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Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

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Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#41

Post by klik99 »

tshaddox wrote: post #38
klik99 wrote: post #23

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…

> 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…

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.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#42

Post by klik99 »

foobarian wrote: post #34
klik99 wrote: post #23

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…

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? :-)

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.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#43

Post by IAmGraydon »

klaff wrote: post #37
IAmGraydon wrote: post #24

Earlier quoted context omitted.

Also a lifelong musician here, and I think you're completely wrong about harmony. Western music (assuming that's what we're talking about here) IS directly derived from harmonic progression. It is truly the core of the music. The underlying chords are the obvious harmonic progression. Melody is just an expression of underlying harmonic structure. Rhythm is meant to emphasize the changes and movement of harmonic struc…

>Timbre itself is meaningless without a note to carry it 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…

That makes some sense, but if you look at a spectrum analysis of any signal that isn't a sine wave (and specially for highly clipped signals like you mention here), they consist of many tens or hundreds of even and odd harmonics, which is what you're referring to here when you say a root/fifth chord under distortion produces a major third phantom note. In truth, it creates many, many phantom notes, and pretty much any instrument, even a flute, does as well. Yes, that's the timbre - the relationship of the harmonics that result from a waveform. That's the very idea behind additive synthesis, where the harmonic nodes are individually created from a series of sine waves. So I guess it could be said that a single non-sine note would produce a harmony (multiple notes with a harmonic relationship), but this is not the same thing as a harmonic progression, where that relationship would change.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#44

Post by crawfordcomeaux »

I stopped automatically judging things 10 years ago and all of a sudden could enjoy listening to everything. Music theory based on pleasure without accounting for this self-manipulation we're brought up to do isn't solid at all. And expectation making is another thing I stopped doing. I now make music that tends to defy expectations and tonality.

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.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#45

Post by klik99 »

ScotterC wrote: post #32
klik99 wrote: post #23

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…

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.

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.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#46

Post by crdrost »

tshaddox wrote: post #38
klik99 wrote: post #23

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…

> 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…

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.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#47

Post by pitchlatte »

TheOtherHobbes wrote: post #31

There are much better overviews of this from Sethares and Tymoczko. 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.

to add, all of this doesn’t account for music outside of that which is a direct descendant of 15th and 16th century contrapuntal music, aka the sort defined by exactly the medieval texts it pokes fun at. any fusions are outside scope, let alone entire non european cultures of music. incredibly ethnocentric and blinkered premise.

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#48

Post by BigTTYGothGF »

I agree that there's a lot to be desired in the pedagogy of music theory, but this is pretty bad. There are so many little things wrong with it that if I started trying to address them all I'd be here forever.

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...)

Re: Harmony Explained: Progress Towards a Scientific Theory of Music (2012)

#49

Post by duped »

simonreiff wrote: post #26

I studied harmony and music analysis many years ago as a piano performance major in school. One thing I will say is that harmony really is not an abstract set of symbols on a page representing chords, but rather is a taxonomy of common specific sequences of simultaneously sounding pitches, abstracting away instruments or larger structural considerations and providing a dictionary that defines the most common patterns…

I think the word "taxonomy" is a really good way to look at music theory. Really, the study is about giving names and notation to things in music so we can write and talk about it at all.

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.

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