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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.
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.
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.
Does metal sound "sad"? Opinions differ. :)
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.
So there must be more to it.
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.
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.
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.
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.
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.
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.
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.
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.
But hopefully I'll get around to reading this at some point. It's one of my favorite topics. I wrote up my own attempt to explain the Western music system here: https://fakestoryofmusic.com
I've also been working on something smaller that focuses on major/minor tonality, specifically. But it's further from being in a place where I want to share it.
It's a challenging read, but extremely thorough and enlightening. Tymoczko wrote a follow up that extends and reformulates his theories, but I haven't gotten through it yet.
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:
https://pmc.ncbi.nlm.nih.gov/articles/PMC7006947/
Without just temperament, we would never have had "The Well Tempered Clavier", Bobby Daren's "Mac The knife", and basically all of western music from the baroque period on.
> 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.
Anyone with a decent understanding of music and acoustics can tell it's silly from the title and abstract alone.
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...)
My biggest overall critique is that you start with the assumption that everything is an algorithm, that the brain works like a computer, and the world can be derived from that.
"To the intuition of anyone who has seen hardware designed it seems very likely that the brain is halving/doubling frequencies by many different powers of two in parallel and then running all of the results through the frequency recognizer at once. If any one matches, the harmonic has been found. If this were so, then tones (and notes) that differ from each other by a factor of two would sound very much alike. "
I don't see why I should care about a hardware designer's opinion on the matter any more than a clockmaker's or a dog trainer's.
"1.5.1 Timbre: Systematic Distortions from the Ideal Harmonic Series" I don't believe you ever mention how you want the intensities in your "ideal harmonic series" to be distribute, so why does changing the relative intensities to get timbre matter? If I have an ideal harmonic series with peaks at 220Hz, 440Hz, 880Hz, etc, what should its intensities be? Timbre also has to take into account the full ADSR envelope.
"That is, two notes (series-es of overtones) made by the same (kind of) instrument will be distorted from the ideal Harmonic Series in the same (or similar) way. This must be the case in order for an instrument or instrument kind to have a uniform, recognizable timbre"
If you get a guitar in standard tuning and play, say, the 5th fret on the 6th string it sounds different than the open 5th string, despite them both being the same 'A'.
"But The Nasca People Of Peru Use A Linear, Not A Logarithmic, Scale!" "Who knows what is going on with the linear scales of the Nasca. I suspect the following: Linear-scale flutes are easy to make ... This culture was small and isolated and so no one ever noticed harmony"
I checked the cited article (Joerg Haeberli (1979). Twelve Nasca Panpipes: A Study. Ethnomusicology, 23(1), 57–74. doi:10.2307/851338 ). Among the things I learned: (1) At least some of the pipes were ceramic (picture here: https://artmuseum.princeton.edu/art/collections/objects/1374...) (and the Brooklyn Museum claims that "hundreds" have been found: https://www.brooklynmuseum.org/objects/51700), this is not consistent with a culture that is just figuring things out (2) "Intervals close to the fifth, major third, minor third, and major second occur".
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.
And what about the discovery that happens when you make your own music? If this was replaced by the perfect scientific theory and a computer program cranking out perfect songs, our incentive for being creative would be greatly reduced.
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).
Like Western electronic music written after 1960, for example. :)
(And electronic music is, like, basically all we have today.)
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.
Harmony is derived from composing music with multiple melodic parts. This is most obvious with counterpoint, but even pop/rock music can be seen this way. The essence of pop/rock is a melody and bass line as the two primary parts, and the rest of the instrumentation often plays harmonies that imply inner voices.
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.
I have one request: if you are going to comment on the paper, please actually read it first. Here is a little test to check that you read it: did you notice the points below?
(1) This is a paper in the field of Computer Science. Having studied music all of your life, even at Berklee, does not qualify you in Computer Science, so be open to learning what Computer Science is. In science we have a practice of making the simplest model we can from which emerge the observed measurements. Hence the remark by Feynman quoted near the top of the paper on how to know when you are right:
"When you get it right, it is obvious that it is right -- at least if you have any experience -- because usually what happens is that more comes out than goes in. Your guess is, in fact, that something is very simple. If you cannot see immediately that it is wrong, and it is simpler than it was before, then it is right. The inexperienced, and crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought."
Many of you seem to like very complex explanations of harmony. Note that Feynman is saying that is not an indication of a theory being right.
(2) This problem has not really been solved before. Even someone like Daniel Levitin was convinced (the last time I spoke to him) that Helmholtz had the correct theory of harmony. However, as I point out in the paper:
* The American Acoustical Society has a collection of experiments, one of which they say (not just me), proves Helmholtz's theory is wrong.
* If Helmholtz is right, playing multiple notes always sounds either a little worse or a lot worse, but never better, and so we would never play two notes at the same time at all; harmony would not exist and there would be nothing to explain.
(3) There is strong evidence for the absolute nature of auditory processing that is not only cross-cultural, but cross-species. In the paper, there is a quotation from Daniel Levitin's book "This is your Brain on Music", where he 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 paper 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.
(4) The explanation of the experience of the minor triad in "Harmony Explained" requires the concept of an inconsistency arising from a redundant recognizer algorithm. Being a musician does not make you an expert in recognizer algorithms and their emergent artifacts, so read what that is before you comment.
The theory of the minor goes like this: two redundant recognizers exist in the brain. When hearing a minor triad:
* one recognizer fires, that of the conjunction of three pairwise intervals of tones,
* whereas another recognizer does not fire, that of 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.
If you object to my assertion that minor triad is well-described as "I recognize it, but something is wrong", try reading the explanation in the paper of the same phenomenon in visual perception called cubism. Say what you will about the minor triad, when you look at Picasso's "Head of Woman" (provided in the paper), does it not disturb you? Would not not describe it as "I recognize it, but something is wrong"? Does your objection to the analysis of the minor still stand in the context of visual art?