Audio harmonics.

Can someone explain to me precisely what harmonics are, and the technical differences between even and odd numbered harmonics?

Are you familiar with normal modes in oscillating systems? Harmonics are simply different normal modes. The lowest possible mode is the "fundamental" or "first harmonic." The next excited mode is the "second harmonic" and so on. In stringed instruments these are different transverse waves on a string. In wind instruments these are different longitudinal compression waves in air. The numbers simply label the different modes, there is not any other technical difference.

It so happens, that by their construction some instruments do not support exciting certain modes. For instance, flutes and saxophones can only sustain fundamental tones and even harmonics. This why the first register change (from the 1st to 2nd harmonic) in these instruments skips an octave. By contrast, the clarinet only allows the fundamental and odd harmonics, which is why its first register change (from the 1st to 3rd harmonic) skips a major twelfth instead of an octave. But that has to do with the physical differences (specifically, the boundary conditions) of the instruments. Odd or even, modes (harmonics) are just modes (harmonics).

I'm a total layman when it comes to practically all branches of physics, so no I don't know about normal modes or oscilating systems.

I'm not sure if you're familliar with different types of amplification or not, but largely vaccumm tube aplifiers are considered worlds better thans solid state amplifiers, the only scientifical reason i can find for this is that tubes create even harmonics and Solid state creates odd number harmonics (didn't know what it meant, so I asked here). Does the harmonic being even/odd nessicarily make something sound better (or remarkably different?) or are there other things in play with tube amps vs. solid state amps?

At very simplified level you could think of harmonics as a byproduct of main sine frequency, that is multiple of the main sine. It appears always along with distortions in amps, and harmonics goes as 1,2,3,4,5,6,7... where odd and even is obvious.

Issue with odd harmonics is that they are perceived as least pleasant by humans, while even harmonics "seem" more natural. (sorta unadjusted instrument vs adjusted instrument playing a chord) Human ear is less sensitive to even harmonics (as they sound more like "chords"), thats why vacuum tube amps are perceived as sounding softer. Technically they might be much worse (like 1-2% THD).

There are some more specifics of tubes that makes use of them much simpler, but that would be quite difficult to explain.

ps. it could fit better into engineering forums

OK, I am not too familiar with audio amplification equipment. I have also heard that tube amps are preferred, but I have never heard that it is because analog amps produce even harmonics and electronic devices produce odd ones (I am a little dubious of this claim).

What I will say though, is that the harmonics that are present give tones their character, or timbre. You may have heard pure tones, with no harmonics (overtones) present. They sound like sterile beeps (think of a Moog synth tone). What is the difference between, say, a saxophone and a clarinet's sound when they are playing "the same pitch?" When a sax and a clarinet play the same note, the sound is different because, in addition to the fundamental note played, each instrument also adds other pitches (harmonics) in different amounts. These additional pitches give the overall sound its individual character, and make them sound different to your ear, even though they are both "middle C."

Edit To put it succinctly: Sounds produced by musical instruments are not beep-like pure pitches, they are really complicated chords. The upper notes in these "chords" are the harmonics, and the particular mix of these are what give instruments their characteristic sounds.

Again, I am skeptical that the reason you give (a simple even/odd dichotomy) is the reason some peope prefer tube amps. If that were really the case then analog amplification of a clarinet sound would leave only a pure tone, since all the clarinet overtones are odd harmonics. But this is not what happens. Faithful amplification means that you accurately amplify a sound -- it's fundamental and all of the harmonic overtones present (both even and odd). More likely in my mind is something along the lines of: electronic amps don't have the bandwidth to accurately amplify all of the harmonic overtones present in a complex sound. Maybe for a given price you can only get a digital amp to reproduce the first 7 or 8 harmonics, but subtle and nuanced parts of, say, a piano sound, might come from higher harmonics. In which case the digital amp would only be able to "throw away" these important higher harmonics, or amplify them by a disproportionate amount, and we would hear this as distortion.

But that's just my speculation; I will leave the rest to those who know.

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For those who aren't familiar with instrument amplification:

All amps are "electronic", Solid state amps are not digital, they are analouge along with tube amps. I really have no idea as to the real reason tube amps are so vastly preferred over solid state amps, I've merely heard that it has to do with the fact that tube amps produce even harmonics which are more pleasing to humans, just trying to verify and quantify that statement.

Perhaps tube amps simply emphasise even harmonics instead of only producing them?

