"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.
“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.
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
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.
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.
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
> 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.
> 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.
> 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.
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.
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.
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.
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.