“playing a major chord sort of implies a bass note a couple octaves below the root of the chord”
Wow! Of course! Lightbulb moment. This isn’t something that occurred to me independently but makes so much sense I wonder how it hadn’t, and it explains a lot of what chords are really all about.
Yeah, chords are interesting. Major triads are basically a 4:5:6 ratio, which is the 4th, 5th, and 6th harmonic of some low bass note. (Different inversions get you 2:3:5 or 3:4:5 or whatever.) A dominant 7th chord gets you one more step in the harmonic series: 4:5:6:7. That 7th harmonic is way out of tune in 12-tone equal temperament, though.
Minor chords are a 10:12:15 ratio, which kind of looks like a bunch of arbitrary chosen numbers, but we could rewrite that as 60/6 : 60/5 : 60/4 and then it sort of make sense that minor would be a sort of mathematical reciprocal of the major. Minor chords can be interpreted either as the 10th, 12th, and 15th harmonics of some bass note or as the first three prime subharmonics that are integer divisions of the fundamental note. Subharmonics don't really occur in nature, though.
>That 7th harmonic is way out of tune in 12-tone equal temperament
You can sing in any tuning though. If you want to hear just-intonation 4:5:6:7 chords, listen to barbershop music, where this chord is a defining part of the style. See:
Wow! Of course! Lightbulb moment. This isn’t something that occurred to me independently but makes so much sense I wonder how it hadn’t, and it explains a lot of what chords are really all about.