[klik99]

I read through a lot of this article and it does a good job explaining the ratios and math behind harmonics and how that makes chords, but ideas like lower ratios are more pleasant and minor chords feel like something is missing (from the article "I do not hear the Harmonic Series itself -- something is missing") is just wrong - if it was right, then the happiest music would be entirely octaves. Though it's built on harmonics and overtones which can be explained objectively, you cannot make a fully scientific theory of harmony since cultural expectations factor in just as much (and maybe even more) than the expectations around harmonics. Music is pleasurable when it mostly meets expectations but surprises you as well, IE it sits just outside of what we expect. It then becomes part of what you expect in the future and music evolves.

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.

[foobarian]

I find the major/minor thing so fascinating. I remember it having the "happy"/"sad" vibes from my earliest memories and have a really hard time with the idea that it could be cultural. But if it's not cultural, then why? Also is the fact that major 9ths have a beach/island vibe cultural due to Brazilian jazz? :-)

[kansface]

> have a really hard time with the idea that it could be cultural

I played in a gamelan ensemble in college. The music was completely foreign. A piece that sounded like a funeral procession was played at weddings. I have a hard time believing the arrangement of music is not cultural - or, at least partially culturally bound.

[klik99]

Yeah, that's really getting to the heart of why the idea of a totally objective theory of music seems legit. Major/minor doesn't exist in a vacuum, there's a lot of other signifiers in the music that are highly correlated. It's not just the major triad, it's the energy of the beat, playing, singing, the bright instruments. If you were a 2 year old and just heard a major chord played on a piano, then a minor chord, then you probably wouldn't get "happy" or "sad" from it. Maybe by 3 or 4 you've already picked up the correlation between "happy music" and "major triad". You pick this stuff up really quick and it's part of your core memories/mental model, so it can feel inherent. It's like the fish that doesn't know what water is.

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.

[rerdavies]

Silly theory for why minor sounds sad: Say "ah", like you've just discovered something interesting. Now say "ah" like you've been told something sad. Notice the pitch difference? And notice how both pitches are about a major third and minor third above normal speaking pitch. Whether that's hard-wired or cultural, I couldn't say. But it would certainly be an interesting thing to research and compare across cultures and musical traditions.

[telotortium]

Is "Take Five" sad-sounding even though it's written in a minor key? Maybe it sounds somewhat "cooler", not as bright as a major key piece of the same tempo and energy would be, but it doesn't sound sad.

[otabdeveloper4]

Metal music is mostly minor.

Does metal sound "sad"? Opinions differ. :)

[calf]

I play piano. It's not just cultural, it is partly like that checkerboard lighting illusion. What is objectively one shade, can in a different context, seem like the opposite shade. Major and minor keys in classical music can sometimes exhibit this property.

[ScotterC]

Right on. In my experience across different art fields, I’d say the only generalizable facet of ‘good’ art/music/etc is the “it sits just outside of what we expect”.

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.

[klik99]

You might like the book Emotion and Meaning in Music - it starts from some outdated psychological ideas (that emotions are only intensity and that we assign positive/negative valence post-hoc) but ties that to early information theory and makes a really compelling theory of music that's all about the interplay between expectation and surprise, across both the physical harmonic ratio stuff this paper talks about and the cultural associations too.

[rebolek]

While I agree that "good" art "sits just outside of what we expect", I must play devil's advocate here and say that the uncanny valley of CGI/AI/... also "sits just outside of what we expect".

So there must be more to it.

[BoingBoomTschak]

Eh, turning that uncanny valley to 11 can be an artform in itself: https://www.youtube.com/watch?v=TGIvO4eh190

[rebolek]

By human? I don't doubt that.

[Affric]

Yep, I have come to believe that as complex adaptive systems made of complex adaptive systems the part of us that experience music do so through being able to predict new information.

If there is no ability to predict it’s random and just noise.

If there is no uncertainty and it’s just purely repetitive then there’s also no new information and it loses the music (see what happens with overplayed pre-recorded songs).

The sweet spot is when we can to some degree predict what’s coming and thus understand it to be information while not being sure of what’s coming so we get the reward of encoding it.

I think this works for pretty much all genres and contexts. Even listening to techno in a dark warehouse while off ones face: the altered state makes most things seem novel no matter how repetitive and your mind doesn’t tune the information out.

But that’s IMO why octave harmonies largely don’t work: the mind perceives no information in the pure octave, and so little joy is gained from it.

[mike_hock]

I don't buy that minor being "sad" is all nurture and no nature. No matter what tempo or rhythm you put on it or what instruments you use to play it, it may not sound sad, it may sound dramatic and powerful instead, but it never sounds upbeat and happy the way major does (or at least can).

[prewett]

Listening to "Fiddler on the Roof" and klezmer music unsettled to me the idea that major is happier than minor. I still think minor tends to sound "sad", but those wedding songs and the Russian dance in FotR are clearly upbeat and celebratory. (Literally upbeat; the Russian dance is more upward-beat, as it gets faster and faster!)

[qlte]

Yes, the klezmer “default” is minor and upbeat.

It’s my favorite example for the “minor != universally sad across cultures” thing since it’s not so “out there” for the Western ear that people would struggle to even hear minor/major/“music” in it at all.

