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

105 points by surprisetalk 3mo ago

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the__alchemist 3mo ago
Check out the 3Blue1Brown video on this topic as well! It goes more in depth on music theory than any music-community one I've seen. (Which tend to be presented as "Here are the rules"; Grant, like this article, goes into the "why"; a step below. With great visuals, of course!
- thecommakozzi 3mo ago
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- dswilkerson 3mo ago
  Please provide a link.
  - the__alchemist 3mo ago
    Oops! It was Minute Physics: https://www.youtube.com/watch?v=tCsl6ZcY9ag https://www.youtube.com/watch?v=tCsl6ZcY9ag
atoav 3mo ago
A good overview on the topic. 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.
- antonyt 3mo ago
  Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
  - dgellow 3mo ago
    Half joking, but Berlin techno :) 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)
    - IAmGraydon 3mo ago
      A long hold of one note doesn't mean there isn't harmonic progression. It just means the progression is slow in that part of the song. It's often done to create a massive contrast that occurs when the progression finally...progresses. In electronic music, this often comes as the drop or some similar kind of break.
      - otabdeveloper4 3mo ago
        No, in electronic music harmonic progressions are done by manipulating timbre. Try it yourself - play one note on repeat and start twirling the cutoff knob.
    - nwatson 3mo ago
      Not quite one note, but "Open Eye Signal" (2023 remaster) by Jon Hopkins has wide spectrum background and heavy rhythms, but once the song gets going the main instrument moves between fifth -> seventh-flat -> sixth -> fifth on repeat, and that's the melody for the song. And yet, to me, it's captivating.
      - dgellow 3mo ago
        Thanks for the suggestion, that’s a really neat discovery! I will try to integrate that in my own music
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okzgn 3mo ago
The logic that something sounds worse simply by combining dissonant notes is questionable, because music constantly combines elements—notes, chords, even different rhythms—without that necessarily implying displeasure for the listener. Convincing.
- pier25 3mo ago
  "Worse" is definitely a subjective appreciation influenced by culture and personal taste.
  - okzgn 3mo ago
    That's why it's questionable, because it's subjective. It would be factual to find the keys to determine what sounds "worse" across the majority of subjective opinions, independent of culture and personal taste.
    - pier25 3mo ago
      Yeah. If anyone doubts this go listen to some gamelan music and see if they can make any sense of it (harmonically speaking). https://www.youtube.com/watch?v=nGCSrC8RN6c https://www.youtube.com/watch?v=nGCSrC8RN6c
  - dhosek 3mo ago
    In the 00s, I sang in the Holy Name Cathedral choir and we did a lot of 20th/21st century choral works with harmonies that strayed very far from the classical tonal vocabulary to the point where when I was doing my own composition work, I realized that I didn’t hear dissonance any more.
claiir 3mo ago
Nice. But, is there a less “conversationally” written piece on the subject? In any event, this stuck with me: > Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases
dr_dshiv 3mo ago
Harmony has always been a principle that refers to more than music, let alone chords. Here is a recent review: https://www.sciencedirect.com/science/article/pii/S240587262200003X https://www.sciencedirect.com/science/article/pii/S240587262... 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)
skew-aberration 3mo ago
I have to highly recommend the book 'Fundamentals of Musical Acoustics' for mathematical/physical explanations of sound and music. Bells having multiple resonant modes, tuning kettle drums, how string materials and plucking methods changes harmonic profiles, why having lots of high frequency harmonics sounds bright (and electric guitars, pianos optimise for this), why sounds without high frequency harmonics sound hollow (nylon strings), virtual pitch, acoustics of rooms, etc. 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.
- schroffl 3mo ago
  Are you talking about "Fundamentals of Musical Acoustics" by Arthur H. Benade? I'm interested in buying the book, but I'm not sure which one you mean. Do you perhaps even have the ISBN?
  - skew-aberration 3mo ago
    That's the one. I read the 2nd edition on kindle. There is only one short chapter on harmony but discussion of tone, intervals, etc is comprehensive.
    - schroffl 3mo ago
      Alright, thanks a lot :)
brudgers 3mo ago
The slight of hand in standard Western European music theory is that stacking 5ths gives you Lydian and its tritone as the foundational seven pitch scale. Major/Ionian is the fourth mode of this scale. 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.
- dhosek 3mo ago
  For that matter, the first 5 stacked fifths gives you the standard pentatonic scale. Extending by a fifth on either end and you get the most common accidentals in Western music (if your first seven give C major you’ll get F# and B♭). I think (but I’m not sure) that some of the non-Western microtonal scales extend the tonality by not ignoring the Pythagorean comma when you’ve done the 12th fifth, but by continuing to stack fifths for more harmonies.
  - brudgers 3mo ago