Perhaps tube amps simply emphasise even harmonics instead of only producing them?
I just don't buy it. Original sounds to be amplified may have both odd and even harmonics. This is not up to the amp, it has to deal with whatever it gets. If an amp only emphasized even harmonics, then it would not be faithfully amplifying. In particular, any sound that consists mostly of odd harmonics would be distorted.

I don't think there is anything to the idea that odd or even harmonics are more or less pleasing to the ear, either. The second harmonic is at the octave, sure, but the third harmonic is at an octave plus a fifth, which is also considered "sonorous." Also, after more than a few harmonics, both odd and even harmonics are spaced extremely close together (ultimately, less than a semitone apart) and produce "dischordant" intervals.

Originally posted by wasteofo2
Can someone explain to me precisely what harmonics are, and the technical differences between even and odd numbered harmonics?

Somebody can, but I'm going to have a go at it.

Ah, well, unfortunately I'm still confused about a few things; but... A frequency that is faster than another frequency by a whole number multiple, 2 times as fast, 3 times as fast..., is called the harmonic of the original frequency. Take one frequency, say, 60 hertz. 60 times 2 is 120, so 120 hertz is the second harmonic of 60, and so on through 3, 4, 5, 6...

Are you familiar with destructive and constructive interference? If not, I first learned about it reading about holograms. Well, take one frequency and then combine it with one or more of its harmonics and they will add to or subtract from that original frequency. All the signals combine to create one big final signal that is shaped differently from the original. I hope that made sense. At any rate (har), it turns out that adding odd numbered harmonics to a signal tends to push it towards a saw tooth shape, so you get that harsh sawtooth sound.

That's all I know so far.

Originally posted by Vosh
I'm sorry, but it's just idiotic to come back with an abstruse answer like that to a question asked by a lay person. I've worked out a list of reasons why some ppl. behave this way: They don't really understand
I'm sorry, but its just stupid to jump on someone when you have no idea of what you are talking about.

I gave short and succint answer to the question. If you can't understand it, even after reading twice, ask.

Person coming from listening music and asking about tube amps is assumed to have rudimentary background to understand what is said without starting with a lecture.

BigRedDot,
you are talking about harmonics already present in the signal, which is what needs to be amplified. Distortion in amps means _addition_ of harmonics that were NOT there. It happens because electronic is not perfect. Tubes and Solid amps are not perfect in different ways, and that is reason why they produce different kinds of distortion harmonics. Tubes are more or less uncapable of adding odd harmonics, while Solids are more prone to produce exactly them.

This is true that some instruments have more odd harmonics, and that amps that add them where unappropriate, are bound to sound more sharp and unpleasant, because they are basically overamplifying what was there and also adding what wasn't there.
And that odd harmonics from distortions sound less pleasant than even harmonics has been established eons ago (heck, ask your grandma). One reason is exactly because there are less even harmonics in the original signal, thus what amps adds there simply doesn't stick out.

Perhaps tube amps simply emphasise even harmonics instead of only producing them?
wasteofo2, all amps are meant to reproduce input signal precisely. Distortion of signal happens due to imperfections. As Vosh has found out, distortions that make sinewave look more like sawtooth is adding odd harmonics (in reality its different from sawtooth, but idea would do).

Why this happens is question about electronics engineering, which is way beyond layman explanations.

Nevertheless, don't rush into buying a tube amp, its mostly attribute of hopeless audiophiles who refuse to consider their issues.

I probably over reacted. Have a hair trigger when I think someone is being unnecessarily abstruse (and this happens all too often and is practically an institution and it irritates me). Beg 'pardon.

I had to start over several times with my own answer because it is after all much much easier to explain by just drawing the sine wave as it appears on an oscilliscope and then adding the harmonics and then draw the final wave that results -- trying to describe all that verbally is tricky even though the actual basic concept is simple.

I am now wondering now if my modem kicks off periodically because of harmonics in the phone lines. Perhaps at certain times there are more ppl. in this apartment complex using their phones (or using appliances; would the mains effect the phones?) than at other times, building up the harmonic distortions that ruin the signal (I'm told that a little gap in the data stream makes the modem think it's supposed to hang up -- and *man* it's annoying!). Or old rickety wires perhaps could create these harmonics... I feel like I'm on Star Trek...

Originally posted by BigRedDot
OK, I am not too familiar with audio amplification equipment. I have also heard that tube amps are preferred, but I have never heard that it is because analog amps produce even harmonics and electronic devices produce odd ones (I am a little dubious of this claim).

