> We show to be incomplete the theory of the heretofore agreed-upon authority on this subject, 19th-century Physicist Hermann Helmholtz [Helmholtz1863]: he says notes are in "concord" because the sound playing them together is "less worse" than that of some other notes. But note that, in this theory, more notes can only penalize, some merely less than others, and so the most harmonious sound should be a single note by itself(!) and harmony would not exist as a phenomenon of music at all.
Hokay, buddy.
A bunch of the material available in this paper is sufficiently common knowledge to appear e.g. on Wikipedia: https://en.wikipedia.org/wiki/Equal_temperament .
The most major novelty here appears to be an attempt to hand-wave some general aesthetic principles for what humans like, and apply these to the brain via some sort of fuzzy "computational approach" (which never, y'know, broaches the point of an actual computer program). A lot of the overarching explanation can be ignored to the benefit of the theory in many cases: for example, it is likely more helpful to a neurobiological understanding of harmony to steal his insight that the minor chord probably sounds "good but off" because it has the right intervals in the wrong order, than to couch it in the author's full explanation with computational assumptions etc.
It's kind of fun to think that we've just discovered some local optimum for enjoyable music and that going in a completely different direction will lead to something both unrecognizable and mind-blowingly awesome. I'm not even remotely convinced that's the case, but it's fun to dream.
> Harmony
The frequency ratio of two or more pitches
> Scale and mode
The set of frequency ratios out of which a given piece of music can be constructed
> The 12-note Western chromatic scale
The modern western chromatic scale is formed out frequency ratios which are powers of the twelfth root of 2, or ~1.059. This is called the "12 note" scale, because 1.059^12 == 2, and our brains are predisposed to find pitches who are multiples of two apart similar. This is because pitch classification in humans (along with many other human senses) measures inbound signal in exponential, rather than linear, terms, and 2:1 is also the simplest ratio by which two pitches can have constructive interference.
As far as why the 12-note scale is the Western scale, there's a fair amount of debate, but most are in agreement that it likely comes from the fact that 12 is a low number with a fair number of integer factors (1, 2, 3, 4, 6). Integer factors translates very directly into constructive wave interference (3:2 has less destructive interference than 101:100). So, one can easily construct many constructive interference ratios out of the (2^^(1/12)) atomic element (e.g. the "major chord", the most common set of three pitches in western music, is (1.059^7):(1.059^4):1 ~= 6:5:4). Each exponent of the twelfth root of two is very close to, respectively: 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 16/9, 15/8
So! Now the only remaining question is just a question of the antropological evidence: do all other cultures also use the twelfth root of two as their simplest harmonic difference? And the answer is very clearly no:
* Indian music uses the twenty second root of two -- the "shruti" https://en.wikipedia.org/wiki/Shruti_(music)
* Indonesian music has many different scales, some based on the 9th root of 2 ( https://en.wikipedia.org/wiki/Pelog ), others based on the 5th root of 2 ( https://en.wikipedia.org/wiki/Slendro which is often paired with a scale based on the 17th root of 2)
* Arabic music uses the twentyfourth root of two ( https://en.wikipedia.org/wiki/Arabic_maqam#Notation although to be fair, this is just the square root of the western twelfth root of two, but this conceit is largely used for notation, while actual performance uses adjustments smaller than the twenty-fourth root of two)
* And plenty of other cultures besides ( https://en.wikipedia.org/wiki/Microtonal_music#Microtonal, https://danielpaulschnee.wordpress.com/2015/05/11/microtonal... etc )
Does this constitute "A large portion of the world (possibly a majority)"? I'd probably say not a majority, but certainly more than 15%, likely at least 25%.
His reference to the major scale as being alternately called "Diatonic" is very confused, as that mode is called "Ionian."
Also, for example, note the naivete of viewing a C Major scale as fundamentally outlined by a piano, while ignoring the interesting tidbit that the notes are named starting with A.
If the piano fundamentally outlines anything, it is the A minor (aeolian) scale, saying it outlines a C Major is no more accurate than saying it outlines a B Locrian.
