where theory and practice can be brought together.
It will take someone smarter than me to do such a thing.

------
squeaky-clean
I don't like the tone of this book, it gets too hung up on the literal word
"theory" in music theory, and also badly explains a lot of concepts in music
theory while insulting them.

For example, the circle of fifths doesn't explain at all why the circle is
cool or useful for chord transitions. It's not a coincidence at all. By
rotating around the circle, your key changes by only one note at a time.

It's also just waaaay to objective about subjective things. Other cultures use
of limited or different musical scales or temperaments is because they are
missing out on real harmony? A major triad sounds best because a factor of 3
and 5 are the "most interesting" intervals?

Section 4.3 is where I'm just quitting.

> "Play C and F# on a piano; it sounds awful" [...] " because someone has even
> written a piece of music based entirely in the most un-harmonic of
> intervals, the Augmented Fourth, and gotten away with it." [...] "There are
> people who can abuse themselves to the point of re-calibrating their
> expectations to all kinds of strange inputs, including thinking that getting
> beaten with whips is fun or that McDonald's tastes good. That doesn't mean
> that those inputs are natural or good or beautiful or true. "

So I don't really like dissonant music, I've only tricked myself into thinking
it's good? The Ben Franklin quote after it just sounds like someone comparing
pop music to anything else. Just because it's Ben Franklin doesn't make it
definitive.

It starts by insulting the assumptions that the diatonic scale and triads are
a given in conventional music theory. But then goes on to make even greater
assumptions as to why some harmonies sound "better" than others. Please prove
it, or it's just as meaningless as the work you're insulting.

~~~
mazelife
Yeah, his discussion of the tritone was where any remaining sympathy or
interest in his argument evaporated for me. His discussion of it is completely
simplistic and not grounded in any way in the complex historical context of
that interval.

Listen to the opening of Debussy's "Prelude to the Afternoon of a Faun"
([https://www.youtube.com/watch?v=EvnRC7tSX50](https://www.youtube.com/watch?v=EvnRC7tSX50)).
Tritones everywhere: flute plays a melody that outlines a tritone (C# to G).
In come the oboes and horns playing a tritone which is part of the A# 7th
chord the harp outlines. Then a Bb dominant seventh, with horns and strings
playing another tritone. Tritones abound until the music finally settles into
the tonic nine bars later, and yet who would argue with the idea that this is
one of the most beautiful openings in music?

It's ironic that he likens works based on the tritone to McDonalds (!?). When
I hear someone savage a work of music they've never heard, and describe the
sound of an augmented fourth as "awful" and call any piece based around the
tritone as "[not] natural or good or beautiful or true" I would suggest that
person's musical taste is limited and simplistic, sort of the musical
equivalent of the McDonald's hamburger.

~~~
squeaky-clean
Beautiful piece, thanks for sharing. I probably would not have noticed how
filled with tritones it is without it being pointed out.

If you wouldn't mind me sharing an example which isn't nearly as beautiful :P
. "43% Burnt" by The Dillinger Escape Plan
([https://www.youtube.com/watch?v=Zv8b6RPbnAc](https://www.youtube.com/watch?v=Zv8b6RPbnAc)).
It starts with an incredibly dissonant and jarring intro. Semitone intervals
on distorted guitars to an almost unpredictable rhythm (there's a pattern, but
it's not apparent in the intro). And the song doesn't really get any gentler
from there. The last bridge before the outro is an aggressive halftone-
wholetone diminished riff on the guitars and non-stop 16th note blast on the
drums. Stop... And then... It comes back to that disgusting intro which loops
until the track fades out. But now, it feels familiar, like home. And with
each loop it sounds better. What started off sounding awful becomes
comfortable in a different context.

~~~
mazelife
I don't know The Dillinger Escape Plan too well, but I like that!

It's funny, but I've noticed that as my musical tastes have broadened over the
years, the line between what sounds "beautiful" and "ugly" has become
considerably more blurry. I can still recognize particular harmonies as
consonant or dissonant, but that mapping in my brain where consonant ->
beautiful and dissonant -> ugly has started to really break down.

One of the first times I noticed this was happening was probably 15 years ago,
listening to Salomé by Richard Strauss. The last scene has this incredible
dissonance, a polychord that's an A7 with an F# stacked on top: two chords
that absolutely do _not_ belong together in any diatonic piece of music.[1]
When I first heard that I thought it sounded awful. Now it has a kind of
strange beauty to my ears and is one of those musical moments that always
sends a shiver up my spine.

[1] Give a listen here if you like:
[https://youtu.be/Op1VoQXXARs?t=431](https://youtu.be/Op1VoQXXARs?t=431) I
started the clip at 7:15, the chord comes in around 8:53 but that whole
section is shot through which these ugly/beautiful sonorities.

