How is it exactly that harmonics... work?

[funkygroover694]

im an avid user of harmonics, love using them in live shows and steal a lot of jacos stuff xD, but i still dont entirely understand how harmonics... work

why is it for example that a harmonic on the first D on the A string and a harmonic on the first A of the D string will sound the same? why is it that a harmonic on the fourth fret of the G string and on the ninth fret of the G string also sound the same?

why is it the higher the note is on the fretboard the lower the pitch of the harmonic? why is it that on sheet music a harmonic that if fretted would be for example a C, but on sheet music the note is notated as a G when played as a harmonic?

dont neccesarily want specific answers for all of these questions, but rather im just using them as guidelines.

so someone please help explain this all to me

thanks!

 

[groooooove]

really its just the overtone series, as far as i understand..

just google "overtone series"

that will probably explain a lot of it.

 

[BassyBill]

why is it that a harmonic on the fourth fret of the G string and on the ninth fret of the G string also sound the same?

why is it the higher the note is on the fretboard the lower the pitch of the harmonic?

The second part of this quote is incorrect, as will be obvious if you think about the first part.

This link will answer all of your questions about harmonics - very detailed info and well presented, too.

Invalid Link Removed

 

[funkygroover694]

The second part of this quote is incorrect, as will be obvious if think about the first part.

This link will answer all of your questions about harmonics - very detailed info and well presented, too.

Invalid Link Removed

lol im stupid. but thank you for the link, ill read that once i have a chance.

 

[JTE]

Quick 'n' dirty- but read the link to find the whole thing- is that the string vibrates in sections. When you play an open string, you have the fundamental pitch of the open string from the string vibrating from the nut to the bridge. But there are also waves that divide the string in different sections. When you touch the string at a node, any of the sections that are bigger than that node are damped so the node rings out. That's why the pitch at the 7th fret and 19th fret are the same pitch- they're dividing the string in thirds. Same reason the 5th and 24th are the same- they're dividing the string in quarters (and if you have the 5th fret harmonic ringing, touching the string at the 12th fret doesn't change anything- it's a node that does two divisions).

John

 

[Intenzity]

Magnets - How do THEY work?

 

[ChrisPbass]

Magnets - How do THEY work?

LL

 

[Erick Lam]

When you play a note, you get a fundamental and the harmonics "on top". When you play an harmonic, you basically get rid of the fundamental and any other harmonic below the played harmonic.

The harmonics are located where the string is divided in equal length.

So you divide the string in half, you get the octave of the fundamental.
Divide in 3, you get a 5th and it's found in two spots.
Divide in 4, another octave. It should be found in three spots but one of those is located at half length so you get the lower octave of the first harmonic instead.

And it keeps going...

1/5 = third
1/6 = octave
1/7 = minor seventh
1/8 = octave
1/9 = ninth
1/10 = third
1/11 = #eleventh
1/12 = fifth

And so on... but the higher you go, the harder it is to make them ring.

You might notice that the 7th harmonic is slightly lower in pitch than the seventh when fretted (the note F in relation to G). That's equal temperament for you. Same for the #eleventh, but that one it pretty hard to produce.

The so-called "false harmonics" work the same way. The only difference is that you create a new fundamental by fretting a note and it's a bit more complicated technically.

Here are two good pictures from Wikipedia that illustrate them: http://en.wikipedia.org/wiki/File:Moodswingerscale.svg
http://en.wikipedia.org/wiki/File:Flageolette.svg

 

[projectMalamute]

When you play a note, you get a fundamental and the harmonics "on top". When you play an harmonic, you basically get rid of the fundamental and any other harmonic below the played harmonic.

The harmonics are located where the string is divided in equal length.

So you divide the string in half, you get the octave of the fundamental.
Divide in 3, you get a 5th and it's found in two spots.
Divide in 4, another octave. It should be found in three spots but one of those is located at half length so you get the lower octave of the first harmonic instead.

And it keeps going...

1/5 = third
1/6 = octave
1/7 = seventh
1/8 = octave
1/9 = ninth
1/10 = third
1/11 = #eleventh
1/12 = fifth

And so on... but the higher you go, the harder it is to make them ring.