    From C the first six stacked fifths give C Lydian, not C major. (You get an F#, the 5th of B as the seventh pitch, not F the 5th of Bb). 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.
    - dhosek 3mo ago
      I was being sloppy and should have said diatonic scale.
      - brudgers 3mo ago
        Sloppiness is why music theory is not scientific. You can’t get to a scientific rationalization of the primacy of the major scale without it.
        acjohnson55 3mo ago
PaulDavisThe1st 3mo ago
I personally consider this to be a better intro, albeit in video form: https://www.youtube.com/watch?v=tCsl6ZcY9ag 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/ https://pmc.ncbi.nlm.nih.gov/articles/PMC7006947/
- acjohnson55 3mo ago
  Yes, not having had the time to read TFA or the paper you shared yet, it immediately stands out to me that the bibliography of the latter paper is far more comprehensive.
bobson_dugnutt5 3mo ago
I don't find this convincing at all. The actual interesting attempt at scientific theory of harmony in this could be distilled to a couple of lines, yet the author rambles endlessly in ways that don't add to the piece at all. I already knew his additions from traditional music theory already, so I can't really see what the purpose of this is.
- dswilkerson 3mo ago
  If this essay can be distilled into a couple of lines, please do that.
montebicyclelo 3mo ago
I was wondering whether this might have an explanation for why I don't really like major music, preferring minor / modal / non-functional harmony... it does: > 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.
- breezybottom 3mo ago
  Consider that you're not actually hearing major and minor intervals, you're hearing approximations of them due to 12TET.
  - analog31 3mo ago
    Depends on the instrument. Temperament is mostly applicable to keyboard and some electronic instruments.
klik99 3mo ago
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.
- ScotterC 3mo ago
  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 3mo ago
    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.
simonreiff 3mo ago
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. Here's an example: Perhaps you're familiar with the idea of major and minor, but you might be unfamiliar with a Picardy third, where a composition is in a minor ("sad") key throughout but ends in that same pitch but on a major ("happy") chord. J.S. Bach used Picardy thirds regularly to end his compositions, but the Picardy third became rarer after Bach's death. Still, it's a beautiful and striking harmonic progression that continues to appear now and then. And now you know EXACTLY why that 1967 song by the Turtles, "Happy Together", has that really nice and memorable ending; that's a modern pop example of a Picardy third. Again, harmony is not abstract; it's the names musicians have given for specific sequential combinations, many of which have been named centuries ago. It's not about nicer or worse; sounds are sounds, but some are combined more often than others and those combined most frequently have well-known names that can be used to explain concisely the "harmonic" aspect of a piece of music.
- duped 3mo ago
  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.
- bollu 3mo ago
  where would I learn a taxonomy of such motifs? I trained for classical piano as a kid, and I'm slowly trying to learn jazz piano as I ease back into it! I'd love to learn more about these types of harmonic ideas and motifs as I get back to playing
  - simonreiff 3mo ago
toolslive 3mo ago
I only skimmed the article. There's a lot of good stuff (debunking a lot of classical harmony) but they miss some important things too. There's nothing about repetition. Repetition legitimizes. Our brain is really good at pattern recognition, and as soon as it can predict something you're more than half way there to make it sound good. There's plenty of chromaticism that works because the brain "gets" the sense of direction.
TheOtherHobbes 3mo ago
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.
- pitchlatte 3mo ago
  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.
- calf 3mo ago
  Are there any readings would you recommend to read if I play classical piano, and especially for Romantic and post-Romantic music ranging from Chopin/Liszt to Debussy/Ravel?
  - acjohnson55 3mo ago
    If you want to go way deep, check out Tymoczko's first book: https://dmitri.mycpanel.princeton.edu/geometry-of-music.html https://dmitri.mycpanel.princeton.edu/geometry-of-music.html 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.
- acjohnson55 3mo ago
  I also jumped straight to the bibliography to look for those two. Not seeing any reference to their work is disappointing and makes me a little pessimistic that digesting the entire piece will be worthwhile, as a scientific piece. He references Helmholtz, but his theories have been surpassed for more than a century. 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 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.
cyanclouds 3mo ago
It's all about big booties 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
a-dub 3mo ago
i tend to think of this stuff in terms of top down information theoretic approaches to composition and bottom up psychophysics of auditory perception. there is some cool work out there where physicists attempt to compute information content of western classical music and then there is all the fun stuff around the biophysics of the cochlea, nonlinear frequency discrimination and frequency selectivity of the ear.
crawfordcomeaux 3mo ago
