#1
I just noticed this physical phenomenon and I assume the answer shouldn't be that complex:

Regarding open harmonics on the guitar (and I assume that basically any, for that matter) strings, when playing the one at ~5 fret it plays the open note 2-octaves above, when playing the one at ~17 fret it plays the open note 3-octaves above, and when playing the one at ~29 fret it plays the 2-octave once again; conversely, when playing the harmonic at ~7 fret it plays the fifth 1-octave above, when playing the one at ~19 fret it still plays the same harmonic, and when playing the one at ~31 fret it then plays the fifth 2-octaves above. What determines this order of octaves?

Thanks professor.
Last edited by TLGuitar at Apr 17, 2015,
#2
I don't know why exactly (I'm not an expert when it comes to physics), but the distance from the 5th fret to the nut is the same as the distance from the 24th fret to the bridge - it's 1/4 of the whole string length. Same with the 7th and 19th frets - it's 1/3 of the whole string length.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#3
Quote by MaggaraMarine
I don't know why exactly (I'm not an expert when it comes to physics), but the distance from the 5th fret to the nut is the same as the distance from the 24th fret to the bridge - it's 1/4 of the whole string length. Same with the 7th and 19th frets - it's 1/3 of the whole string length.


Oops, you're right. Kind of stupid that I didn't figure it out. Because you don't really press down the fret and block the side opposite to where the pick is struck, the vibration is a result of the whole string (or part of it that is free, if you play harmonics combined with actual fretting) vibrating, and thus the "twin-harmonic" is just a mirroring of it from the other edge of the string.

Edit: And I also thought for some reason that the next 2nd-octave is another 12 frets from 17th at 29th, but it's at 24th as you mentioned. Looking at it simplistically, to me they both seem to divide the two equal half of the +1-octave harmonic at 12th fret to another two halves (or to quarters of the whole sting), thus going up another octave, while the harmonic at the ~17th fret seem to go half way through the half going from 12th to 24th fret, thus going yet another octave up to +3-octaves from the open note as I mentioned in the OP.
Last edited by TLGuitar at Apr 17, 2015,
#4
Maggara has it exactly right.

Harmonics are whole-number ratios above the fundamental.
"There are two styles of music. Good music and bad music." -Duke Ellington

"If you really think about it, the guitar is a pointless instrument." - Robert Fripp
#6
I just know if the 9th fret harmonics don't ring right not tuned right
#7
The pitch that a vibrating string produces is determined by the rate at which it vibrates; it's frequency.

The frequency at which a string vibrates is affected by several factors.

One factor is the amount of tension the string is placed under. Higher pitches are created by increased tension being placed on the string (this is what the tuning heads do).

Another factor is the mass of the string. A heavier string vibrates slower than a thinner string. This is why the higher strings on the guitar are thinner.

Another factor is the length of the string. When you half the length of a string it produces a note an octave higher. You shorten the string by fretting it and that produces a higher pitch.

An interesting phenomenon of a vibrating string is that you can create harmonics. These harmonics are created by using nodes to allow the string to vibrate in equal divisions.

Thus you can make the string vibrate in two equal parts. To do this you would create a node at the halfway point on the string (by resting your finger there and plucking the string. This produces a pitch that is an octave above the fundamental pitch of the string.

You can half that half to make the string vibrate in four equal parts. This is an octave above again. If you made it vibrate in eight equal parts is an octave above that. And on and on it goes.

You can also make it vibrate in thirds. This gives you a perfect fifth above the octave above the fundamental. If you half the third you get a string vibrating in six equal parts and you have a perfect fifth an octave higher. If you half that you go up another octave.

So far we have seen what happens when the string is divided in half (octave), in thirds (octave plus perfect fifth), in quarters (two octaves), in sixths (two octaves plus perfect fifth), in eighths(three octaves above fundamental.

But what about if it vibrates in five equal parts? Then we have a slightly flat major third. If it vibrates in seven equal parts then we have something below a minor seventh.

