4 ms·

I'm going out a limb here and saying "your ears interpret them in terms of their relationship to thirds and everything else is a fiction" Although: a) I have

I'm going out a limb here and saying "your ears interpret them in terms of their relationship to thirds and everything else is a fiction" Although: a) I have only given this a moment's thought and... b) The term "fiction" here is relative as all music theory is a fiction to some degree. c) "Ears" here is short hand for a weird mixture of maths, physics, brain structure and learned cultural expectations. I'm kinda clutching at a valid idea here though - despite the above flakiness.

klodolph 2y ago
“Your ears interpret them in terms of their relationship to thirds” I don’t really see a basis for this one. I think if we really dig into it, the use of thirds is somewhat arbitrary and has more of a historical basis to it than any other foundations (rather than physical or physiological foundations). Thirds really do fall apart when you start looking at quartal harmony, tone clusters, and all sorts of modern harmony. Thirds even get stretched to the limit in a lot of very traditional, “safe” harmony. I think on some level, we are just using thirds because of the mathematical coincidences in our systems of harmony. Cultural explanations are the biggest ones.
- schwartzworld 2y ago
  It’s not that arbitrary. A lot of what we define as consonance comes from the harmonic series, the set of overtones you can access by doubling, tripling, etc the frequency of the fundamental tone. If you look at this series, the third is the first interesting interval. Fundamental - octave - fifth - octave - third - fifth - flat 7
  - klodolph 2y ago
    The harmonic series really, really does not explain why harmony comes in thirds. The minor 7 is not in the harmonic series. It’s just not there. This is not a nitpick or a quibble—the minor 7 is just a completely different interval, separate from the just intonation 7:4 interval. To my ears, it is like saying that red and yellow are the same color. What about augmented or diminished chords? How do they fit into this theory? What about, say, the 9? Why do we put a 9 in a chord, and not a 2? Why do we like the b9? Why do we use a #11? There’s a million little historical and cultural factors going on here. You can come up with a sort of apologia to explain why thirds make sense, but this doesn’t mean that thirds are in any sense fundamental in some physical or physiological sense.
    - schwartzworld 2y ago
      If you look at the evolution of how music and harmony progressed in western music, fifths were seen as consonances, then later thirds. Minor 7ths weren’t much of a thing until like the 1400s. Augmented intervals were still not really even used during the baroque. You can discount the fundamentalness of thirds, but it’s there.
      - klodolph 2y ago
        That’s a historical, cultural foundation for thirds—exactly the point I am making.
        pohl 2y ago
        Norman D Cook's work is interesting in this context. This is a great talk, if anyone is curious: https://www.youtube.com/watch?v=CrmnaiyS5EE https://www.youtube.com/watch?v=CrmnaiyS5EE This thread reminded me of the "Conclusions" slide.
        andybak 2y ago
        If you accept a physical basis for fifths (by virtue of the harmonic series) then surely it's not a major leap (no pun intended) from that to thirds? As you get further along the series you're moving from simple to complex ratios. Thirds are next in line after 4ths/5ths and they have a function that solves some obvious harmonic problems. A lot of this has echoes in the historical development of music and the commonalities between harmony in different parts of the world. There's a reason cultures independently discover similar constructs i.e. the pentatonic scale
        klodolph 2y ago
        > If you accept a physical basis for fifths (by virtue of the harmonic series) then surely it's not a major leap (no pun intended) from that to thirds? It’s not a leap to go from the fifth (as an interval, two notes) to the major triad, three notes. However, if you consider major triads, you’re just dipping your toe in the water as far as chords are considered. The question is not, “Why does the major third above the root appear in chords?” but rather “Why do we build chords out of stacked thirds, which can be minor, major, or even diminished or augmented?” At this point, the part about the major third appearing in the harmonic series lacks explicatory power. Consider, for example, that a chord “built out of thirds” can contain a major or minor seventh, a minor second, or an augmented fourth. Just as examples.
rerdavies 2y ago
That might have been true in the 19th century. (Although Bach, infamously, uses some pretty advanced harmony that stands up very well against modern harmony). I think you're spot on with learned cultural expectation though. As a musician, you have to learn how to hear quartal harmony and polychord harmony. The sounds and the logic of how things fit together are different from triadic harmonic theory. As an audience, though, I think you're probably so used to quartal harmony and (to a slightly lesser extent) polychord harmony that I don't think you'd find it at all unusual to hear a chord without a third in it. That particular chunk of harmonic theory was added near the end of the 19th century by composers like Debussy, and subsequently became completely embedded in hollywood movie music, so you are completely culturally used to it. You probably wouldn't even notice that what you're listening to has no 3rd. 19th century audiences weren't so comfortable about it. The only real problem is that classical music theory gets quite broken when it comes to quartal and polychordal music. No accident, because compositional techniques involving quartal and polychordal music were deliberately designed to get away from classical music theory.

