Ultimately minor sounds sad because it's been used that way for a long time and it's what we expect. I was listening to Trout Mask Replica and my wife said it sounded like her home town funeral music (I later heard some myself and yeah she was right) - Captain Beefheart doesn't sound sad to me, but it does to her. The funeral music uses major 5 note scale.
And on "But I've Been a Musician All My Life / Studied Music In College and I've Never Heard Any of This Before!" - ratios and how chords derive from that was absolutely part of my education at Berklee. This article is good for the objective parts, but really self-congratulating for the subjective/experiential part of it.
These days I liken it more to the idea of ‘surprise’ in information entropy which denotes an informative signal then to revealing any sort of objective truth.
I've been working with some people building a music model from scratch and it really surprises me how much correlation there is across different features. It's been difficult applying that to general sound effects, because music is highly correlated in ways more general sound isn't.
That's only true if you're expecting a "fully scientific theory of harmony" to mean "a theory that can precisely predict how popular/enjoyable any given piece of music will be." But I don't think that's a reasonable goal, since (as you say) individuals are complex and culture is even more complex.
It's not unlike, say, pain or discomfort, which we can also develop scientific theories for. We can discover how pain works physiologically and psychologically, but our theories are never going to fully explain why individuals or cultures might welcome and even seek out certain types of pain in certain contexts.
I had a similar dream as a freshman in physics, I had learned that the organ of Corti was a spiral-shaped transducer in a little special bone and I dreamed of snail shells and proving that harmonies formed interesting geometric patterns on the darned thing, and how maybe people who seemed chronically tuneless might be shown to have malformed ear bones -- until I finally got to see images of them in a bio textbook and realized that my dreams had to be crushed, this blobby thing, whatever else you say, is not working geometrically.
So a science of how music works physiologically and psychologically, is able to explain why rock and later certain forms of ambient and trance "felt good" to folks -- it took them right back into the womb: the distortion on the guitars felt like the swishing amniotic fluid, the four-on-the-floor sounded like a heartbeat, the indecipherable high-pitched vocals sounded like Mama's voice peeking through the noise. But beyond that, it's our experience with twanging strings and air blowing through wind instruments and the like, which informs what sounds familiar to our grown ears. And the proof is how robotic and alien pure sine waves sound: this is a part of your organ of Corti complaining, "hey, when these hairs are tickled usually those ones also tickle -- but they're just standing flat, what the hell is going on."
Lots of everyday things tickle the organ of Corti in patterns that resemble a major chord, so that sounds familiar to it. When you play a minor chord you deprive it of stimulation to some of those hairs but stimulate the ones a little more outward, and the organ says "there's something off, this thing is lower than I'd expect" and it's some sociology that you can do to say "when people are hurt they can communicate this most effectively to other pack animals through lower more mournful cries" and so there are semi-biological semi-cultural expectations that govern "lower = sadder" especially at low tempos. But you can do the same in reverse, play a sus4 chord, and it sounds weirdly brighter and you feedback through those semi-biological expectations in reverse, weird but with more energy than expected. But you can also just play minor scales uptempo and then they also change, the minor scale at a higher tempo has somehow more energy and less sadness than the major scale -- indeed rock music is full of minor pentatonic licks that nobody would ever describe as sad or painful or discomforting.
There's an interesting idea though that there could be a deeper why specific sounds and their combinations are the things we create names for, but that's an intersection of cognition/physics/culture that goes beyond elementary music theory.
Consonance is somewhat frequency-dependent. For more, Google Critical Band and ERB.
The happy/sad idea is pretty much a high-school oversimplification. It's true for beginners, not at all true beyond that.\
It's quite rare to find music with straight major and/or minor triads with no other colours.
https://www.youtube.com/watch?v=tCsl6ZcY9ag
This is a more recent paper (2019) that I think is better constructed and more aware of the in-field work than TFA:
Anybody interested in this stuff would be better off with something like Tuning Timbre Spectrum Scale (https://sethares.engr.wisc.edu/ttss.html) or Music a Mathematical Offering (https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...)