These harmonic overtones that you can hear in a string actually can be heard when the open string is plucked. The open string includes different levels of different overtones and this plays a large part in what creates the timbre of a specific instrument.

As you go higher in the harmonic series the overtones become less prominent. The lower harmonics are much easier to hear.

Note when you play a harmonic that the whole string vibrates in equal parts. You can actually see it vibrate and see the nodes at which it doesn't vibrate. It's pretty cool. This is different than when you fret a string and only part of the string vibrates.
Si
#8
Thanks, great answer, though these are the parts I already knew or figured by now.

I think there's also a ~major 2nd harmonic; maybe you could give me an answer to this: as I already stated in my above comment, I figured out that the harmonics can be divided to halves that go an octave higher at each iteration. But is there any chance that the weaker or possibly barely audible harmonics are also integer divisions (other than 2) of the main harmonics of the string? For example, what would play if you'll pluck the "fifth of the fifth" (9th of the string's entire length according to your data)?
#9
I mean I studied this stuff pretty thoroughly for a thesis last year. But seriously you could just refer to this chart for the first 10, then work the rest out using the formula.

http://en.wikipedia.org/wiki/Guitar_harmonics

The ninth you mentioned is actually 2 octaves + a neutral second from the fundamental. It is coincidentally also the ninth harmonic in the harmonics series of a guitar.
#10
Quote by GoldenGuitar
I mean I studied this stuff pretty thoroughly for a thesis last year. But seriously you could just refer to this chart for the first 10, then work the rest out using the formula.

http://en.wikipedia.org/wiki/Guitar_harmonics

The ninth you mentioned is actually 2 octaves + a neutral second from the fundamental. It is coincidentally also the ninth harmonic in the harmonics series of a guitar.


Well, so it basically agrees with what I was suggesting! The fifth of the fifth is a second. I just went by 20Tigers' data of the (just) fifth happening at the 1/3 and contemplated whether then the 1/3 of the 1/3 would create a harmonic corresponding to a note of a fifth of a fifth.
#11
Quote by TLGuitar
Thanks, great answer, though these are the parts I already knew or figured by now.

I think there's also a ~major 2nd harmonic; maybe you could give me an answer to this: as I already stated in my above comment, I figured out that the harmonics can be divided to halves that go an octave higher at each iteration. But is there any chance that the weaker or possibly barely audible harmonics are also integer divisions (other than 2) of the main harmonics of the string? For example, what would play if you'll pluck the "fifth of the fifth" (9th of the string's entire length according to your data)?

Try playing harmonics on the first four frets. There are some pretty high pitched harmonics (and they are really close to each other). They may be hard to make ring out properly, but high gain distortion will help.

I think G string is the easiest string to play harmonics on.

The harmonic on approximately the 4th fret is the major third two octaves higher than the fundamental. It's the easiest harmonic to play after the octave, octave+5th and two octaves.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#12
Hah, I want to see if I got the math right... I made some formula to translate the fret number to its horizontal position along the string (I know you could simply measure the string... but just for the sake of it). I took a random integer (11) and divided the value of the whole string by it, and then matched it with a fret value, and it came up with about 1.656593; according to the Wikipedia article this integer should produce a tritone flattened from the equal temperament by 49 cents? Probably because it's so barely audible I can't find any guitar-related article mentioning this overtone.
#13
It should be slightly to the right of the middle of the second fret. I'll put up a recording of all the natural harmonics playable later tonight, if you'd like
Last edited by GoldenGuitar at Apr 19, 2015,
#14
Quote by GoldenGuitar
It should be slightly to the right of the middle of the second fret. I'll put up a recording of all the natural harmonics playable later tonight, if you'd like


Well, what I got is just below one and two thirds of a fret, but when I measured the length of my E string from the nut to the bridge and divided it by 11 it came up with a length slightly longer than what the formula would get on my guitar's frets... Maybe it's because the frets are probably corrected for the bending you apply onto a string when fretting it and end slightly behind than where they would on a perfectly straight string?