Harmonics vs. Chord Tones

[Rockin Mike]

This may turn out to be embarrassingly simple, but I have not been able to wrap my head around it.

Correct me if I'm wrong, but as I understand it:
A note, tone, pitch, whatever you call it, is a vibration at a frequency. In the real world they are usually complex waveforms comprised of several frequencies related mathematically.

A pure wave with no complex additive frequencies sounds like a sine wave, a tuning fork, a theremin. A bass string, on the other hand, is rich with additive frequencies (overtones, harmonics) and we generally debate which brand of strings has the most pleasing set of those harmonics.

Why are these other frequencies not perceived as separate notes? Why is that complex waveform not perceived as a chord?

As I understand it a chord is two (or more) notes, i.e. mathematically related frequencies, vibrating at the same time. Same definition as a single note with overtones (or harmonics, or timbre, or whatever you call it).

Same definition, two completely different sonic animals. Why?

[Vince Klortho]

A single bass note has additive frequencies called harmonics and each of those harmonics are at a frequency that is an even multiple of the fundamental frequency. For example, the low E on a bass (E1) is at approximately 40Hz. It's actually at 41 but for simplicity let's say it's 40. When you play the low E the frequencies of the harmonics will be at 80, 120, 160, 200, 240, 280, 320, etc. It is the balance of the note's fundamental frequency and its harmonics that determine the tone of the instrument.

When a chord is played there are multiple notes which are usually not an octave apart so their fundamental frequencies are not an even multiple of the lowest note. This is how they are distiguishable as separate notes. If you play two notes an octave apart that is a simple chord but sometimes they are not distinguishable as separate notes because it sounds like one really fat note and that is because the frequencies are even multiples of each other.

[HolmeBass]

In a chord, each ringing note has a harmonic series, and the interactions of those harmonics help the ear differentiate it as two notes.

I am pretty sure a tuning fork rings with a harmonic series of overtones, too.
http://www.acs.psu.edu/drussell/Publ...ssell-Fork.pdf

[Mushroo]

I love this kind of question! The basic reason is that our brains have this really cool ability to reduce or simplify all of those different harmonic pitches into a single sound that we can process as one thought. Otherwise we would have a hard time understanding each other's voices, for example, if we heard all of the various harmonics/overtones as separate sounds. (As an aside, there are throat singers in Tuva who have actually figured out how to undo this, and make the harmonics of their voice sound like a chord of separate notes!) Or if a predator was chasing us, we'd hear a dozen different cats of all different sizes chasing us, instead of our brain realizing that sound is one BIG cat with lots of rich overtones in its growl! It's an especially neat cognitive ability because of how the different frequencies disperse through the air; for example we can perhaps deduce someone's location based on whether their voice sounds muffled, or tinny, or echoey!

I think this is a skill that some people have better than others, and that can be improved with practice. For example an expert classical musician might hear every instrument in a symphony moving in intricate counterpoint, whereas a layman would hear only an overall tonal "color" evoking an emotional response. My experience is similar to Vince's that I sometimes have trouble distinguishing an octave as two separate notes.

[Rockin Mike]

Harmonics are all octaves?
I know I can get a fifth by touching my string 2/3 of the way down it's length.
Also I know the range of my hearing is only a few octaves. If all overtones (harmonics, whatever) were an octave apart there would be darn few of them available to color notes, and would not explain the large (huge, infinite) range of tone qualities in the world.

Mushroo's point about how we evolved to perceive a pitch+overtones as a single note is interesting, but still doesn't explain how the brain knows when to classify something as a single pitch+overtones versus a chord.

I have heard singers who can apparently produce a chord. Some of David Lee Roth's stuff is like that.

Maybe it's like those optical illusions where if you stare at it a certain way it appears to be something else. I wonder if somebody with a synth could produce something that sounds like a note, then tweak it a little and make it jump out at you as a chord.

Thanks all for the responses, very interesting and I think I have a better (though still incomplete) grasp on the topic.

[Vince Klortho]

No, harmonics are not all octaves. If we use the E1 note again at an approximate 40Hz, the octaves of E will be at 80, 160, 320, and 640Hz. There is a doubling of frequencies. Harmonics are even multiples as you can see here. The harmonics of E will be at 80, 120, 160, 200, 240, 320, and 360Hz. There are some harmonics that are not octaves - not a doubled frequency.

By the way, when you look at the first picture on that page there is an interesting relationship that can be seen. The number of the harmonic is also the number of nodes the wave has. The first harmonic has one node and double the base frequency. The second harmonic has two nodes and is three times the base frequency. The nodes are the intersecting points of the wave.

Here's another interesting page. It lists the frequencies for musical notes and you can see the doubling of frequencies with the octaves. You can also correlate the frequencies of harmonics with what notes they are. For example, being precise this time, for the E1 at 41Hz its second harmonic is at 123Hz and that is a B. If you play these notes on the guitar you can hear that.

[mambo4]

Perhaps 2 + notes simultaneous produce wave interferance patterns in which we recognize chords. Just a guess.

[bander68]

Brass instruments function purely around what you're talking about. It's called the Overtone Series. Put simply, a trumpet only has 3 valves, and therefore only a handful of combinations. In order to play more than 7 or 8 notes, brass players play on the next level, or "partial" of the overtone series. At that point, they repeat the same finger patterns to get all of the notes in between. A standard Bb trumpet has an exact set of partials when played without pressing any of the valves. Those are (1st thru 8th partial): C, C, G, C, E, G, Bb, C. In the lower range, the notes of the overtone series are farther apart. As you go up, those notes get very close together.