You might notice that the 7th harmonic is slightly lower in pitch than the seventh when fretted (the note F in relation to G). That's equal temperament for you. The 11th harmonic is also higher than the tempered #11.

The so-called "false harmonics" work the same way. The only difference is that you create a new fundamental by fretting a note and it's a bit more complicated technically.

Here are two good pictures from Wikipedia that illustrate them: http://en.wikipedia.org/wiki/File:Moodswingerscale.svg
http://en.wikipedia.org/wiki/File:Flageolette.svg

This is all more or less right. Couple of things:

-that list of the upper harmonics has some mistakes, should look like this:

1/5 = third
1/6 = fifth
1/7 = (very flat) minor seventh
1/8 = octave
1/9 = ninth
1/10 = third
1/11 = (very, very flat) #eleventh or (very, very sharp) fourth
1/12 = fifth

-the harmonics are more than a little bit out of tune compared to an equal tempered scale. Any of the thirds are a good 14 cents flat. The 11th overtone is 49 cents flat compared to a tempered #11. That's a full quartertone, or almost exactly half way between a 11 and a #11. The minor 7th is a good third of a semitone flat.

Here's a good link:
http://en.wikipedia.org/wiki/Harmonic_series_(music)

 

[Erick Lam]

Oops! My mistake. I edited my post so it reads correctly the first time. I mixed the #11 with major seventh which is sharper then the tempered scale. The only thing though, is the fretless player in me would say it's the tempered scale that is out of tune, not the other way around. Damn frets!

 

[Rob22315]

Something else to think about - if all you heard was the fundamental note - you'd find it very plain and boring. It's the harmonics that adds richness to the sound.

 

[namraj]

Something else to think about - if all you heard was the fundamental note - you'd find it very plain and boring. It's the harmonics that adds richness to the sound.

If you play a harmonic all you are hearing is the fundamental note? It's a stationary wave oscillating at only one frequency, or so is my understanding.

 

[Rob22315]

If you play a harmonic all you are hearing is the fundamental note? It's a stationary wave oscillating at only one frequency, or so is my understanding.

Mostly - more so than a plucked string. That's why the tone is more bell-like but it's still not completely pure.

 

[namraj]

Mostly - more so than a plucked string. That's why the tone is more bell-like but it's still not completely pure.

Thats just semantics, as near as damn it, it's a pure note, theoretically it should be totally a pure note, and practically at loud enough volumes can be used to vibrate other things and if that coincides with the natural frequency of the object can be used to cause catastrophic failure. Then again so can a non-pure frequency but a pure frequency would work better because other harmonics in the note could cause phasing issues.

Also with regards to the fundamental note being "boring" I disagree, as most sounds we hear are a combination of frequencies, what can be more exciting than a single individual frequency.

Also I think the OP was asking about Harmonics as in Stationary Wave harmonics, not the harmonics caused when playing a fretted note, which do, I agree add "richness" to a note, but don't make it any less "boring".

 

[funkygroover694]

When you play a note, you get a fundamental and the harmonics "on top". When you play an harmonic, you basically get rid of the fundamental and any other harmonic below the played harmonic.

The harmonics are located where the string is divided in equal length.

So you divide the string in half, you get the octave of the fundamental.
Divide in 3, you get a 5th and it's found in two spots.
Divide in 4, another octave. It should be found in three spots but one of those is located at half length so you get the lower octave of the first harmonic instead.

And it keeps going...

1/5 = third
1/6 = octave
1/7 = minor seventh
1/8 = octave
1/9 = ninth
1/10 = third
1/11 = #eleventh
1/12 = fifth

And so on... but the higher you go, the harder it is to make them ring.

You might notice that the 7th harmonic is slightly lower in pitch than the seventh when fretted (the note F in relation to G). That's equal temperament for you. Same for the #eleventh, but that one it pretty hard to produce.

The so-called "false harmonics" work the same way. The only difference is that you create a new fundamental by fretting a note and it's a bit more complicated technically.