Solid state devices have distortion characteristics that result in even harmonics being produced while tube amplifiers have distortion characteristics that result in odd harmonics. This is true for every single pure tone that is input into the amp. If you put in a flute sound or a clarinet sound then each harmonic of the sound while suffer some distortion.

Again, I am skeptical that the reason you give (a simple even/odd dichotomy) is the reason some peope prefer tube amps. If that were really the case then analog amplification of a clarinet sound would leave only a pure tone, since all the clarinet overtones are odd harmonics. But this is not what happens. Faithful amplification means that you accurately amplify a sound -- it's fundamental and all of the harmonic overtones present (both even and odd).

You are right. Any decent amplifier will produce all the harmonics of the sound input to it. The distortion caused by the amplifier is additional harmonics caused by its imperfections. All the overtones are reproduced but each tone suffers some distortion. Since the distortion increases with signal amplitude, the strongest tones suffer the most distortion.

The difference in tube vs. transistor distortion is often held up for the reason many people prefer tube amps. I don't think that's the whole story although I do prefer tube amps for my guitar.

If you put in a flute sound or a clarinet sound then each harmonic of the sound while suffer some distortion.
Ok that makes perfect sense. Thank you for the clarification.

Originally posted by BigRedDot
I just don't buy it. Original sounds to be amplified may have both odd and even harmonics. This is not up to the amp, it has to deal with whatever it gets. If an amp only emphasized even harmonics, then it would not be faithfully amplifying. In particular, any sound that consists mostly of odd harmonics would be distorted.

When I'm referring to amplifiers, I mean instrument amplifiers, not stereo speakers or anything. Instrument amplifiers goal is not to faithfully reproduce the exact sound coming from the instrument, but to be a sort of extention of the instrument and add it's own tone to it. If you play the same instrument through different kinds of amps it will sound very different, which is why there is such a large variety of different amplifiers, becuase people like different tones for their instruments.

Originally posted by wimms

wasteofo2, all amps are meant to reproduce input signal precisely. Distortion of signal happens due to imperfections. As Vosh has found out, distortions that make sinewave look more like sawtooth is adding odd harmonics (in reality its different from sawtooth, but idea would do).

Nevertheless, don't rush into buying a tube amp, its mostly attribute of hopeless audiophiles who refuse to consider their issues.

Either I'm misunderstanding your point, or you're just plain wrong in saying "all amps are meant to reproduce input signal precisely". Any given amplifier company will have many different models which are supposed to have distinct tonal qualities.

I was always under the impression that distortion of a signal (at least in the sense of distortion used in heavy metal recordings) was caused due to the fact that the signal being fed into the amp was too great and the amp needed to compress the signal, kind of like if you have an image and make it smaller using MS paint the quality will go down.

As a confessed audiophile, tube amps are the only amps for me. They're louder than solid state amps with the same size speaker and wattage, they're much more easy to customize and, at least to me, they sound much better as a whole.

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Originally posted by wasteofo2
Either I'm misunderstanding your point, or you're just plain wrong in saying "all amps are meant to reproduce input signal precisely". Any given amplifier company will have many different models which are supposed to have distinct tonal qualities.
You are confused. Function of amp is to have precise amplification. You are talking about something else. Of amps that sound very differently one is pile of crap. Perhaps musicians call about anything that draws power an amp.

As a confessed audiophile, tube amps are the only amps for me. They're louder than solid state amps with the same size speaker and wattage, they're much more easy to customize and, at least to me, they sound much better as a whole.
Oh. Though, "sound much better" is typically achieved by pulling bass and treble to the sky in these rings. If its more important that it sounds good instead of right, then sure.
Though, with really good amps you'd starve before you could note any difference.

Originally posted by wimms
You are confused. Function of amp is to have precise amplification. You are talking about something else. Of amps that sound very differently one is pile of crap. Perhaps musicians call about anything that draws power an amp.

The following are clips of the same person, playing the same song, with the same guitar and amp, the only difference being the speakers used in the amp. I don't know if maybe my ear is more delicate than yours, but I can hear a very noticable difference between the seperate recordings, though none sound like crap.
http://members.cox.net/savage/tmp/ShivaV30.MP3
http://members.cox.net/savage/tmp/ShivaGreenback.MP3
http://members.cox.net/savage/tmp/ShivaCL80.MP3
http://members.cox.net/savage/tmp/ShivaV30.MP3

If you have any guitarist friends, ask to go to a guitar shop with them and have them try out a fender amp and then a mesa boogie amp of simmilar wattage with the same guitar and have the amps set simmilarly, Perhaps you won't hear a difference, but the guitarist probabally will.

