The Logic Off Topic list

Hi Debbie,

>Can any one explain to me the relationship between harmonic content and
>waveform of sound waves?
You've asked kind of a hard question, actually.
Let's try this ... when you're at a party thrown for you by your friends, 
you get kind of a warm and mushy feeling because you're surrounded by a 
group of people who care about you. Looked at that way, the exact number 
doesn't matter. Now if we filter out a certain number of those friends of 
yours -- say all the ones who like football -- then you might still be 
surrounded by your friends, but the character of the group has changed. 
That, essentially, is the purpose of filtering -- to change an original 
sound by taking out some of the components.

It would be a strange way to go about it, but we could try and analyse what 
it was that made it such a good party. We could try saying there wee 23 
fishing people; 36 dressed in red; 15 who took holidays in Ibiza and so on 
and so forth. Each of those criteria would be a way of trying to describe 
the whole group of people, the effect they had, and how they interacted 
with each other to produce that particular group.

The details don't matter too much, but a French mathematician called 
Fourier produced a theory that any sound whatever could be described as a 
conglomeration of sine waves. Lot more complex, but that was the basic 
idea. And there was a German physicist called Helmholtz who was pretty much 
the person who started acoustical theory by trying to understand exactly 
what it was that made sounds 'musical'. People like that applied numbers to 
musical sounds and made it amenable to physics.

The basic waveforms that we know of and that you can see on any synth are 
given names to describe their basic overall shapes: square, triangle, saw 
etc. Unfortunately, no real noise falls exactly into any of those criteria, 
but they are attempts to indicate what are the most characteristic waves 
present in any given sound.

The harmonic content of a sound is an attempt to say which particular 
partials or overtones are present in any sound. Each sound is felt to have 
a 'fundamental frequency' (we'll ignore percussion sounds and things like 
that which tend to have a very indeterminate frequency). That's the first 
harmonic. The second harmonic or first partial (terminology is 
inconsistent) in the 'natural harmonic series' is the octave which is 
produced simply by doubling the fundamental. At this point, all bets are 
pretty much off as to what's going to happen in any given sound. Depending 
on the physical characteristics of the sound producing device, other 
partials are added in above that. A triangle wave, for example, has two 
lines on either straight. That linear shape is caused by the fact that 
anything producing a wave of that kind is softish and with only a small 
number of odd-numbered harmonics. Think of a flute, which has something of 
a 'hollow' sound. A square wave has only odd partials, while a sawtooth has 
both odd and even ones giving it a brighter sound that is often used as a 
basis for brass instruments. So ... some instruments tend not to produce 
any 'odd-numbered' partials, while others might produce only odd ones etc 
etc. Some instruments will produce only a few irregularly numbered 
overtones with no simple-numbered relationship to the fundamental (think 
percussion and metallic sounds). A part of the skill of being a synth 
programmer is in identifying what overtones and sounds and filtering 
mechanisms are present in any given sound.

>I know what various waveforms are just don't know the relationship between
>harmonic content.
You've pretty much answered your own question, actually. There is no 
absolutely certain and definite relationship between a waveform and a given 
harmonic content. The harmonic content is kind of like trying to count up 
how many of which given groups of people are at your party. How many guys, 
how many in red hats, how many bringing their own beer, how many ...... 
Whereas ... when you just say that you had a great party, all we know is 
what effect that given group of people had. In that kind of way, when we 
point at the wave we're simply trying to describe the overall effect that 
that given collection of partials has. But when we try to count up the 
people and put them in their separate groups, we're taking a different 
approach to the same problem. Truth is ... the fundamental problem of 
synthesis, whether we do it by sampling, frequency modulation, subtractive 
synthesis, physical modelling or anything else is really very simple. It's 
pretty much impossible to get a truly accurate representation of any given 
sound. The more money you throw at it and the  faster your processor the 
more likely it is that whatever you are doing gets close to the original wave.

So ... the relationship between harmonic content and waveform can in a way 
be seen as a question of money and experience. I get you've got a synth 
there in your house that a really good programmer could use to get very 
close to any sound you want ... whereas a rank amateur couldn't get close 
to anything, really, if you gave them the most expensive synth on the planet.

It's a bit frustrating, but the best way to get a handle on this is to 
close your eyes and play with the levers on a synth. Play a note and just 
kind of get an idea for what it sounds like. Then .... just tweak a knob 
and see what it does to it. It's all very well to say that what you are 
doing is 'opening a filter', but there's not much point in that description 
if you can't ally it to some kind of gut feeling inside yourself of what's 
happening to that actual sound. One thing you can be pretty sure of, 
though, is that when you add higher and higher partials, whose amplitude is 
also higher and higher, then you are adding more and more 'noise' to your 
sound. Possibly a good way to add a touch of 'fret noise' to a guitar patch 
for example?

Bottom line ... nobody can give you a handy-dandy rule for moving from wave 
form to harmonic content because there ain't no simple rule -- just general 
guidelines. Two waveforms that look different can sound exactly the same; 
two waveforms with identical harmonic content can look very different 
indeed if we just play around with their phase differences yet they will 
sound exactly the same because that's not the kind of thing the ear is 
attuned to -- until we start creating deliberate beatings and stuff like 
that by playing them against each other.

>Hope u are all having a lovely Sunday of rest.
Yes, thank you.

>Hopefully I will speak to you all soon.
OK

>Keep smiling.
You too. Hope what I have said was helpful. I'm sure there were mistakes 
somewhere because I'm not a professional at this at all ... just an 
amateur. Hopefully someone who knows something will come in and correct it 
if necessary then we'll both be a bit more intelligent.

Kool Musick
Keep Musick Kool


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