Author: Matt74
Date: 2021-11-17 11:45
The overtone series is a natural phenomenon. It's the physical law that makes intervals sound "in tune", and what makes harmony work. Without it you couldn't have music.
If you pluck a string (like a guitar string) you get one note. If you touch it very lightly exactly in the middle and pluck it you get an octave above that. If you touch it 1/3 along the length you get the 5th above that. Etc. The places where you touch it are called "nodes".
The same thing happens if you use the same size string at the same tension, but half as long, 1/3rd as long, etc. That's why you touch the string right above certain frets. The 12th fret high E is half the length of the E string, etc.
I think Boethius discusses all of this, but I don't have my text anymore and I might be getting part of it mixed up with something else more explicit.
The reason pure intervals sound good is that they "fit" physically into the others according to whole number ratios. The "nodes" match up, and the frequencies align numerically. When they are out of tune you hear "beats", which are the frequencies and/or wavelengths not matching up - like blinking lights that are out of sync. They're physically clashing with one another. The air is turbulent rather than resonant. That's why it FEELS so much better when you are in tune. The horn vibrates more.
When people say that certain overtones are "out of tune" what they mean is that some of the higher partials are not notes that you can find on a piano. (Or maybe that the physical limitations of the vibrating body cause the frequency of the higher partials to be imperfect.) I hope they don't mean that they aren't equally tempered, because that would be backwards.
It's also why you can hear higher notes when you listen to a piano string decay. When you hit the note the fundamental is strongest. As the note gets softer there isn't enough energy in the string to make the whole thing bounce back and forth along it's entire length. So, it starts wobbling in a standing wave around 1/2 its length, then 1/3, then 1/4, and so on until there isn't enough energy left and it stops. The notes you actually hear depend on the properties of the string and its imperfections. That's also why you can press some of the keys without sounding the notes, play other notes, and the first ones will be vibrating at the frequency of the higher notes. It's also why opening the pedal makes the thing sound gianormus. It's because all the strings are vibrating sympathetically. Not just randomly, but with all of the matching partials. You are doubling all of the notes and partials.
When you create any sound overtones are present, and it is the mixture of the most prominent overtones that makes a flute sound different than a clarinet. Noise and other things play a role, but the overtone mixture is very important. A clarinet sounds really pure or hollow because it's missing half the overtones.
All temperaments are compromises because some keys sound bad, and they all sound a bit different. Lots of people think that composers used this to their advantage. That may be true with keyboard music, and by its influence maybe even wind and string music. The reason they allowed some keys to sound bad is because they wanted other ones to sound good. They weren't willing to give up the good intervals. Eventually they just gave up and settled with equal temperament. They didn't really have any choice because music got too chromatic. It's sort of like the compromise that no one is entirely happy with, but everybody accepts because it works best for everyone. That's why piano music is so melancholy, IMO. Everything is slightly out of tune.
When I was fooling around with the guitar I always tuned it differently when playing in E/A and G/D. You have to tune the B string to either the G or the E. You can't have it both ways. You either get the pure 5th, or the pure 3rd, but not both. It makes a huge difference. (supposedly Eddie Van Halen used the third). I NEVER tuned my guitar using the 4th fret method. It sounds like a car crash. I always tuned the octaves and fifths.
You may find that some clarinet fingerings work well for one key or piece, but not another.
This guy has some cool videos comparing temperaments:
https://www.youtube.com/watch?v=kRui9apjWAY&t=917s
- Matthew Simington
Post Edited (2021-11-17 11:55)
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The Clarinet BBoard
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