~~~
squeaky-clean
That chord! I remember it from when I went down a long Wikipedia/internet
rabbit hole reading about polychords. It's absolutely amazing how composers
will use the chords to represent emotions or the personality of their
characters.

I think the line between beautiful and ugly has gotten blurrier for me too.
Artistically, I don't actually think they're opposites anymore. One needs the
other to be fully realized, otherwise it just sounds too plastic.

I first got into really dissonant music around high school, I think mostly
just in an attempt to be "edgy" and different. There's a lot of music that
just tries too hard to sound heavy (I can't listen to like 99% of grindcore
anymore. It just sounds like trying to piss of my parents). But I started
finding things that used dissonance artistically and not just for shock, and I
love it. Now the music that hits hardest and sounds "heaviest" to me aren't
the songs that just shove abrasive sounds in your face as quickly and loudly
as possible. But the ones with lots of contrast and empty space, and slowly
building tension before slamming into something. You know what they say, if
everything is loud, then nothing is loud.

I'm listening to Strauss now because of your examples. I think I might have to
go on a classical binge for the next week or so just because of this
conversation!

------
beat
"Music theory" tends to be incredibly narrowminded and Eurocentric. Harmonic
theory? Outside of Europe and European-derived forms, harmony is very rare.
There are melodic traditions that do not use harmony, yet are just as
traditional and sophisticated (Arabic, Hindustani, and Carnatic music all come
to mind), and there are purely rhythmic traditions (various African, Arabic,
central Asian, etc). And in the modern world, there is ambient, music built
out of tone rather than rhythm/harmony/melody.

Having studied and played several different traditions to varying degrees, one
thing I've learned is that music is equally sophisticated everywhere. There's
this idea that classical and jazz are more sophisticated than "folk" forms.
It's BS.

~~~
aridiculous
Perhaps I'm being a tad too pedantic in this followup, but can you elaborate
further? It's difficult for me to square how every style of music is _equally_
sophisticated. I'm taking sophisticated to roughly mean 'complex'.

I'm not promoting classical music as _superior_ to folk, but can we not
reasonably say that a Bach fugue is more _complex_ than Simon and Garfunkel?
Using two Eurocentric examples to control for bias.

~~~
kazinator
Simon and Garfunkel absolutely depends on performance; it doesn't have the
same musical _content_ as a Bach fugue.

A somewhat poor, though adequate, performance of a Bach fugue with an
instrument that doesn't have great tone will still convey a great deal of
Bach's meaning.

A performance by average vocalists of a Simon and Garfunkle tune, backed by
some average lounge band will just be a laughable farce.

It can't be saved by the musical content, because that is there in
insufficient quantity.

Pop music is all in the nuance and tone that doesn't get notated in sheet
music.

The result is that performing a _convincing_ cover of some pop music requires
a very high musical standard. Whereas a five-year-old kid can play some
passable Bach on the piano that we can enjoy as Bach, just by hitting most of
the right notes from the sheet music at mostly the right time.

~~~
ZenoArrow
> "Whereas a five-year-old kid can play some passable Bach on the piano that
> we can enjoy as Bach, just by hitting most of the right notes from the sheet
> music at mostly the right time."

Sure, you can get pleasure from that, but at the highest level classical music
is very much about interpretation. People may think that classical music is
about following the notes exactly, but it's not quite true, the way the player
interprets a piece is what brings a piece to life (or not), and these subtle
touches are not directly transcribed in the sheet music.

