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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 o

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
        It lacks explicatory power past the triad. Sure, if you look at major triads only, and ignore extended harmony, it works fine. But it’s also not that useful if you look only at triads, because there just aren’t that many triads.
    - schwartzworld 2y ago
      > Consider, for example, that a chord “built out of thirds” can contain a major or minor seventh, a minor second, or an augmented fourth. According to modern harmonic rules those are valid. For a long time, these were not harmonies you'd hear in music. Really only since counterpoint fell out of style, since it forbids augmented intervals.
      - klodolph 2y ago
        Counterpoint didn’t have “chords” anyway.

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
      It lacks explicatory power past the triad. Sure, if you look at major triads only, and ignore extended harmony, it works fine. But it’s also not that useful if you look only at triads, because there just aren’t that many triads.
  - schwartzworld 2y ago
    > Consider, for example, that a chord “built out of thirds” can contain a major or minor seventh, a minor second, or an augmented fourth. According to modern harmonic rules those are valid. For a long time, these were not harmonies you'd hear in music. Really only since counterpoint fell out of style, since it forbids augmented intervals.
    - klodolph 2y ago
      Counterpoint didn’t have “chords” anyway.