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 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.
BigTTYGothGF 3mo ago
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 https://sethares.engr.wisc.edu/ttss.html) or Music a Mathematical Offering (https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...)
- dswilkerson 3mo ago
  Responses that say "If I started listing criticisms I would never finish" usually have none. Name 3.
  - BigTTYGothGF 3mo ago
    I gave a couple in my other reply, the most damning (imo) was that you completely ignore the cochlea. 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/137461 https://artmuseum.princeton.edu/art/collections/objects/1374...) (and the Brooklyn Museum claims that "hundreds" have been found: https://www.brooklynmuseum.org/objects/51700 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".
nttylock 3mo ago
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Rochus 3mo ago
The central insight (consonance involves both physical properties of sound and active perceptual pattern recognition) is interesting, but as a musician I see the following issue: the harmonic series can motivate certain local sonorities, but it cannot generate the operative grammar of common-practice Western harmony; the paper recognizes the tuning problem, yet treats it as a regrettable engineering compromise, when it is actually constitutive of the harmonic system it claims to explain.
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iainctduncan 3mo ago
You know those HN posts where someone who barely knows how to program decides to tell you why language X is terribly designed? This is that. Anyone with a decent understanding of music and acoustics can tell it's silly from the title and abstract alone.
- dswilkerson 3mo ago
  Does Daniel Levitin, author of "This is your brain on music", count as someone with "a decent understanding of music and acoustics" ? He thinks that Helmholtz explained harmony (he told me personally). However, as the essay points out, (1) The American Acoustical Society collection has an experiment stretching frequencies from 2.0 to 2.1 that they conclude shows that Helmholtz was wrong, and (2) if Helmholtz was right, there would be not harmony at all, as the essay points out. So even someone like Levitin is wrong.
MetaWhirledPeas 3mo ago
I don't think I want a scientific theory of music. That would take the fun out of it. I like music that matches my tastes while still managing to surprise me. What else do I need to know about music? 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.
- dswilkerson 3mo ago
  This is like saying we should not study physics because if we did then all art could be automatically generated.
  - MetaWhirledPeas 3mo ago
    Are you saying demystifying music is as important as understanding physics?
- Nekorosu 3mo ago
  No worries. This one is based on so many untested assumptions that you can easily ignore it.
Nekorosu 3mo ago
Calling this a scientific theory seems premature. It is mostly a speculative model built on untested assumptions about cognition, with no empirical validation of its central claims.
dswilkerson 3mo ago
This seems to be the 9th time that my paper on harmony has been on Hacker News. I wonder if it has been on HN more than any other paper on arxiv: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&query=%22Harmony%20Explained%22%20Scientific&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... 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?
vikramkr 3mo ago
Awfully dismissive of non western tonal harmonic systems for a universal theory of music? The whole idea that musical traditions that use less harmonic structures just haven't unlocked all the structures available is kind of absurd - those musical traditions have been developing for the same amount of time - and there's a pretty huge blind spot for other traditions. The whole microtones just being ornamentations - no that's absolutely not the case. Trying to ignore/hand wave away all the counterexamples and force them into your system is how you get epicycles. If you're gonna do a universal theory of music it would be a good idea to engage deeply with more than one system. As a universal theory of harmonica maybe that's fine but it's sloppy and motivated reasoning
- vikramkr 3mo ago
  More directly the stuff about ranking different cultures on a scale of musical sophistication that ends in western harmonic music and dismissing obvious counterexamples as cultures that just haven't gotten there yet or just use other feature as ornamentation or just happened to not stumble on things because they were at the lowest level of musical sophistication is almost comically ethnocentric. Its an easy hammer to reach for when your counterarguments are not European (though in this case you're having to ignore an awful lot of European music and the huge influence of Greek music on the middle East) but yeesh
danbmil99 3mo ago
I think the most fascinating thing about music (from a mathematical/scientific perspective) is the fact that the principal harmonics of equal temperament are so close to the mathematical ideals. Fourths and fifths are so close trained musicians typically cannot hear the difference. Major thirds are farther from the ideal but still are less than 1% off. That can be heard by the trained ear, but in the real world there are chorus effects (multiple voices/instruments at nominal but slightly varied pitch), vibrato, reverb etc. such that in most cases a just major 3rd sounds fine. 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.