klodolph 2y ago

“Your ears interpret them in terms of their relationship to thirds” I don’t really see a basis for this one. I think if we really dig into it, the use of thirds is somewhat arbitrary and has more of a historical basis to it than any other foundations (rather than physical or physiological foundations). Thirds really do fall apart when you start looking at quartal harmony, tone clusters, and all sorts of modern harmony. Thirds even get stretched to the limit in a lot of very traditional, “safe” harmony. I think on some level, we are just using thirds because of the mathematical coincidences in our systems of harmony. Cultural explanations are the biggest ones.

schwartzworld 2y ago
It’s not that arbitrary. A lot of what we define as consonance comes from the harmonic series, the set of overtones you can access by doubling, tripling, etc the frequency of the fundamental tone. If you look at this series, the third is the first interesting interval. Fundamental - octave - fifth - octave - third - fifth - flat 7
- klodolph 2y ago
  The harmonic series really, really does not explain why harmony comes in thirds. The minor 7 is not in the harmonic series. It’s just not there. This is not a nitpick or a quibble—the minor 7 is just a completely different interval, separate from the just intonation 7:4 interval. To my ears, it is like saying that red and yellow are the same color. What about augmented or diminished chords? How do they fit into this theory? What about, say, the 9? Why do we put a 9 in a chord, and not a 2? Why do we like the b9? Why do we use a #11? There’s a million little historical and cultural factors going on here. You can come up with a sort of apologia to explain why thirds make sense, but this doesn’t mean that thirds are in any sense fundamental in some physical or physiological sense.
  - schwartzworld 2y ago
    If you look at the evolution of how music and harmony progressed in western music, fifths were seen as consonances, then later thirds. Minor 7ths weren’t much of a thing until like the 1400s. Augmented intervals were still not really even used during the baroque. You can discount the fundamentalness of thirds, but it’s there.
    - klodolph 2y ago
      That’s a historical, cultural foundation for thirds—exactly the point I am making.
      - pohl 2y ago
        Norman D Cook's work is interesting in this context. This is a great talk, if anyone is curious: https://www.youtube.com/watch?v=CrmnaiyS5EE https://www.youtube.com/watch?v=CrmnaiyS5EE This thread reminded me of the "Conclusions" slide.
      - andybak 2y ago
        If you accept a physical basis for fifths (by virtue of the harmonic series) then surely it's not a major leap (no pun intended) from that to thirds? As you get further along the series you're moving from simple to complex ratios. Thirds are next in line after 4ths/5ths and they have a function that solves some obvious harmonic problems. A lot of this has echoes in the historical development of music and the commonalities between harmony in different parts of the world. There's a reason cultures independently discover similar constructs i.e. the pentatonic scale
        klodolph 2y ago
        > If you accept a physical basis for fifths (by virtue of the harmonic series) then surely it's not a major leap (no pun intended) from that to thirds? It’s not a leap to go from the fifth (as an interval, two notes) to the major triad, three notes. However, if you consider major triads, you’re just dipping your toe in the water as far as chords are considered. The question is not, “Why does the major third above the root appear in chords?” but rather “Why do we build chords out of stacked thirds, which can be minor, major, or even diminished or augmented?” At this point, the part about the major third appearing in the harmonic series lacks explicatory power. Consider, for example, that a chord “built out of thirds” can contain a major or minor seventh, a minor second, or an augmented fourth. Just as examples.

rerdavies 2y ago

That might have been true in the 19th century. (Although Bach, infamously, uses some pretty advanced harmony that stands up very well against modern harmony). I think you're spot on with learned cultural expectation though. As a musician, you have to learn how to hear quartal harmony and polychord harmony. The sounds and the logic of how things fit together are different from triadic harmonic theory. As an audience, though, I think you're probably so used to quartal harmony and (to a slightly lesser extent) polychord harmony that I don't think you'd find it at all unusual to hear a chord without a third in it. That particular chunk of harmonic theory was added near the end of the 19th century by composers like Debussy, and subsequently became completely embedded in hollywood movie music, so you are completely culturally used to it. You probably wouldn't even notice that what you're listening to has no 3rd. 19th century audiences weren't so comfortable about it. The only real problem is that classical music theory gets quite broken when it comes to quartal and polychordal music. No accident, because compositional techniques involving quartal and polychordal music were deliberately designed to get away from classical music theory.