4 ms·

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 th

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.
        andybak 2y ago
        > At this point, the part about the major third appearing in the harmonic series lacks explicatory power. I really don't think it does. Fifths (and their inverted form fourths) are the most consonant interval (ignoring octaves as the trivial case). Most cultures develop musical processes that involve fifths very early on in their history. Where do you go from fifths if you want to add another voice? If you have three notes and you want the most consonant result - you put a note that forms a third between the root and the fifth. Given a few basic assumptions ("prefer simpler integer ratios") there's no better way to play 3 non-octave notes together.

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.
      - andybak 2y ago
        > At this point, the part about the major third appearing in the harmonic series lacks explicatory power. I really don't think it does. Fifths (and their inverted form fourths) are the most consonant interval (ignoring octaves as the trivial case). Most cultures develop musical processes that involve fifths very early on in their history. Where do you go from fifths if you want to add another voice? If you have three notes and you want the most consonant result - you put a note that forms a third between the root and the fifth. Given a few basic assumptions ("prefer simpler integer ratios") there's no better way to play 3 non-octave notes together.