105 points by surprisetalk 3mo ago

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the__alchemist 3mo ago

Check out the 3Blue1Brown video on this topic as well! It goes more in depth on music theory than any music-community one I've seen. (Which tend to be presented as "Here are the rules"; Grant, like this article, goes into the "why"; a step below. With great visuals, of course!

thecommakozzi 3mo ago
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dswilkerson 3mo ago
Please provide a link.
- the__alchemist 3mo ago
  Oops! It was Minute Physics: https://www.youtube.com/watch?v=tCsl6ZcY9ag https://www.youtube.com/watch?v=tCsl6ZcY9ag

atoav 3mo ago

A good overview on the topic. 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.

antonyt 3mo ago
Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
- dgellow 3mo ago
  Half joking, but Berlin techno :) 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)
  - IAmGraydon 3mo ago
    A long hold of one note doesn't mean there isn't harmonic progression. It just means the progression is slow in that part of the song. It's often done to create a massive contrast that occurs when the progression finally...progresses. In electronic music, this often comes as the drop or some similar kind of break.
    - otabdeveloper4 3mo ago
      No, in electronic music harmonic progressions are done by manipulating timbre. Try it yourself - play one note on repeat and start twirling the cutoff knob.
  - nwatson 3mo ago
    Not quite one note, but "Open Eye Signal" (2023 remaster) by Jon Hopkins has wide spectrum background and heavy rhythms, but once the song gets going the main instrument moves between fifth -> seventh-flat -> sixth -> fifth on repeat, and that's the melody for the song. And yet, to me, it's captivating.
    - dgellow 3mo ago
      Thanks for the suggestion, that’s a really neat discovery! I will try to integrate that in my own music

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okzgn 3mo ago

The logic that something sounds worse simply by combining dissonant notes is questionable, because music constantly combines elements—notes, chords, even different rhythms—without that necessarily implying displeasure for the listener. Convincing.

pier25 3mo ago
"Worse" is definitely a subjective appreciation influenced by culture and personal taste.
- okzgn 3mo ago
  That's why it's questionable, because it's subjective. It would be factual to find the keys to determine what sounds "worse" across the majority of subjective opinions, independent of culture and personal taste.
  - pier25 3mo ago
    Yeah. If anyone doubts this go listen to some gamelan music and see if they can make any sense of it (harmonically speaking). https://www.youtube.com/watch?v=nGCSrC8RN6c https://www.youtube.com/watch?v=nGCSrC8RN6c
- dhosek 3mo ago
  In the 00s, I sang in the Holy Name Cathedral choir and we did a lot of 20th/21st century choral works with harmonies that strayed very far from the classical tonal vocabulary to the point where when I was doing my own composition work, I realized that I didn’t hear dissonance any more.

claiir 3mo ago

Nice. But, is there a less “conversationally” written piece on the subject? In any event, this stuck with me: > Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases

dr_dshiv 3mo ago

Harmony has always been a principle that refers to more than music, let alone chords. Here is a recent review: https://www.sciencedirect.com/science/article/pii/S240587262200003X https://www.sciencedirect.com/science/article/pii/S240587262... 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)

skew-aberration 3mo ago

I have to highly recommend the book 'Fundamentals of Musical Acoustics' for mathematical/physical explanations of sound and music. Bells having multiple resonant modes, tuning kettle drums, how string materials and plucking methods changes harmonic profiles, why having lots of high frequency harmonics sounds bright (and electric guitars, pianos optimise for this), why sounds without high frequency harmonics sound hollow (nylon strings), virtual pitch, acoustics of rooms, etc. 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.

schroffl 3mo ago
Are you talking about "Fundamentals of Musical Acoustics" by Arthur H. Benade? I'm interested in buying the book, but I'm not sure which one you mean. Do you perhaps even have the ISBN?
- skew-aberration 3mo ago
  That's the one. I read the 2nd edition on kindle. There is only one short chapter on harmony but discussion of tone, intervals, etc is comprehensive.
  - schroffl 3mo ago
    Alright, thanks a lot :)

brudgers 3mo ago

The slight of hand in standard Western European music theory is that stacking 5ths gives you Lydian and its tritone as the foundational seven pitch scale. Major/Ionian is the fourth mode of this scale. 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.