Meanwhile, there's interesting stuff in there nonetheless.
An interesting phenomenon is that C Ionian harmony can be 'flipped' to A Aeolian by mirroring all the notes around the central D. The C chord becomes A minor, G7 becomes Dm6, F6 becomes Em7. The melody can switch as well; the contour is reversed yet the tune retains its essence.
Do you have any links regarding this?
https://en.wikipedia.org/wiki/Spectral_music
Tristan Murail is a well known composer of spectral music.
http://www.tristanmurail.com/en/outils.html 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/Atonality
Apologies for only bringing Wikipedia links, but they are pretty good launching points for learning more.
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.
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.
I've got a piece in C#m at 87 bpm [0]. I'll play a piano instrument which is being fed into a distortion (the distortion makes the beat frequency much more apparent) and slam an Ab1 and A1 at the same time. That's 55.00hz - 51.91hz [0], which gives a 3.09 hertz beating. Or a period of 323.6ms [0]. So you have two notes close together, which sounds very dissonant, they're bass notes which makes it muddy, and it's so distorted, you can barely tell what the actual notes are. But it swells up and down on the tempo like a rhythmic device.
[0] Anyone who looked up a tempo -> ms chart is going to say "WTF, that's not in time with 87 bpm." Which is correct, but because pianos are stretched tuned (and so is the virtual instrument I use), the numbers I provided aren't exactly true. I never bothered to measure the exact frequencies, but I kept adjusting things until everything sounded right by ear.
Let me explain it for you:
Hypothesis / Theory: The keys on the keyboard are laid out in their particular queer way because of X.
Evidence: (1) the Major Scale, (2) the Standard Chord Dictionary, and (2) the difference between the Major and Minor Triads.
Falsifiability: Do any of the evidence in 1, 2, and 3 fit the theory?
Fitness test: How simple is the theory, as compared to competing theories? How many assumptions (aka "free parameters") are there?
The author explains how competing theories have more assumptions and free parameters that his theory does not require.
This is clearly science. It's just written in a different style than you're accustomed to. Please read and critique the content of the article. If you so firmly believe that it isn't science, then you should be able to easily refute it using science, rather than just superficially (superstitiously) claiming "That's not science! You don't understand!"
Prove it! Critique the content, man!
* the Major Scale,
* the Standard Chord Dictionary, and
* the difference in feeling between the Major and Minor Triads.
• Standard Chord Dictionary. What does that even mean? Please map that onto gregorian chant or even Monteverdi Vespers of 1610.
• As I've indicated elsewhere, a Major 3rd in 13th century France is actually a discord, not a resolution.
If the author had indicated that he was only referring to 19th century European classical music, I'd have been cool with it. But the author isn't even referring to the European musical tradition in general.
I'm not understanding what you're explaining. Feel free to ignore me, or explain it more, but I still don't see any actual science in what you're talking about. I see technical terminology, but not scientific method.
The layout of keys on the keyboard is not a natural phenomenon that needs a scientific theory to explain, that was a (somewhat arbitrary) choice that has been canonized. The layout was decided in past history for known reasons that mix music theory, engineering and human factors, it wasn't something that science ever had a direct say in.
If this paper is science, what precisely does it explain that we didn't already know? Music theory isn't a science, and nobody ever claimed it was. Music theory is an art.
What, exactly, does this sciency sounding theory here demonstrate? I acknowledge that it's a useful framework for understanding intervals for physicists and computer scientists, but I don't see it actually showing why the major scale is major, and how to use that fact to compose music, do you? Does it somehow prove why a minor chord following a major chord sounds good to most people? Does it scientifically prove why a minor chord sounds sad and major happy? Does it prove why Turkish music sounds good to Turkish people and not to Canadians? I don't see anywhere in this document that anything about harmony is proposed and then proved via scientific method. I'm not sure it's possible, or a particularly useful goal either.
This document only covers a very tiny fraction of music theory, so it simply can't be a good replacement for music theory until it's much, much bigger.
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.