Here are two good pictures from Wikipedia that illustrate them: http://en.wikipedia.org/wiki/File:Moodswingerscale.svg
http://en.wikipedia.org/wiki/File:Flageolette.svg

hehe i actually found artificial or "false" harmonics easier to perform than natural harmonics when i was learning, oddly enough. but thanks for the explanations and links everybody, its awesome to finally understand a technique after 5 years xD

 

[Rob22315]

Thats just semantics, as near as damn it, it's a pure note, theoretically it should be totally a pure note, and practically at loud enough volumes can be used to vibrate other things and if that coincides with the natural frequency of the object can be used to cause catastrophic failure. Then again so can a non-pure frequency but a pure frequency would work better because other harmonics in the note could cause phasing issues.

Also with regards to the fundamental note being "boring" I disagree, as most sounds we hear are a combination of frequencies, what can be more exciting than a single individual frequency.

Also I think the OP was asking about Harmonics as in Stationary Wave harmonics, not the harmonics caused when playing a fretted note, which do, I agree add "richness" to a note, but don't make it any less "boring".

No, it's not semantics. Perhaps you've never heard a pure sine wave which is all that's left when you get rid of the extra frequencies. Listen to one and you'll find it lacks any character or depth. If every instrument only produced a sine wave, they'd all sound identical.



The act of plucking a string, either normally or as a harmonic creates harmonics. Sounds like you might have enough background in electrical engineering to have been through a fourier analysis of a step function or impulse function so you already know this?


Yes, the OP was talking about the playing technique for harmonics, not harmonics in general but I thought the sidebar was worth mentioning.

 

[funkygroover694]

yeah as far as my knowledge goes, every time you play a note you have the base note or fundemental, and then overtones of multiples of the frequency over that note, and the volume of these overtones allows you to distinguish instruments and such. if you could get a series of speakers that could produce a single overtone by itself, then by adjusting there volume and such you could make the sound of any note on any instrument. this is called timbre

 

[namraj]

No, it's not semantics. Perhaps you've never heard a pure sine wave which is all that's left when you get rid of the extra frequencies. Listen to one and you'll find it lacks any character or depth. If every instrument only produced a sine wave, they'd all sound identical.



The act of plucking a string, either normally or as a harmonic creates harmonics. Sounds like you might have enough background in electrical engineering to have been through a fourier analysis of a step function or impulse function so you already know this?


Yes, the OP was talking about the playing technique for harmonics, not harmonics in general but I thought the sidebar was worth mentioning.

I'm a civil engineer (student), And I have heard a pure sine wave, and ok so a harmonic doesn't sound quite like an electronicly produced sine wave, but it is pretty close, as close as naturally possible with out the use of very carefully programmed oscillators.

I'm not sure what the fourier analysis of a step function or impusle is, I will look it up.

 

[Rob22315]

I'm a civil engineer (student), And I have heard a pure sine wave, and ok so a harmonic doesn't sound quite like an electronicly produced sine wave, but it is pretty close, as close as naturally possible with out the use of very carefully programmed oscillators.

I'm not sure what the fourier analysis of a step function or impusle is, I will look it up.

It's been a while (as in close to 30 years) but IIRC, an impulse applied to a resonating element like a guitar string results in a sine wave at the fundamental frequency and a series of harmonics at multiples of the fundamental with exponentially decreasing amplitude. The fourier analysis is the math that lets you calculate that frequency response or, in other words, translate from a signal represented in time to that same signal represented frequency. When I was an engineering student, the mechanically oriented folks had a course with similar mathematics but applied to mechanical systems. For us EEs, it was Signals and Systems.

 

[namraj]

It's been a while (as in close to 30 years) but IIRC, an impulse applied to a resonating element like a guitar string results in a sine wave at the fundamental frequency and a series of harmonics at multiples of the fundamental with exponentially decreasing amplitude. The fourier analysis is the math that lets you calculate that frequency response or, in other words, translate from a signal represented in time to that same signal represented frequency. When I was an engineering student, the mechanically oriented folks had a course with similar mathematics but applied to mechanical systems. For us EEs, it was Signals and Systems.

We cover similar maths in Dynamics, although we don't look at isolating fundamentals.