dhosek 3mo ago
For that matter, the first 5 stacked fifths gives you the standard pentatonic scale. Extending by a fifth on either end and you get the most common accidentals in Western music (if your first seven give C major you’ll get F# and B♭). I think (but I’m not sure) that some of the non-Western microtonal scales extend the tonality by not ignoring the Pythagorean comma when you’ve done the 12th fifth, but by continuing to stack fifths for more harmonies.
- brudgers 3mo ago
  From C the first six stacked fifths give C Lydian, not C major. (You get an F#, the 5th of B as the seventh pitch, not F the 5th of Bb). 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.
  - dhosek 3mo ago
    I was being sloppy and should have said diatonic scale.
    - brudgers 3mo ago
      Sloppiness is why music theory is not scientific. You can’t get to a scientific rationalization of the primacy of the major scale without it.
      - acjohnson55 3mo ago

PaulDavisThe1st 3mo ago

I personally consider this to be a better intro, albeit in video form: https://www.youtube.com/watch?v=tCsl6ZcY9ag 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/ https://pmc.ncbi.nlm.nih.gov/articles/PMC7006947/

acjohnson55 3mo ago
Yes, not having had the time to read TFA or the paper you shared yet, it immediately stands out to me that the bibliography of the latter paper is far more comprehensive.

bobson_dugnutt5 3mo ago

I don't find this convincing at all. The actual interesting attempt at scientific theory of harmony in this could be distilled to a couple of lines, yet the author rambles endlessly in ways that don't add to the piece at all. I already knew his additions from traditional music theory already, so I can't really see what the purpose of this is.

dswilkerson 3mo ago
If this essay can be distilled into a couple of lines, please do that.

montebicyclelo 3mo ago

I was wondering whether this might have an explanation for why I don't really like major music, preferring minor / modal / non-functional harmony... it does: > 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.

breezybottom 3mo ago
Consider that you're not actually hearing major and minor intervals, you're hearing approximations of them due to 12TET.
- analog31 3mo ago
  Depends on the instrument. Temperament is mostly applicable to keyboard and some electronic instruments.

klik99 3mo ago

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.

ScotterC 3mo ago
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 3mo ago
  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.

simonreiff 3mo ago

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. Here's an example: Perhaps you're familiar with the idea of major and minor, but you might be unfamiliar with a Picardy third, where a composition is in a minor ("sad") key throughout but ends in that same pitch but on a major ("happy") chord. J.S. Bach used Picardy thirds regularly to end his compositions, but the Picardy third became rarer after Bach's death. Still, it's a beautiful and striking harmonic progression that continues to appear now and then. And now you know EXACTLY why that 1967 song by the Turtles, "Happy Together", has that really nice and memorable ending; that's a modern pop example of a Picardy third. Again, harmony is not abstract; it's the names musicians have given for specific sequential combinations, many of which have been named centuries ago. It's not about nicer or worse; sounds are sounds, but some are combined more often than others and those combined most frequently have well-known names that can be used to explain concisely the "harmonic" aspect of a piece of music.

duped 3mo ago
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.
bollu 3mo ago
where would I learn a taxonomy of such motifs? I trained for classical piano as a kid, and I'm slowly trying to learn jazz piano as I ease back into it! I'd love to learn more about these types of harmonic ideas and motifs as I get back to playing
- simonreiff 3mo ago

toolslive 3mo ago

I only skimmed the article. There's a lot of good stuff (debunking a lot of classical harmony) but they miss some important things too. There's nothing about repetition. Repetition legitimizes. Our brain is really good at pattern recognition, and as soon as it can predict something you're more than half way there to make it sound good. There's plenty of chromaticism that works because the brain "gets" the sense of direction.

TheOtherHobbes 3mo ago

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.

pitchlatte 3mo ago
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.
calf 3mo ago
Are there any readings would you recommend to read if I play classical piano, and especially for Romantic and post-Romantic music ranging from Chopin/Liszt to Debussy/Ravel?
- acjohnson55 3mo ago
  If you want to go way deep, check out Tymoczko's first book: https://dmitri.mycpanel.princeton.edu/geometry-of-music.html https://dmitri.mycpanel.princeton.edu/geometry-of-music.html 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.
acjohnson55 3mo ago
I also jumped straight to the bibliography to look for those two. Not seeing any reference to their work is disappointing and makes me a little pessimistic that digesting the entire piece will be worthwhile, as a scientific piece. He references Helmholtz, but his theories have been surpassed for more than a century. 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 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.

cyanclouds 3mo ago

It's all about big booties 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

a-dub 3mo ago

i tend to think of this stuff in terms of top down information theoretic approaches to composition and bottom up psychophysics of auditory perception. there is some cool work out there where physicists attempt to compute information content of western classical music and then there is all the fun stuff around the biophysics of the cochlea, nonlinear frequency discrimination and frequency selectivity of the ear.

crawfordcomeaux 3mo ago

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 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.