~~~
kazinator
And like pop music, those interpretations come and go. We don't even have
access to interpretations that were made prior to the age of recorded music!
The Bach or Brahms score is the artistic gem which carries the timeless,
enduring value. The interpretation is just a kind of ephemeral, stylistic
whipping cream ladled on top. Today you like how Bob plays Paganini; tomorrow
Bob is forgotten and Mike is the hot shit in Paganini interpretations.

~~~
ZenoArrow
No no, the performance is very important. A piece that sounds dull and
uninteresting from one performer can sound full of life from another
performer. Of course it helps if you have better source material, but that can
only carry someone so far.

As for forgotten interpreters, before the days of recording I'd agree with
you, but now we have recordings of greats from the past that's no longer the
case. For example, in the case of classical guitar, people still admire the
playing of players that are no longer with us, such as Segovia, and will still
play their recordings. Whilst it's good to support new players too, a great
performance is a great performance, it doesn't matter how long ago it was
performed if it's still possible to listen to it.

------
tobr
The writer starts out complaining that the distinction between "chord" and
"scale" is arbitrary. He then proceeds to derive the major chord and major
scale using a bunch of arbitrary decisions. For example, why does he stop
adding notes to the major chord when he has three of them? And look at what he
does when he starts constructing the major scale from the major chord:

> Well, we like the Major Triad, so let's make another one, but starting with
> a different note as the fundamental. To preserve as much theme with the
> previous triad, let's start with the "closest" notes to the C that we have
> in our first triad: The first note other than C that we hit was 3/2 times
> the Root, also called the Perfect Fifth; therefore let's build a triad using
> 3/2 times C4 = G4 as the fundamental.

And then

> Ok, that was so much fun let's go in the other direction as well.

Why not just continue with the harmonic series, rather than construct a new
chord from the fifth? Why continue with a fifth _below_ the root, and not
continue in the established direction? Because these changes would lead to a
completely different answer. He knows which answer he wants to end up with, so
he picks a path that will lead there. This is numerology.

~~~
baddox
> For example, why does he stop adding notes to the major chord when he has
> three of them?

This particular complaint isn't very valid. The author explicitly writes that
he could keep going, but is going to stop at three for reasons that will be
explained later. He then explains later that the next note (the 7:4 interval)
doesn't work well on equal tempered instruments because it ends up sounding
like a dominant/minor seventh chord instead of a harmonic/barbershop seventh
chord.

------
jkingsbery
"You can't start a science textbook like that" ... actually, lots of math and
science textbooks assume a certain level of knowledge, and start more-or-less
that way.

There also seems to be confusion about what Music Theory actually is - it's
(usually!) not an attempt to axiomize music, rather it's an attempt to take a
musical corpus and explain how pieces in it tend to work (which is why one
sees different music theory text books for Jazz and Classical, for example).

~~~
squeaky-clean
> There also seems to be confusion about what Music Theory actually is - it's
> (usually!) not an attempt to axiomize music, rather it's an attempt to take
> a musical corpus and explain how pieces in it tend to wor

I think they try to address this in 1.3 but it comes out more as a complaining
and misunderstanding. People get way too hung up on the term "music theory". I
have friends who are professional musicians who refuse to learn music theory.
Not because they don't like learning it, or they think it stifles their
creativity (which are fine reasons to not learn it, you don't have to). But
they refuse because they "don't believe in it" or "my music doesn't fit the
definition of music theory". Which is totally incorrect, because like you
said, music theory is an attempt to explain existing pieces and how they tie
together. Not describe some magical pre-existing rules created by our ears and
the universe.

It's like learning the grammatical rules behind a natural language. English
isn't carved into a mountain somewhere, or programmed into our DNA, it's
entirely made up by people, and you're free to break all the rules. But then
you're unlikely to be understood. And if you are understood, we'll probably
end up giving a name to whatever you did!

~~~
TheOtherHobbes
The problem is that in many books music theory means 18th century classical
theory.

This is fine as far as it goes, but music has moved on a lot since then and no
one - not even film composers - write in that style any more.

So you have the _idea_ of a music theory - which is the set of elements that
defines a style - and then you have _one particular_ music theory, which isn't
used any more, although some of the ideas are still creatively useful.

Not many people understand that hip hop, dubstep, deep house, death metal,
jazz, and shoegaze all have unique theories of their own.

They're defined by elements - some of which are simple cliches, and some of
which are more creative - that make the style recognisable.

If you know the elements and how to put them together, you know the style.
Simple as.

Classical book theory gives you a small start towards understanding how this
works, if you want to take it. But you have to do the rest yourself.

A lot of producers don't bother. They learn one style intuitively, and that's
all they know. Other producers want more. Neither has a monopoly on great
music.

Does axiomising music help? It may give you a few hints about harmony. _But
that 's all._

It's not even close to being a complete description of classical theory, and
it completely fails to say anything useful about the theories of more modern
pop styles.

