5 ms·
That's not quite right. The overtones are the harmonic series, not just octaves (1:2, 1:4, 1:8, etc..) but an octave and a fifth (1:3), two octaves and a third
by elihu 5y ago
That's not quite right. The overtones are the harmonic series, not just octaves (1:2, 1:4, 1:8, etc..) but an octave and a fifth (1:3), two octaves and a third, (1:5), etc..
In a piano, the bass and treble strings have a lot of inharmonicity. They don't behave like ideal strings for various reasons, so the harmonics aren't exact multiples of the fundamental frequency. Piano tuners deal with this be stretching the octave, so that the piano sounds in tune even though it kind of isn't.
Having a super long bass string instead of a short double-wound bass string probably behaves more like an ideal string (with harmonics that are closer to whole-number multiples of the fundamental), so it should sound like it has a more definite pitch and less like a gong.
Interestingly, we don't really perceive the fundamental frequencies of the low notes in a piano much at all in the first place. If you filter them out, the notes will sound about the same -- we take most of our perceptual cues from the higher harmonics, and our brain just inserts the implied bass fundamental. In the same way, playing a major chord sort of implies a bass note a couple octaves below the root of the chord -- if all the harmonics are there, then we expect it to be there.
- LanceH 5y agoThank you.
- LeonB 5y ago“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.
- elihu 5y agoYeah, 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.
- mrob 5y ago>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: https://en.wikipedia.org/wiki/Harmonic_seventh_chord https://en.wikipedia.org/wiki/Harmonic_seventh_chord
- elihu 5y agoYep. It's also possible to re-tune a piano to a 7-limit just intonation scale that makes use of that 7th harmonic. https://www.youtube.com/watch?v=D4oKzSRs3sA https://www.youtube.com/watch?v=D4oKzSRs3sA