BigTTYGothGF 3mo ago

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 https://sethares.engr.wisc.edu/ttss.html) or Music a Mathematical Offering (https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...)

dswilkerson 3mo ago
Responses that say "If I started listing criticisms I would never finish" usually have none. Name 3.
- BigTTYGothGF 3mo ago
  I gave a couple in my other reply, the most damning (imo) was that you completely ignore the cochlea. 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/137461 https://artmuseum.princeton.edu/art/collections/objects/1374...) (and the Brooklyn Museum claims that "hundreds" have been found: https://www.brooklynmuseum.org/objects/51700 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".

nttylock 3mo ago

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Rochus 3mo ago

The central insight (consonance involves both physical properties of sound and active perceptual pattern recognition) is interesting, but as a musician I see the following issue: the harmonic series can motivate certain local sonorities, but it cannot generate the operative grammar of common-practice Western harmony; the paper recognizes the tuning problem, yet treats it as a regrettable engineering compromise, when it is actually constitutive of the harmonic system it claims to explain.

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iainctduncan 3mo ago

You know those HN posts where someone who barely knows how to program decides to tell you why language X is terribly designed? This is that. Anyone with a decent understanding of music and acoustics can tell it's silly from the title and abstract alone.

dswilkerson 3mo ago
Does Daniel Levitin, author of "This is your brain on music", count as someone with "a decent understanding of music and acoustics" ? He thinks that Helmholtz explained harmony (he told me personally). However, as the essay points out, (1) The American Acoustical Society collection has an experiment stretching frequencies from 2.0 to 2.1 that they conclude shows that Helmholtz was wrong, and (2) if Helmholtz was right, there would be not harmony at all, as the essay points out. So even someone like Levitin is wrong.

MetaWhirledPeas 3mo ago

I don't think I want a scientific theory of music. That would take the fun out of it. I like music that matches my tastes while still managing to surprise me. What else do I need to know about music? 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.

dswilkerson 3mo ago
This is like saying we should not study physics because if we did then all art could be automatically generated.
- MetaWhirledPeas 3mo ago
  Are you saying demystifying music is as important as understanding physics?
Nekorosu 3mo ago
No worries. This one is based on so many untested assumptions that you can easily ignore it.

Nekorosu 3mo ago

Calling this a scientific theory seems premature. It is mostly a speculative model built on untested assumptions about cognition, with no empirical validation of its central claims.

dswilkerson 3mo ago

This seems to be the 9th time that my paper on harmony has been on Hacker News. I wonder if it has been on HN more than any other paper on arxiv: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&query=%22Harmony%20Explained%22%20Scientific&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... 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?

vikramkr 3mo ago

Awfully dismissive of non western tonal harmonic systems for a universal theory of music? The whole idea that musical traditions that use less harmonic structures just haven't unlocked all the structures available is kind of absurd - those musical traditions have been developing for the same amount of time - and there's a pretty huge blind spot for other traditions. The whole microtones just being ornamentations - no that's absolutely not the case. Trying to ignore/hand wave away all the counterexamples and force them into your system is how you get epicycles. If you're gonna do a universal theory of music it would be a good idea to engage deeply with more than one system. As a universal theory of harmonica maybe that's fine but it's sloppy and motivated reasoning

vikramkr 3mo ago
More directly the stuff about ranking different cultures on a scale of musical sophistication that ends in western harmonic music and dismissing obvious counterexamples as cultures that just haven't gotten there yet or just use other feature as ornamentation or just happened to not stumble on things because they were at the lowest level of musical sophistication is almost comically ethnocentric. Its an easy hammer to reach for when your counterarguments are not European (though in this case you're having to ignore an awful lot of European music and the huge influence of Greek music on the middle East) but yeesh

danbmil99 3mo ago

I think the most fascinating thing about music (from a mathematical/scientific perspective) is the fact that the principal harmonics of equal temperament are so close to the mathematical ideals. Fourths and fifths are so close trained musicians typically cannot hear the difference. Major thirds are farther from the ideal but still are less than 1% off. That can be heard by the trained ear, but in the real world there are chorus effects (multiple voices/instruments at nominal but slightly varied pitch), vibrato, reverb etc. such that in most cases a just major 3rd sounds fine. 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.