The math part is simply irrelevant to most musicians. Musicians use chords and
lines as expressive tools, not as theorems. Knowing where frequency ratios
come from is kind of interesting, but there's a lot more going on in music.
Trying to mathify it won't get you closer to that.

~~~
auggierose
So I like your explanation a lot, it's actually the best explanation of music
theory I've come across so far (if its true, that is :-))

Nevertheless, I think math can be very useful to describe the various music
styles, elements that make up these styles, and the ways to compose these
elements. That would be using math in a descriptive way. I like for example
the 2 book series "Musimathics"
([http://www.musimathics.com/](http://www.musimathics.com/)). In the end,
nobody knows how much of music can be understood by viewing it through the
mathematical lens. I suspect quite a lot, if not all.

------
pcsanwald
I've mentioned this before, but for me, the definitive work on this vast
subject is "The Harmonic Experience" by W.A. Mathieu. He really gets into low
prime ratios, why they sound good to us, and also why the building blocks of
modern western harmony are approximations of those ratios, rather than the
real thing.

A fascinating read for anyone interested in the subject.

~~~
soundwave106
Seconded.

The one law I think you can say about harmony and melody, is that there seems
to be a universal preference towards low frequency ratio combinations. EG: in
all of world music, it seems octaves (2/1) fifths (3/2), fourths (4/3), and
thirds (5/4) occur quite often and are the fundamental driving force of so
many styles. They are seen as more "pure sounding" to the ear. Regarding the
linked paper, the low ratio concept has been known for a while, and linking it
to the harmonic series is fine.

But there's more to music than simple pure ratios. Even many simple pop songs
often offers transitions between "purity" and "impurity" (the simple dominant
seven to tonic resolutions is enough to show this.) This is where the linked
paper fell short... way short. It seemed to imply in 4.3 that there is no room
for dissonance (or, to describe it without using Western terms, stepping away
from the pure ratios, perhaps to resolve to purity... or perhaps not...)
whatsoever in music, which is very laughable to anyone who's actually
composed. 4.2.1 also almost seemed to apply a certain sense of Western
cultural superiority... even though I would argue that Western culture
actually is a case against his ideas. (As in... equal temperament decreases
the "purity" by detuning some of the ratios, particularly the thirds. But a
greater freedom is allowed for key modulation, and I agree with Mathieu that
the ambiguity 12TET opens up is a feature in itself. Let's not go into the
large amount of dissonance in some art such as 20th century classical, jazz,
even some pop particularly in the alternative realm).

I'm currently in the middle of Mathieu's book. The main disadvantage of his
style is that it is a bit "flowery" which may not appeal to those who like
reading their math more exactly. But one big advantage of W.A. Mathieu is that
he seems well versed in three very different backgrounds (Indian classical
music, jazz and Western classical music, although definitely heavier on the
first two). For those familiar with neo-Riemannian theory, I consider his book
a good tie-off with that side of music theory, not completely the same, but
tangentially related. Unlike some neo-Riemannian books, because of Mathieu's
background, I believe it avoids both some of the cultural mistakes that other
music theory books seem to make and also avoids the mistake of trying to be
the "one theory to rule them all".

~~~
pcsanwald
I love the nature of his prose, but it's definitely not for everyone. One of
the best things about the book for me was his emphasis on understanding the
concepts through experience (singing against a drone), but of course this
isn't everyone's goal.

Still, for me, it continues to be a life-changing read which fundamentally
altered the way I think about and hear music, and I've worked as a
professional musician for more than 20 years.

------
dmritard96
"music: * the Major Scale, * the Standard Chord Dictionary, and * the
difference in feeling between the Major and Minor Triads. "

Doesn't this already carry a ton of biases in that these are largely
constructs of Western music? Certain pieces are based on physics, an octave is
a doubling of frequency and the way a major chord fits together to some degree
is a constructive interference. I studied music performance and compsci and
its amazing to me how much magic and mysticism the music schools believe in.
It was also pretty eye opening to see how much they believed that western
music was the center of the human sound intersection world. It wasn't until
taking a world music class that you realize how myopic even these researchers
can be.

