4 ms·

I agree that the central scientific question is whether harmony is a metaphor or mechanism, e.g., for psychological constructs like Cognitive Dissonance. My gue

I agree that the central scientific question is whether harmony is a metaphor or mechanism, e.g., for psychological constructs like Cognitive Dissonance. My guess is that harmony is so pervasive that it ceases to have original meaning -- like in the manner that every atom is a harmonic oscillator or how brainwaves are based on an "octave" structure (e.g., Beta is double Alpha, Gamma is double Beta, etc). However, this question of metaphor or mechanism should be resolvable with science, eh? However, I disagree that harmony is primarily a western phenomena. It is a central feature to Confucianism and Daoism. It also plays a major role in Native American philosophy.

PaulDavisThe1st 6y ago
I was talking specifically about harmony in a musical context as being very western.
- dr_dshiv 6y ago
  Well, the point still applies. The small integer ratios of harmony apply even to the rhythms of gamelan. And, of course, octaves are more-or-less universal across cultures.
  - PaulDavisThe1st 6y ago
    This starts to get silly. "Small integer ratios" apply to huge numbers of natural phenomena, because "small integers" and "ratios" are properties of the world we live in. Pointing out that "harmony is another example of small-integer ratios" seems fairly devoid of content to me, especially when the primary user of musical harmony has long abandoned those pure integer ratios to allow modulation and other desired compositional techniques. Octaves are not universal across cultures. Byzantine music has no octave equivalence, for example. There was even a paper cited here on HN recently showing lack of octave awareness in different cultures (the paper may have had some flaws, but was interesting).
    - dr_dshiv 6y ago
      Silly indeed. The fact that integer relations are mathematical relations that bear so heavily on physical phenomena is precisely the point. That's what the ancients got so damned excited about. You may not find meaning in it, but it certainly drove the development of science and philosophy from Plato to Galileo to Kepler to Descartes to Newton, etc. Now, in recognizing that integer relationships are, in fact, an imperfect description of a pervasive phenomena -- that's why the ongoing investigation is so interesting and challenging. Don't we expect what is pervasive in physics to apply to psychology, culture and economics? I'd argue that the mathematical "imperfections" of modern music point to better models of what universal harmony really is. Overall, the point is that we haven't yet solved harmony. Not even remotely. And i'd love a reference on why you think Byzantine music doesn't have octaves when the Greek music it grew out of most certainly did.
      - PaulDavisThe1st 6y ago
        1) "Do not mistake your models for reality" (Lord Kelvin, sometime in the late 1800s) ... many of things that we describe with "small integers and ratios" are not in fact small integers and the ratios are rooted in our observations and thinking. The natural world is more fractal than integral, but the notion of "oh! that thing is a lot like two times that other thing" was a notion more accessible to natural philosophers and early philosopers. 2) No, I see absolutely no reason to "expect what is pervasive in physics to apply to psychology, culture and economics". 3) I don't have a citation for you on the Byzantine stuff, but have been discussing it a lot recently with a musician who grew up on it and continues to perform it, and he was explaining to me how they have no notion of octave equivalency and that because of their tuning and scale systems, when you go up or down the number of steps that "should" correspond to an octave, you end up somewhere other than 2*freq or freq/2. Remember, this is in part why equal tempered tuning was developed: if you stick to "pure" just intonation (precise integer ratios), you can't construct intervals that fit nicely into the octave (e.g. pick a note, go up some number of intervals. Pick the ending note, go down the same intervals, you don't end up back where you started). This stuff is all covered in basic music theory. My understanding from this Byzantine musician is that their musical tradition basically just said "we don't care", and went with a tuning/scale system where you don't just (as in our western system) go up or down N (12 in our case) and end up an octave from where you started.
  - mkl 6y ago
    From a story a couple of weeks ago, octaves, while common, seem to be learned: https://news.ycombinator.com/item?id=23624596 https://news.ycombinator.com/item?id=23624596
  - imoverclocked 6y ago
    That may be, but they are still learned according to https://www.quantamagazine.org/perceptions-of-musical-octaves-are-learned-not-wired-in-the-brain-20191030/ https://www.quantamagazine.org/perceptions-of-musical-octave...

PaulDavisThe1st 6y ago

I was talking specifically about harmony in a musical context as being very western.

dr_dshiv 6y ago
Well, the point still applies. The small integer ratios of harmony apply even to the rhythms of gamelan. And, of course, octaves are more-or-less universal across cultures.
- PaulDavisThe1st 6y ago
  This starts to get silly. "Small integer ratios" apply to huge numbers of natural phenomena, because "small integers" and "ratios" are properties of the world we live in. Pointing out that "harmony is another example of small-integer ratios" seems fairly devoid of content to me, especially when the primary user of musical harmony has long abandoned those pure integer ratios to allow modulation and other desired compositional techniques. Octaves are not universal across cultures. Byzantine music has no octave equivalence, for example. There was even a paper cited here on HN recently showing lack of octave awareness in different cultures (the paper may have had some flaws, but was interesting).
  - dr_dshiv 6y ago
    Silly indeed. The fact that integer relations are mathematical relations that bear so heavily on physical phenomena is precisely the point. That's what the ancients got so damned excited about. You may not find meaning in it, but it certainly drove the development of science and philosophy from Plato to Galileo to Kepler to Descartes to Newton, etc. Now, in recognizing that integer relationships are, in fact, an imperfect description of a pervasive phenomena -- that's why the ongoing investigation is so interesting and challenging. Don't we expect what is pervasive in physics to apply to psychology, culture and economics? I'd argue that the mathematical "imperfections" of modern music point to better models of what universal harmony really is. Overall, the point is that we haven't yet solved harmony. Not even remotely. And i'd love a reference on why you think Byzantine music doesn't have octaves when the Greek music it grew out of most certainly did.
    - PaulDavisThe1st 6y ago
      1) "Do not mistake your models for reality" (Lord Kelvin, sometime in the late 1800s) ... many of things that we describe with "small integers and ratios" are not in fact small integers and the ratios are rooted in our observations and thinking. The natural world is more fractal than integral, but the notion of "oh! that thing is a lot like two times that other thing" was a notion more accessible to natural philosophers and early philosopers. 2) No, I see absolutely no reason to "expect what is pervasive in physics to apply to psychology, culture and economics". 3) I don't have a citation for you on the Byzantine stuff, but have been discussing it a lot recently with a musician who grew up on it and continues to perform it, and he was explaining to me how they have no notion of octave equivalency and that because of their tuning and scale systems, when you go up or down the number of steps that "should" correspond to an octave, you end up somewhere other than 2*freq or freq/2. Remember, this is in part why equal tempered tuning was developed: if you stick to "pure" just intonation (precise integer ratios), you can't construct intervals that fit nicely into the octave (e.g. pick a note, go up some number of intervals. Pick the ending note, go down the same intervals, you don't end up back where you started). This stuff is all covered in basic music theory. My understanding from this Byzantine musician is that their musical tradition basically just said "we don't care", and went with a tuning/scale system where you don't just (as in our western system) go up or down N (12 in our case) and end up an octave from where you started.
- mkl 6y ago
  From a story a couple of weeks ago, octaves, while common, seem to be learned: https://news.ycombinator.com/item?id=23624596 https://news.ycombinator.com/item?id=23624596
- imoverclocked 6y ago
  That may be, but they are still learned according to https://www.quantamagazine.org/perceptions-of-musical-octaves-are-learned-not-wired-in-the-brain-20191030/ https://www.quantamagazine.org/perceptions-of-musical-octave...