I love the dissection of harmony from a physics/computation point of view; I'm going to read this in more detail.<p>But the wrapping is quite off-putting to me; the author seems to misunderstand <i>both</i> music theory <i>and</i> 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.<p>"The more factored a theory and the more emergent the observed phenomena from the theory, the more satisfying the theory." - Feynman.<p>It's ironic that this better explains existing music theory than the one presented here, even though Feynman wasn't talking about music theory.<p>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.<p>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.<p>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.
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).<p>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.<p>[1] <a href="http://dmitri.mycpanel.princeton.edu/bio.html" rel="nofollow">http://dmitri.mycpanel.princeton.edu/bio.html</a><p>[2] <a href="http://dmitri.tymoczko.com/sciencearticle.html" rel="nofollow">http://dmitri.tymoczko.com/sciencearticle.html</a><p>[3] <a href="https://www.amazon.com/Geometry-Music-Counterpoint-" rel="nofollow">https://www.amazon.com/Geometry-Music-Counterpoint-</a>
Extended-Practice/dp/0195336674<p>[4] <a href="http://dmitri.tymoczko.com/teaching.html" rel="nofollow">http://dmitri.tymoczko.com/teaching.html</a>
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.<p>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.
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.<p>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.<p>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?<p>Section 4.3 is where I'm just quitting.<p>> "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. "<p>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.<p>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.
"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.<p>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.
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:<p>> 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.<p>And then<p>> Ok, that was so much fun let's go in the other direction as well.<p>Why not just continue with the harmonic series, rather than construct a new chord from the fifth? Why continue with a fifth <i>below</i> 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.
"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.<p>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).
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.<p>A fascinating read for anyone interested in the subject.
"music:
* the Major Scale,
* the Standard Chord Dictionary, and
* the difference in feeling between the Major and Minor Triads. "<p>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.
William Sethares has already done some excellent work towards formalizing consonance and dissonance. See:<p><a href="http://sethares.engr.wisc.edu/consemi.html" rel="nofollow">http://sethares.engr.wisc.edu/consemi.html</a><p>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.
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.
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.<p>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.<p>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...<p>also its more or less the standard explanation for western musical theory, not sure what is novel here...<p>but i like it.
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.<p>Well-Tempered? Equal Tempered? Mean Tone? Pythagoric?<p>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.<p>Should I have kept reading?
<i>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.</i><p>Translation: Western music is based on the diatonic scale.<p><i>Diatonic harmony moves in two directions: Horizontal and Vertical.</i><p>Translation: Music consists of notes played one after each other, and at the same time as each other.<p><i>By combining these two movements... we derive the scale-tone seventh chords in the key of C</i><p>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.<p>Wanting to sound unnecessary grandiose can be a problem with textbooks in almost any field.
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?<p>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'.<p><a href="https://www.youtube.com/watch?v=lXymPInuMkM" rel="nofollow">https://www.youtube.com/watch?v=lXymPInuMkM</a><p><a href="https://en.wikipedia.org/wiki/The_Nature_of_Order" rel="nofollow">https://en.wikipedia.org/wiki/The_Nature_of_Order</a><p><a href="https://en.wikipedia.org/wiki/Keith_Jarrett" rel="nofollow">https://en.wikipedia.org/wiki/Keith_Jarrett</a>
There exists a related and impressive body of work towards understanding the geometric structure of elements of music theory, see e.g. <a href="https://www.google.com/url?sa=t&source=web&rct=j&url=http://dmitri.mycpanel.princeton.edu/geometry.pdf&ved=0ahUKEwjPn6mK1PDNAhVl0oMKHYySC_4QFgggMAE&usg=AFQjCNE222eyXk0bv3DtrJdG28jY9DX7lQ" rel="nofollow">https://www.google.com/url?sa=t&source=web&rct=j&url=http://...</a> and references therein.
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.<p>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.
Here is much better theory:<p>Music And Measure Theory – A connection between a classical puzzle about rational numbers and what makes music harmonious. <a href="https://www.youtube.com/watch?v=cyW5z-M2yzw" rel="nofollow">https://www.youtube.com/watch?v=cyW5z-M2yzw</a>
You should perhaps watch this incredible video from PyCon 2016 given by Lars Bark about music, road trips, software development, and fractals!<p><a href="https://www.youtube.com/watch?v=bSfe5M_zG2s" rel="nofollow">https://www.youtube.com/watch?v=bSfe5M_zG2s</a>
I take this opportunity to re-advertise my own alternative approach to developing a scientific theory of music: <a href="http://whatismusic.info/" rel="nofollow">http://whatismusic.info/</a>.
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?<p>Seems interesting tho, I might keep reading, I would like to see another approach to harmony.
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.
This article helped me grasp how the major/minor scales are constructed by using the idea of consonance and dissonance.<p>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.
Not exactly on topic but I wanted to ask:<p>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?
For anyone interested the intersection of rhythm and harmony:
<a href="https://www.youtube.com/watch?v=_gCJHNBEdoc" rel="nofollow">https://www.youtube.com/watch?v=_gCJHNBEdoc</a>
"...phenomena of any machine that must make sense of sound, such as the human brain"<p>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.
Note that the post currently links to version 1, which was uploaded in 2012 (<a href="https://arxiv.org/html/1202.4212v1" rel="nofollow">https://arxiv.org/html/1202.4212v1</a>). There is an updated version from 2014 (<a href="https://arxiv.org/html/1202.4212v2" rel="nofollow">https://arxiv.org/html/1202.4212v2</a>).<p>For arXiv posts, unless a specific version is under discussion, it's probably best to link to the abstract page without the version tag:<p><a href="https://arxiv.org/abs/1202.4212" rel="nofollow">https://arxiv.org/abs/1202.4212</a><p>This lets folks see if there are multiple versions of the preprints and multiple formats to view those preprints.
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.'
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.
Pulses and waves compounded in whole number ratios form periodic and stable, i.e. consonant, waveforms.<p>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.
Wonderful paper. And wow, the author has really managed to piss a lot of people off!<p>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.<p>This paper provides one of the first theories at the foundations of music! How exciting is this!