~~~
dmritard96
Also very relevant:

[http://www.theatlantic.com/science/archive/2016/07/music-
to-...](http://www.theatlantic.com/science/archive/2016/07/music-to-our-
western-ears/491081/)

------
mrob
William Sethares has already done some excellent work towards formalizing
consonance and dissonance. See:

[http://sethares.engr.wisc.edu/consemi.html](http://sethares.engr.wisc.edu/consemi.html)

This new paper looks worse than Sethares' as it only considers timbres based
around the harmonic series, ignoring important sounds such as tuned
percussion, and ignoring the possibilities for genuine harmonic novelty with
synthesisers. It cites Terhardt (1974) as "modern" while completely ignoring
more recent work.

------
jng
I urge anyone interested in this topic to read Helmholtz's "On the sensations
of tone", a fascinating 19th-century tour-de-force trying to understand music
sensation as coming from physical principles, deriving the standard western
intervals and consonance/dissonance from first principles (beats between upper
partials), and for which he is considered the father of acoustics. He spent 8
years researching in order to produce it, and is to me a great example of a
19th century hacker.

------
apalmer
Ehhh.. fundamentally I think this argument is flawed. It assumes harmony as
the underlying driver of music. Majority of music across history is not
harmonic oriented. Really only in western music is harmony the driving force
behind music.

now western music is extremely popular but that is really driven by historical
coincidence that europe colonized the world, rather than the appreciation for
the music itself.

I do think the points are well thought out, and seem reasonable... but ignores
way too much empirical reality to be taken very serious as a 'scientific'
explanation for music...

also its more or less the standard explanation for western musical theory, not
sure what is novel here...

but i like it.

~~~
toomim
Well, there's harmony, melody, rhythm, and words. Melody derives from harmony.
I agree that this doesn't cover rhythm or words.

------
gardano
Given that in the first few pages of this article, the author never mentioned
temperament (tuning) systems, I had a heck of a time parsing the argument.

Well-Tempered? Equal Tempered? Mean Tone? Pythagoric?

I had a hard time even concentrating on the argument when the basic assumption
regarding horizontal (melodic) vs vertical (harmonic) had some badly unstated
assumptions.

Should I have kept reading?

~~~
squeaky-clean
> Should I have kept reading?

If you know a bit of music theory, I wouldn't recommend it. I skimmed the
whole thing and it basically just ruined my morning by pissing me off, haha.

~~~
thevibesman
Thanks for the warning! I guess I'll save it for after my meetings today so
I'm more smiley ;)

Hopefully I can still comment / reply by then because the discussion here is a
bit interesting.

EDIT: Okay, I'm actually more interested in reading this because of how much I
disagree with the first sentence of the abstract:

> Most music theory books are like medieval medical textbooks: they contain
> unjustified superstition, non-reasoning, and funny symbols glorified by
> Latin phrases.

I'd have to disagree with all three of these points. As others have pointed
out, I get the sense the author mistook the fact that the subject is called
"Music Theory" to mean that "Music Theory" == "The Theory of Music", when
instead it is an umbrella topic of things like "species counterpoint" and
"tonal harmony" which are both a study of how music was written in a
particular style, not an overarching theory of how music works.

> funny symbols glorified by Latin phrases

I think the is a reason in school, students often study music theory and music
history concurrently, is so they understand how and why these "funny symbols"
evolved (i.e. to use music to help standardize the liturgy of the early
Catholic church---western music traces its roots back to Gregorian Chant,
those glorifying "Latin phrases").

------
sampo
_The harmony of of popular music and jazz is based on the diatonic of major
scale. Each of the twelve scales is a frame forming the harmonic system._

Translation: Western music is based on the diatonic scale.

 _Diatonic harmony moves in two directions: Horizontal and Vertical._

Translation: Music consists of notes played one after each other, and at the
same time as each other.

 _By combining these two movements... we derive the scale-tone seventh chords
in the key of C_

Translation: We can build the scale-tone 7-chords (root + third + fifth +
seventh played at the same time) on top of any note in the scale.

Wanting to sound unnecessary grandiose can be a problem with textbooks in
almost any field.

------
AnthonyNagid
I have a theory that papers seeking a true break through in music theory
should be exploring Christopher Alexander's work 'The Nature of Order'. We
need music thoerists / scientists / programmers to be fleshing out Alexander's
thoeries in relation to music. Shouldn't the scientific spirit take us where
we haven't looked yet?

To illustrate my point with a musical example I'd like to refer to Keith
Jarrett's recording 'Hymns / Spheres'. This is a musician who has become as
intimate as a human can with classical and jazz. In a C. Alexandrian fashion,
Jarrett takes all of these elements and applies them on an ancient cathedral
organ in Germany and trancends both genres and his usual way of playing. The
lowest hanging fruit in terms of understanding what's going on here more
completely is not in music theory or acoustics but in Christopher Alexander's
'Nature of Order'.

[https://www.youtube.com/watch?v=lXymPInuMkM](https://www.youtube.com/watch?v=lXymPInuMkM)

[https://en.wikipedia.org/wiki/The_Nature_of_Order](https://en.wikipedia.org/wiki/The_Nature_of_Order)

[https://en.wikipedia.org/wiki/Keith_Jarrett](https://en.wikipedia.org/wiki/Keith_Jarrett)

------
dbranes
There exists a related and impressive body of work towards understanding the
geometric structure of elements of music theory, see e.g.
[https://www.google.com/url?sa=t&source=web&rct=j&url=http://...](https://www.google.com/url?sa=t&source=web&rct=j&url=http://dmitri.mycpanel.princeton.edu/geometry.pdf&ved=0ahUKEwjPn6mK1PDNAhVl0oMKHYySC_4QFgggMAE&usg=AFQjCNE222eyXk0bv3DtrJdG28jY9DX7lQ)
and references therein.