[qlte]

I’m not seeing how that’s inconsistent with it being culturally derived?

Your brain is still just pattern matching “minor = sad” based on thousands of hours of examples from the western canon consumed throughout your life regardless of how you dress it up with rhythmic variations.

[tshaddox]

> you cannot make a fully scientific theory of harmony since cultural expectations factor in just as much (and maybe even more) than the expectations around harmonics.

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.

[crdrost]

It's worse than that though -- the things that you are born enjoying, are loud oceanic white-noises and a deep thumping backbeat with occasional muddied high-pitched vocals.

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.

[klik99]

I meant "fully scientific theory of harmony" in the same way your second paragraph does, not as predictor of popularity but predictor of what kind of effect it raises in the listener. A big part of how music effects the listener is sociology, which sure is scientific, but I tried to use scientific in the way the article uses the term, IE from objective first principles and not culturally specific/learned response.

[nkrisc]

I think you could make a scientific theory of harmony (and perhaps music or even sound more generally) through the physiological lens of human perception. Straying a bit from music, but some sounds are fairly universally unpleasant, so there may be some objective basis for some sounds, and harmonies, being more “pleasurable” than others.

[telesilla]

>happiest music would be entirely octaves

While chords certainly do have a perception of emotion, it's resolution and chord progression that seals the deal whether it's perceived as joyful or sad or otherwise.

[dswilkerson]

> if it was right, then the happiest music would be entirely octaves

Not necessarily: if you read the essay, one assumption is that the brain is halving and doubling frequencies to fit them all into one frequency magnitude, an obvious optimization for reducing circuitry. If so, then an octave is too simple to fire the recognizer for a particular harmonic series; instead we need an input that places it relative to the other tones even after the halving/doubling.

Consider the fact that we name both middle C and high C as "C" because, even though they are different notes, they sound so similar that we literally deliberately confuse them notationally as they play the same role in harmony: one can be used to replace the other.

> Music is pleasurable when it mostly meets expectations but surprises you as well, IE it sits just outside of what we expect.

Ok, but where do the expectations come from? Your assertion that it is all culturally relative ("nurture") and none from the structure of the most efficient algorithm for recognizing the harmonic series ("nature") has no basis in fact; you just assert it without proof.

In contrast, there is strong evidence for the absolute nature of auditory processing. In the essay, there is a quotation from Daniel Levitin's book "This is your Brain on Music" where it discusses an experiment he witnessed in graduate school where music was played through wiring directly into the brain of an owl. The music was played into the brain with the root removed; when coming out of the brain of the owl, brain had restored the root (see the essay for details).

That means that virtual pitch (1) is created by the structure of the brain, not by a cultural expectation, and (2) further, that it is created by the brain of, not just a human, but of an owl! This is a very strong argument for the assertion that the processing of sound and the artifacts thereof are quite universal, not just across cultures, but across species.

> ratios and how chords derive from that was absolutely part of my education at Berklee

So at Berklee they teach recognizer algorithms and artifacts thereof? I did not know that Berklee is that strong in computer science. The explanation of the experience of the minor triad in "Harmony Explained" requires the concept of an inconsistency arising from a redundant recognizer algorithm.

In this case, one recognizer fires, that of the conjunction of three pairwise intervals of tones, whereas another recognizer does not fire, that if the triple of tones in order. This combination of firings is inconsistent because it is not possible for it to occur by playing any single normal harmonic series on, say, a flute. To generate it, one must play multiple notes and then use the effect of the recognizer of intervals pairing up tones from across the notes.

That is, this is a new kind of auditory perception that can be created as an artifact of the auditory recognizer algorithms of the brain, but cannot be heard otherwise. This is harmony.

If this this was taught to you at Berklee, please tell me which course that was and what the textbook is so I can look it up in the course syllabus and table of contents.

[BigTTYGothGF]

> one assumption is that the brain is halving and doubling frequencies to fit them all into one frequency magnitude

You've got an awful lot of assumptions in there that I don't think are at all supported, and this is one. It's also contradicted by 3.5.2 in the article: if the brain were actually doing this, then you could, say, replace the 9th by the 2nd.

> Ok, but where do the expectations come from? Your assertion that it is all culturally relative ("nurture") and none from the structure of the most efficient algorithm for recognizing the harmonic series ("nature") has no basis in fact; you just assert it without proof.

I interpreted "mostly meets expectations but surprises you" as referring to things like chord progressions creating tension and resolving it, for which you don't need major triads. (and of which there's no discussion in the article).

> In contrast, there is strong evidence for the absolute nature of auditory processing

I'm perfectly happy to grant that an owl experienced the sensation of a pitch at a frequency that was not actually present, but there's something missing here that's also totally missing from the article: the role of the cochlea. The brain doesn't experience sounds, i.e. the pressure waves in the air, the brain experiences electrical signals transmitted to it that, tinnitus aside, come from excitement of the cochlea by those pressure waves. How do we know that there isn't some kind of mechanical resonance somewhere in the ear that fills in the missing root? And if we know there isn't in the human ear, how do we know the same for the owl?

> The explanation of the experience of the minor triad in "Harmony Explained" requires the concept of an inconsistency arising from a redundant recognizer algorithm.

Once upon a time the explanation of the propagation of light required the concept of a luminiferous ether.