> Throughout this derivation of different chords, you will note that a gradual progression or degradation from high-theme/low-complexity (Major Triad, Harmonic Series chords) to low-theme/high-complexity (Minor and Ambiguous chords). This progression is suggested by our measure of interestingness from Section 2.4 "Interestingness: Just Enough Complexity". That is, as we progress, more and more of the theme of the Harmonic Series is lost and more and more complexity is introduced. Notice that this progression seems to mirror that of musical sophistication as well: musically untrained listeners like Major chords while more musically trained listeners are more tolerant to loss of theme and more interested in complexity. (I met a signal processing engineer who had played piano for something like 18 years and who simply did not like Major chords at all.) Other fields seem to progress similarly: white wine is preferred by new wine drinkers, whereas more "complex" red wines are an acquired taste.
My impression is that most sounds have their effect on us due to psychological association with familiar sources of those sounds, and that melody and harmony are fundamentally more subjective - they depend on looser associations with motion, mood, the human voice, the changes and developments of sounds in our environment.
It also refers to the “first” scientific experiment: an empirical test of the generalization of a mathematical model of harmony — from ratios of string lengths to ratios of chime thickness (as recorded by Aristotle’s student Aristoxenus)
Not that there’s anything wrong with that…except when it comes to science as a basis for an argument from authority.
Like all music, people like what they like.
You don’t get the perfect fourth until you go all the way around the circle of fifths.
You cannot stack perfect fifths and get a major scale.
My general issue with things like these is the simple fact, that as a lifelong musician I find the "less worse" harmonic combinations (to quote the abstract) often very boring. Aside from great composers like Bach et al I find the harmonic relationship of the notes played one of the least interesting aspects of the music, and expression, timbre, rhythm, phrasing much more important and noteworthy. A set of great musicians can play a single note for minutes and get it to sound amazing, this has always fascinated me more.
Music theory IMO has historically a too strong focus on the harmony (or the lack thereof) between notes. Not that it isn't important, but with some texts you get the feeling it wouldn't matter to the authors whether the piece was heard expressively played on a grand piano or cut together from equal leveled sine waves.
In my experience harmonies are greatly influenced by the relative levels of the notes and the overtone content within each note, to a degree you can make a supposed "harmonic" chord sound bad and a supposed disharmonic one sound good.
And dissonance has cultural and physiological components...
And other traditions focus on rhythm over harmony...
That said this looks like a good introduction.
Also, other traditions focus on melody over harmony (e.g. Carnatic and Hindustani), although they have to consider harmony as a by-product of polyphonic music (i.e. more than 1 instrument).
You can have a whole set developing motifs, then multiple minutes of a single note being played in the middle, and somehow that sounds awesome (if you’re into it)
Maybe go on Youtube and listen to music that you might not be familiar with?
Cage, Schaffer, Stockhousen, Boulez are some composers in the tradition of European classical music.
If you go outside that tradition, there’s even more. Endlessly more.
All of the many parts of western music serve the harmonic progression. This is because human emotion attaches itself most strongly to harmonic progression, and music is the art of manipulating human emotion through sound.
>A set of great musicians can play a single note for minutes and get it to sound amazing, this has always fascinated me more.
Someone already asked, but give me an example.
I suppose that is literally true but I think of timbre (especially after reading Sethares who I mentioned earlier) as telling me about the notes that are brought along for the ride but aren't shown on the sheet music. It's well known that a distorted powerchord introduces a major 3rd (and not the 12TET major third) as well as a phantom or missing bass note and other higher notes which may or may not be perceptible in a given piece. Quite a bit different from what two flutes playing a root and fifth will give you.
The cuties with cooties
Corporate duties and African rubies
It's the doobies and boobies
That see K's like Louie
Shake out the loogies
And K-shape the Louis
Here's a statistical mechanics paper that I don't quite understand yet, but seems more aligned with the physics of harmony.
https://www.science.org/doi/10.1126/sciadv.aav8490
Harmony isn't just the chords made, though. It's about the progression between chords,too.