4 ms·

"It is also important to know that chords are built on thirds." Except for the ones built on seconds ("cluster chords"), fourths ("quartal chords"), fifths ("q

"It is also important to know that chords are built on thirds." Except for the ones built on seconds ("cluster chords"), fourths ("quartal chords"), fifths ("quintal chords"), the chords that make jazz work, and for obsessive/completists, polychords.

Ylpertnodi 2y ago
Zappa used 2nds a lot, for his improvs. Allows a lot of freedom to both major or minor or both.
- pohl 2y ago
  See also the very recent "Symptom Of Life" by Willow Smith, a cluster chord bonanza.
- badlibrarian 2y ago
  I considered sending the first ten seconds of Clair de Lune through this thing to see what nonsense it would spit out. Tech people tinkering in the humanities (and vice versa) is always good for fun.
  - scrozier 2y ago
    This is one of my favorite categories of HN posts. But hey, if it engenders some interest in ______ (fill in arts category), then it's all good.
andybak 2y ago
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.
wglass 2y ago
And don’t forget the barbershop 7th!
klysm 2y ago
The thing is though you can get to every note by stacking enough thirds - I don’t think it’s a particularly bad perspective
- shermantanktop 2y ago
  You can get to every note by stacking enough of literally anything but octaves. Such is the power of the modulus operator. Thirds appear to me to be pretty much the fundamental particle of western harmony.
  - klysm 2y ago
    That’s not true though, whole tones and tritones won’t cover the whole chromatic scale
    - shermantanktop 2y ago
      Got me! You’re right. Ok, gotta remove multiples of factors of twelve, so 2 (whole), 3 (dim), 4 (aug), 6 (tritone), 8 and 9 are out. That leaves 1, 5, 7, 10, and 11, plus all the variants from adding n*12 (e.g. 13 or 25). So my bold assertion didn’t work out too well.
      - klysm 2y ago
        There’s some really interesting theory that stems from that relationship too. For example, there are only three distinct diminished “loops”. These each define tonal centers because each pair of tritones uniquely identifies a 5 chord. You can view a fully diminished chord as a “gateway” of sorts into 4 different keys, depending on what root note you slap on it.

Ylpertnodi 2y ago

Zappa used 2nds a lot, for his improvs. Allows a lot of freedom to both major or minor or both.

pohl 2y ago
See also the very recent "Symptom Of Life" by Willow Smith, a cluster chord bonanza.
badlibrarian 2y ago
I considered sending the first ten seconds of Clair de Lune through this thing to see what nonsense it would spit out. Tech people tinkering in the humanities (and vice versa) is always good for fun.
- scrozier 2y ago
  This is one of my favorite categories of HN posts. But hey, if it engenders some interest in ______ (fill in arts category), then it's all good.

andybak 2y ago

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.

wglass 2y ago

And don’t forget the barbershop 7th!

klysm 2y ago

The thing is though you can get to every note by stacking enough thirds - I don’t think it’s a particularly bad perspective

shermantanktop 2y ago
You can get to every note by stacking enough of literally anything but octaves. Such is the power of the modulus operator. Thirds appear to me to be pretty much the fundamental particle of western harmony.
- klysm 2y ago
  That’s not true though, whole tones and tritones won’t cover the whole chromatic scale
  - shermantanktop 2y ago
    Got me! You’re right. Ok, gotta remove multiples of factors of twelve, so 2 (whole), 3 (dim), 4 (aug), 6 (tritone), 8 and 9 are out. That leaves 1, 5, 7, 10, and 11, plus all the variants from adding n*12 (e.g. 13 or 25). So my bold assertion didn’t work out too well.
    - klysm 2y ago
      There’s some really interesting theory that stems from that relationship too. For example, there are only three distinct diminished “loops”. These each define tonal centers because each pair of tritones uniquely identifies a 5 chord. You can view a fully diminished chord as a “gateway” of sorts into 4 different keys, depending on what root note you slap on it.