~~~
dangerlibrary
without the google referral link (pdf)

[http://dmitri.mycpanel.princeton.edu/geometry.pdf](http://dmitri.mycpanel.princeton.edu/geometry.pdf)

------
bluetwo
As a life-long lover of music and programmer who decided in his 30's to try
learning an instrument, I share his frustration with traditional music theory
instruction and desire to explain using more physics-based models.

I'm curious if his spent any time developing tools that might leverage his
theories. I ended up developing a midi-toolset for composition based on my
attempts at understanding the space.

~~~
drauh
Using physics-based models will make it even more frustrating and complicated.
You'd have to take into account "temperament" or tuning, which someone else
has already mentioned. Then, the relationship between frequencies is dependent
on what intervals one decides should sound good.[0]

Music theory is an abstraction: it tries to make a transient activity (musical
performance) amenable to being described on paper. Maybe an appropriate
analogy is mathematics to physics. You can't learn to program a computer by
learning only abstract grammar.

[0]
[https://en.wikipedia.org/wiki/Equal_temperament](https://en.wikipedia.org/wiki/Equal_temperament)

------
nabla9
Here is much better theory:

Music And Measure Theory – A connection between a classical puzzle about
rational numbers and what makes music harmonious.
[https://www.youtube.com/watch?v=cyW5z-M2yzw](https://www.youtube.com/watch?v=cyW5z-M2yzw)

------
denfromufa
You should perhaps watch this incredible video from PyCon 2016 given by Lars
Bark about music, road trips, software development, and fractals!

[https://www.youtube.com/watch?v=bSfe5M_zG2s](https://www.youtube.com/watch?v=bSfe5M_zG2s)

------
pjdorrell
I take this opportunity to re-advertise my own alternative approach to
developing a scientific theory of music:
[http://whatismusic.info/](http://whatismusic.info/).

------
bigjcr
The questions the author asks in the first chapter make me wonder whether I
want to keep reading or not; his comments to those questions look full of
arrogance or just sarcasm. You don't start learning music theory in a jazz
theory book, so you wouldn't be asking those questions if you started learning
music from a music theory book. Or at least you wouldn't have that kind of
comments. Or are they just intended jokes?

Seems interesting tho, I might keep reading, I would like to see another
approach to harmony.

------
dminor14
There is nothing fundamental about the major scale or triad, they didn't even
exist 300 years ago, they are an invention of western culture. The author is
not aware of previous work of Hindemith, who derived them from purely acoustic
phenomena, or the advanced mathematical/musical theories of Mazzola. In other
words, like most scientists who delve into art, they look at it as a trivial
pursuit and are not diligent.

~~~
baddox
I don't see why the alleged fact that the major triad didn't exist 300 years
ago implies that there is nothing fundamental about them. Even if the
biological reasons for their sound perception are as claimed in this article,
people would still have to discover that and start using it to create music.

------
costcopizza
Does anyone else not care to know what makes music sound good and enjoy the
mystery and emotional complexity of it?

~~~
theseatoms
Even if we knew exactly what physics made music sound good, that doesn't take
any of the mystery out of physics itself.

------
nirajshr
This article helped me grasp how the major/minor scales are constructed by
using the idea of consonance and dissonance.

It is sort of like a derivation of a mathematical formula. So many other books
just give you the scales as given. For that alone, it was an insightful read.

------
sunnyps
Not exactly on topic but I wanted to ask:

I have never learnt how to play a musical instrument (sadly) but I would like
to dabble in computer generated music and music theory. What's the best way to
get started with this?