What does this have to do with bass string overtones? Everything. Those overtones are the exact same intervals as a trumpet's. These tones occur in nature. Have you ever heard the wind blowing and making a tone when whistling thru a fence, or grabbed a piece of grass and put it between your thumbs and blown to make a noisemaker? Same intervals. Those plastic tubes you swing around to make noise - if you swing them faster, they'll pop up to the next tone in the Overtone Series.

Here's the wiki version of it.

http://en.wikipedia.org/wiki/Harmonic_series_(music)

[mambo4]

the OP's question is not "what are overtones"

the question is "if overtones are simultaneous vibrations, and chords are also simultaneous vibrations, the why don't overtones sound like chords?"

[Mushroo]

Originally Posted by mambo4

the OP's question is not "what are overtones"

the question is "if overtones are simultaneous vibrations, and chords are also simultaneous vibrations, the why don't overtones sound like chords?"

Because our brains contain the "auditory processing software" to recognize the standard overtone series caused by a vibrating object.

[Ezmar]

Has nobody mentioned the issue of relative volume? The fundamental is the strongest tone, and the overtones are significantly weaker, and it's the relative balance if these that creates timbre.

Bells actually can have overtones stronger than the fundamental, which gives them a unique sound.

[Vince Klortho]

For the bass usually the first harmonic is stronger than the fundamental. Read the first page of this article and have a look at this page also.

[bander68]

Originally Posted by Ezmar

Has nobody mentioned the issue of relative volume? The fundamental is the strongest tone, and the overtones are significantly weaker, and it's the relative balance if these that creates timbre.

Bells actually can have overtones stronger than the fundamental, which gives them a unique sound.

Bingo! Which is why I brought the explanation of overtones up. Unfortunately I was pressed for time when I wrote the other post and stopped.

Another thing to consider is the distance between them. The nearest tone to the fundamental is an octave away, and that won't be a chord. then another 5th to the 5th. The 3rd, which would give the chord sound our ears would recognize is a full 17 th from the fundamental, and it's the 5th toneof the overtone series. It would be too weak to balancewiththe fundamental.

[Vince Klortho]

No, it is NOT bingo ! It is WRONG. The fundamental frequency is not the strongest one of the note. Read the two links I posted.

[Jazz Ad]

Originally Posted by Rockin Mike

Harmonics are all octaves?
I know I can get a fifth by touching my string 2/3 of the way down it's length.

No but they are all at least an octave away from the root, which is the lowest note of the series, not the strongest.
The 3rd harmonic (what you get by dividing the string in 3 equal parts) is an octave+a fifth.

Originally Posted by Vince Klortho

For the bass usually the first harmonic is stronger than the fundamental.

2nd harmonic. The 1st harmonic IS the fundamental.

[onlyclave]

Originally Posted by mambo4

the OP's question is not "what are overtones"

the question is "if overtones are simultaneous vibrations, and chords are also simultaneous vibrations, the why don't overtones sound like chords?"

Because the overtones are lower in amplitude and give the fundamental it's timbre. Two fundamentals add together to create a chord and their overtones create the timbre.

"Harmonic" probably shouldn't be used in this context.

[JoeWPgh]

Think of it like paint. Almost any colors will have a touch of red in them when you look at mix charts. But a color only looks red when it looks red. The fundamental is the overriding tone you hear, so that's what that note is. The overtones, or harmonics are subtle ingredients to the tone of a note. To make a chord out these overtones/harmonics would require an extreme saturation of them - like adding more tint to paint until it looked red.

[Rockin Mike]

Originally Posted by onlyclave

Because the overtones are lower in amplitude and give the fundamental it's timbre. Two fundamentals add together to create a chord and their overtones create the timbre.

"Harmonic" probably shouldn't be used in this context.

So, there would be some threshold at which the ear would have a hard time discerning whether it's a tone+overtone or a chord. Some bells are like that.

Interesting.

[Rockin Mike]

Originally Posted by JoeWPgh

Think of it like paint. Almost any colors will have a touch of red in them when you look at mix charts. But a color only looks red when it looks red. The fundamental is the overriding tone you hear, so that's what that note is. The overtones, or harmonics are subtle ingredients to the tone of a note. To make a chord out these overtones/harmonics would require an extreme saturation of them - like adding more tint to paint until it looked red.

That is a very interesting analogy. Our brain differentiates light into 7 basic colors for no good reason. It also differentiates pitch into 7 basic (diatonic) notes derived from frequencies a perfect fifth apart, the 5th being the lowest overtone that is not actually an octave (same note).

[bander68]

Originally Posted by Vince Klortho

No, it is NOT bingo ! It is WRONG. The fundamental frequency is not the strongest one of the note. Read the two links I posted.

I just read them. Fascinating! I love being wrong and learning something new. I know this is a bass forum, but it has me wondering if that also explains why brass instruments consider all of their fundamental pitches to be impractical for use in most music. Sorry, they're interconnected since I'm a brass player first and just learning bass.

This changes my perception of overtones, although I'm not sure what i can do with it. I still think they're too far apart to hear any sort of chord produced, but they most definitely are part of what our ears hear without realizing it. An absence of those overtones- would it even sound like music anymore? The timbre would be completely altered.