understanding Harmonics

Hi All,
I hope some one with a bit of experience can help me on this one.I,ve been studying music theory for the last year and I,m trying to put some of this knowledge into sound production.
I looked at the Hamonic series for example and I can see that after the fundamental,comes the Octave,then the Fifth then the second octave etc etc until the cows come home.
Is this the same principle people are talking about when they use synthesizers to make their own sounds ?.Eg when peope say this sound contains al the Odd Harmonics (is that square or sawtooth I can,t remember) they really saying
F 1 3 5 7
F The Octave The Fifth Mayor Third Flattened seventh

Or am I overcomplicatng this ? (Wouldn,t be the first time !)
Appreciate any startng advise on this,then I,ll look a bit further into it,
Cheers,
kev

A harmonic is simply a sine wave whose frequency is some multiple of another sine wave. A 2KHz tone, for example, could be thought of as the second harmonic to 1KHz. 3KHz would be the third harmonic, and so on.

Complex waveforms - any complex waveform, no matter how complex (let's see how many times I can use "complex" in a sentence) can be mathematically broken down into some number of constituent sine waves. A square wave, for example, consists of a fundamental frequency and a bunch (theoretically infinite but practically a "whole lot") of odd harmonics. A sawtooth waveform, on the other hand, is comprised of a fundamental and a whole bunch of even harmonics.

A waveform that is comprised mostly of even harmonics (2x, 4x, 8x... the fundamental) has a distinctively different sound than one that is rich in odd harmonics. Some sounds have both even and odd harmonics, and they sound different still. It is primarily the ratio of harmonics that give any sound its tonal character.

Natural sounds typically have, in addition to lots of harmonics, many frequencies that are not harmonically related to the fundamental. That's the tipoff in our heads that a sound is synthesized rather than sampled -- we are subconsciously aware of the simplicity of a sound that lacks nonharmonic content and associate it with fake sounds.

The relationship between notes on the piano and harmonics is complex (I like that word). None of the notes in a given scale are actually harmonics of one another, but the nice sounding combinations (e.g. root + fifth) are harmonically related in a roundabout way. I forget right now what it is, but it's something like the third harmonic of the root is also the second harmonic of the fifth, or something like that. Whatever it is, there is a physical reason why the root, third and fifth sound good together. It's because some of their harmonics are harmonically related. Whew, that's a mouthful.

Hope any of this made sense, Kev.

An octave is twice the frequency, a fifth is 1.5 times the frequency, and so on. But piano tuning is fudged a little so it sounds equally in tune or out of tune regardless of which key you play in.

Complex yet simple at the same time.

The differance between sounds that are synthesized electronically and sounds that are 'natural' is that a synthesizer can recreate a natural sound at one pitch and at one volume level. Then this same sound including all the overtones is transposed up and down the keyboard so you get the chipmunk effect. To get different volume levels the synth plays back the same sound with the same overtones at different volumes. While with an acoustic instrument every note produces a different ratio or 'mix' within the overtones. Lower notes have less fundamental, more overtones, higher notes have more fundamental with fewer overtones. Each string on a guitaar produces a differnt mix of overtones. Notes played soft have more fundamental and less overtones, while notes played loud have both more fundamental and more overtones. Down picked notes have overtones differnt from up picked notes, finger plucked notes, muted notes, etc etc. So you can see on an acoustic instrument the type of overtones produced can have thousands - millions - of different values depending on pitch and volume and playing style. And a good guitarist is actually controlling which of these overtones happen when, in real time, by the way he plucks, picks, mutes, fingers the frets, bends, etc etc. Synthesizers use workarounds to try to mimic this, like taking multiple samples of the same instument and spreading them over the keyboard, or crossfading between them as the volume goes up. A non sampling synth uses control voltages to try to mimic, for instance having the filter cutoff frequency go down as you play higher on the keyboard. Also a synthesizer produces mathematically perfect sound, while an acoustic instrument is pieces of different types of wood and metal and fiber glued and bolted together in a mechanism that compromises between producing perfect sound, and creating a perfect interface that allows human fingers to control that sound. Of course the former produces cold, mechanical, robotic music while the later produces warm, rich, vibrant music loaded with character. From the dawn of sound synthesis a major struggle has been how to make synthesizers less perfect.

Yes every sound you hear is made of sine waves.

Yes a sine wave is a fundamental only.
So if I were to play a sine wave,and then use a spectrum analyser,it would show just one one frequenecy...the frequency of the note on the keyboard used to trigger its sound ?
Theoretically true but it can be effected by what amp and speakers you play through, the room you're in, how the gain is set etc.

So in the case of a square wave,playing at 110Hz this would be the same as multitude of sine waves playing at 1x (110Hz) 3x (330Hz) 5x (550Hz) etc ???!!How does this relate to the harmonic series ?
yes with a specific and different volume for each sine wave, and eventually passing above the range of human hearing. The harmonic series is the fundamental (110hz), the first overtone 2x (220hz), the second overtone 3x (330hz), etc. etc. Every acoustic sound comes from a vibrating body (with a natural amplifier). The fundamental is the entire body vibrating as one, the first overtone is the body vibrating in halves, the second overtone is the body vibrating in thirds etc.

yes, i took physics of music and electronic composition in college.

At times at low pitches the ovetones completely overpower the fundamental, sometimes the fundamental is completely absent. Some fundamentals are below the range of hearing, but the harmonices are not. Especially true of instruments like timpani, gongs, cymbals. It is possible to actually high pass filter all the low frequencies out of a bass sound so that only the overtones are left, and the brain will fill in and 'hear' the fundamental frequency, even though it is not there!

As far as high notes they could possibly have a lot of overtones, but they are above the range of hearing. The high notes of flutes piccolos, organs, and recorders was what i was thinking of. Other instruments would have more overtones even in the high range i think.

Another thing to keep in mind is that the harmonic series only applies to sounds with a pure pitch. As the pitch becomes less pure, you find frequency components that have little or nothing to do with the harmonic series.

Bash a cymbal, for example, and you get all sorts of miscellaneous garbage. Even something like a big tube chime, while it has a definite pitch that you can identify and hum, has a significantly distorted "harmonic series."

If you ever get a chance to hear an anvil ring, it's an experience I highly recommend. You take a couple of identical 200lb cast-iron anvils, and mill an opening in the bottom of one about the size of a frozen orange-juice can. Then you put that one upside down, fill the cavity with black powder, and set the other anvil right-side up on top of it. Set off the powder, and you'll get a WHOOM! and an immense cloud of white smoke; and somewhere in that cloud of smoke will be 200lb of cast iron, ringing in an amazingly complex way due to A) its complicated shape, and B) the fact that it's not being damped at all because it's not hanging from anything. It's really quite amazing. I'm sure there's much more to notice about the sound, but I never do because I'm always running around under the cloud cackling like an idiot trying to be somewhere other than where the anvil lands when it comes back down out of the cloud.

Oh--and it's dangerous, could kill you, don't do it without adult supervision, etc. Although I expect once you grow up enough to qualify as an adult, you'll know better than to go around ringing anvils. Luckily my uncle, who is always happy to provide the anvils if I provide the powder, hasn't qualified as that kind of adult yet by the age of 73.

wow I like the sound of that anvil stunt straight away !!!!