~~~
ZenoArrow
If you want to dabble in computer generated music, I'd suggest Sonic Pi is a
good place to start, especially if you're comfortable with coding.

[http://sonic-pi.net/](http://sonic-pi.net/)

You may also be interested in Syntorial, which is a synthesizer design course,
teaching you how to design synthesizer sounds:

[http://www.syntorial.com/](http://www.syntorial.com/)

Music theory is a huge field. I'd say the circle of fifths is a good starting
point into exploring music theory.

[https://en.m.wikipedia.org/wiki/Circle_of_fifths](https://en.m.wikipedia.org/wiki/Circle_of_fifths)

[https://m.youtube.com/watch?v=d1aJ6HixSe0](https://m.youtube.com/watch?v=d1aJ6HixSe0)

------
hkailahi
For anyone interested the intersection of rhythm and harmony:
[https://www.youtube.com/watch?v=_gCJHNBEdoc](https://www.youtube.com/watch?v=_gCJHNBEdoc)

------
holri
"...phenomena of any machine that must make sense of sound, such as the human
brain"

A machine is a man made artifact. A brain is a living artifact, we do not
understand it and it can not be built by us.

~~~
kefka
I don't know about that. Sex is pretty simple. Certainly simpler than making
an engine :)

------
kingkawn
Anything to say about music is better said by making it.

------
wry_discontent
Maybe I'll finally be able to understand music.

------
privong
Note that the post currently links to version 1, which was uploaded in 2012
([https://arxiv.org/html/1202.4212v1](https://arxiv.org/html/1202.4212v1)).
There is an updated version from 2014
([https://arxiv.org/html/1202.4212v2](https://arxiv.org/html/1202.4212v2)).

For arXiv posts, unless a specific version is under discussion, it's probably
best to link to the abstract page without the version tag:

[https://arxiv.org/abs/1202.4212](https://arxiv.org/abs/1202.4212)

This lets folks see if there are multiple versions of the preprints and
multiple formats to view those preprints.

~~~
sctb
Thank you! We've updated the submission link.

------
GFK_of_xmaspast
It's a discredit to the arxiv that this paper is still up, and I have to
assume it's because there are just many fewer 'music theory nuts' out there
than 'quantum physics nuts.'

~~~
drauh
I don't think it's a discredit. arXiv is a preprint database, which means
nothing is refereed. It's under "Computer Science", but that's just the
author's own classification.

I don't think there's a way for the admins of arXiv to remove a paper. Once a
paper is in the arXiv, it's there permanently: even the authors themselves can
only update.[0]

E.g. this bit of quackery "Electromagnetic Signals from Bacterial DNA"[1]

[0] [https://arxiv.org/help/withdraw](https://arxiv.org/help/withdraw)

[1] [https://arxiv.org/abs/1104.3113v1](https://arxiv.org/abs/1104.3113v1)

~~~
GFK_of_xmaspast
Crackpot stuff gets disappeared tho?

~~~
drauh
I don't think so. The link [1] I posted is crackpot.

See also: * [https://motls.blogspot.com/2006/05/crackpot-papers-on-
arxiv....](https://motls.blogspot.com/2006/05/crackpot-papers-on-arxiv.html) *
[https://arxiv.org/abs/gr-qc/0605023](https://arxiv.org/abs/gr-qc/0605023)
(dated 2006)

------
simbalion
I've read a number of music theory books and guides, and not one of them
contained: "unjustified superstition, non-reasoning, and funny symbols
glorified by Latin phrases". In fact all were based on mathematics and at
least some science.

------
multinglets
Pulses and waves compounded in whole number ratios form periodic and stable,
i.e. consonant, waveforms.

But oh yeah some people just play all random frequencies or like a dog. A dog
can be music. It's such a huge mystery, music.

------
toomim
Wonderful paper. And wow, the author has really managed to piss a lot of
people off!

People get really upset when you present work that points out flaws in their
own thinking, using a different style than they've come to accept. It comes
across as an attack from a different tribe, and they get all tribal at you.
You can tell because they attack the style as much as (or more than) the
content.

This paper provides one of the first theories at the foundations of music! How
exciting is this!