If you are a guitarist and still maintain that all good amps sound the same, then either your perception of what a "good amp" is is very very particular and you only like one particular sound, you don't have a refined ear for tone, or you haven't heard many different amps in your life.

Originally posted by wimms

Oh. Though, "sound much better" is typically achieved by pulling bass and treble to the sky in these rings. If its more important that it sounds good instead of right, then sure.
Though, with really good amps you'd starve before you could note any difference.

I actually hate that scooped (prominant lows and highs) sound and prefer something more mid oriented.

I just don't see how you can say that good amps will all sound the same, especially considering any "good" amp company will have many different models all designed to sound unique. Again, go try out a fender then a mesa boogie, both are highly regarded and both sound ridiculously different

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You are talking about different thing. What you call amp is really "Guitar Amp" thats far from being simply amplifier. I don't know what they do with signal to achieve different sounds, but I can assure you that its not general state of all audio amplifiers to sound differently, and I'm pretty convinced that they have something else besides amp inside the units you test that actually are responsible for differing sound.

What you call "good amp" and what I mean by "good amp" are different things, apparently. Amplification is a function of increasing input signal by amount of some gain factor. There is only ONE way to do it right, so that output signal is related to input signal exactly by factor of N. Any deviation, and its called distortion. What you seem to call "good amp" is really "tasteful distortion", ala that same "overdrive" thingy used in heavy metal.
What I meant by "crap amp" was not "crap sound", these things are separate. I meant that the amp deviated from precise amplification.

So, in my dictionary, "good amp" means that which represents input signal precisely. And two good amps have to be damn similar in that. Thus if you have really good amps to listen, it must be damn hard to make a difference. And thats reality in audio amps.

Hope that clarifies confusion.

Integral
Staff Emeritus
Gold Member
This has really turned into a discussion best dealt with by the Engineers, so off to engineering we go.

As to why odd harmonics are "less pleasing" then even. In Fourier Analysis the sum of all odd harmonics produces a square wave. It is generally true that the human ear and psychic prefer "smooth" variations rather then abrupt ones. So if for some reason the electronics emphasize odd harmonics over even the result will be a final wave form which is approaching a square wave, thus less pleasing to the ear.

The connection between odd harmonics and square waves goes both ways, in the electronics if there is anything that attempts to cause a step function change (that is a square wave form) it will instead add odd harmonics to the signal. The more abrupt the transition the more odd harmonics that will be created.
Keep in mind that electronic devices maintain a continuous signal, by continuous here I am referring to a mathematical definition of continuity. This means a picture of the signal can be drawn without picking up you pencil and that it is always moving forward with time. In other word perfect square waves are NOT allowed. Any attempt at a square wave results in many (as in high n) odd harmonics.

We must separate Heavy Metal from main stream when it comes to sound amplification. In Heavy Metal distortion is a desirable feature. I would bet that the signal is over driven at every possible step of the way. Over driving an amp tends to induce clipping, which results in square waves, thus odd harmonics.

Now with this in consideration, I am surprised that you prefer the the tube amp and its tendency to favor even harmonics (as you claim) as this would tend to damp out the odd harmonics you are attempting to force. Hummm....

What you seem to be saying is that the solid state amp reproduces the effects I am trying cause TO FAITHFULLY.

Perhaps some of the engineering types can add to this.

Originally posted by Integral

We must separate Heavy Metal from main stream when it comes to sound amplification. In Heavy Metal distortion is a desirable feature. I would bet that the signal is over driven at every possible step of the way. Over driving an amp tends to induce clipping, which results in square waves, thus odd harmonics.

Now with this in consideration, I am surprised that you prefer the the tube amp and its tendency to favor even harmonics (as you claim) as this would tend to damp out the odd harmonics you are attempting to force. Hummm....

What you seem to be saying is that the solid state amp reproduces the effects I am trying cause TO FAITHFULLY.

Perhaps some of the engineering types can add to this.

This is just a guess, but perhaps why I find tube amps to give a better distorted sound is that it's more evenly balanced between even and odd harmonics, while a solid state amp would heavily favor odd harmonics.

Integral
Staff Emeritus