Music & Sinewaves - Definition & Existence

[tomelex]

First, as an electronic tech, 30+years, I learned about a sinewave,

definition: a wave that can be expressed as the sine of a linear function of time, space or both.

Key here to me is the word expressed.

The sinewave I learned about was a phasor going anti-clockwise in a circle. Thus, the sin button on my calculator responds to that "circle" type sinewave, and ONLY that type.

That corresponds to what we learned about generators, physically magnets in a circle and you rotated the coils within and got out the sinewave (of what I call a circle), the one that the calculator button represents. I orginally thought this was the only type of sinewave due to the fact that that is what was taught in school and in electronics courses! Damn confusing!


But, per the definition above (from 1976 Radio Shack dictionary of electronics), that phasor does not have to be rotating through a circle, but any waveform shape, and as long as we take the opposite over the hypotenuse we get a sinewave.

Now, there are a lot of engineers out there that seem to be talking nyquist and fourneir and such, and acting like music is made up of sinewaves. That is fine, but in all my searching, only a tuning fork and I think one other instrument or so actually produce the particular "circular" type of sinewave as seen from an electronic generator.

Am I right about this, that there are very few true "circle" sinewaves in music, although tons of them in regards to the definition of a sinewave.

Also, am I right to be cautious about understanding that just because we can construct any waveform from "sinewaves" , that does not mean they actually exist in the waveform.

I am sorry if this is a long post but I thought it better to show how I was approaching this so you could see my logic/lack of logic etc.

Thanks,

Tomelex

 

[vk6kro]

You can construct waveforms that are not sinewaves by combining the outputs of a suitable number of sinewave generators that allow you to inject various levels of harmonically related sinewaves.
You can also do this with computer generated sinewaves. Just mixing 1000 Hz , 3000 Hz and 5000 Hz gives a rough squarewave and adding extra odd harmonics generates better squarewaves although you do have to fiddle with the levels of the signals.

You can also extract individual sinewaves from complex waveforms using filters, as long as the complex waveform is repetitive. That is, it is not just random speech or other noise.

So, yes, it is fair to say that the sinewaves actually exist in the waveforms and they are not just some mathematical convenience.

 

[tomelex]

Hi vk6kro,

Thank you for replying.

You bring up an interesting thing about filters. The whole point I am dealing with I think is that there are almost no "circular" sinewaves in music. (ie the one that gives you the numbers in the sine tables or the one function designed into calculators sin button).

A mechnanical engineer friend feels that filters may convert a "non-circle" sinewave into a "circle" sinewave.

I have experimented with RIAA filters for example, and they will ony accept sinewaves from a function generator to give out sinewaves, any other waveform you put in (in the audio freq band) seems to convert to a sinewave, but at the time I did not look to see if the new sinewave it created was a "circle" sinewave.

Any ideas on this out there?

Does an RC circuit "create" a "Circular sinewave" from a non circular sinewave input?


Cheers!

 

[uart]

Yes Tom you’re correct in thinking that “pure sine waves” rarely exist by themselves in music. It’s not quite the same thing as saying that they don’t exist in music at all though, it’s better to think of them being there but buried in a load of “harmonics” (frequency multiples of the base note).

As you mentioned tuning forks give a close approximation to a pure sine wave as do bells, but most other instruments produce waveforms that have enough harmonic content to make them look decidiedly non-sinewave.

It’s instructive to think about what actually makes a particular musical note (eg middle C) and why that very same note can sound different on an oboe than it does on say a steel string guitar. All that constitutes a particular note is really that it’s basic (lowest frequency) repetition rate is some particular frequency, eg 220Hz for “A below middle C” and so on.

So what makes that same note sound quite different on an oboe compared to the guitar? The two main features that give an instrument it’s distinctive sound are time domain envelopes “aka attack and decay” and timbre.

Attack and decay are straight forward to understand, a plucked instrument like the guitar has a steeper attack than a wind resonant instrument for example, so that’s part of what differentiates their sound.

But what about during a sustained note, guitar and oboe still sound very different so it can't be attack and decay alone that’s the difference. That’s where timbre comes in. It turns out that what constitutes timbre is basically just the varying amount of harmonic content (frequency multiples of the root sine wave component) that gives the different sound quality.

A steel string guitar has more harmonic content (less like a pure sine wave) than classical guitar for example, and that’s what gives it it’s characteristically different sound. Further the musician may vary the harmonic content of each instrument by the way they play it, to add their own characteristics to the instruments sound. Striking the strings (of either guitar) closer to the middle of the string gives less harmonic (closer to pure sine) while striking them nearer the bridge give more aggressive harmonics.

It’s an interesting topic and I hope the above gives you a bit more insight into it.

 

[brewnog]

Uart covers everything I was going to say, great post.

 

[tomelex]

Thanks uart and brewnog. I appreciate your responses and yet, I am still reaching deeper as follows:

Along these lines, can someone explan if an RC filter, for example, (what ever filter actually, bandpass, blah blah) when it decodes from a complex waveform, a waveform that it is "tuned" to, is that decoded waveform a "pure or as I call it circular" sinewave?

We throw the term sinewave about all over the place because we mathematically use that concept, and that is fine, but the sin on my calculator button only works with a pure sinewave, which I think is referenced to a phasor rotating through a circle, and thus in graph form producing a "pure" sinewave...post #1 has definition of any old "sinewave".


When an audio filter filters out a fundamental from a complex wave or or whatever, if we do get a pure sinewave (reference to phasor and circle), how the heck does it do that conversion? I am beginning to think that a "pure circular sinewave as derived by us humans can only pretty much come about by having that "phasor rotating about a circle" only, and thus find it hard to think that an audio filter de or re constructing a complex wave would reproduce such an exacting sinewave definition.

I have looked in my electronic books and on the web, and everywhere they just say you get a sinewave out, and here on this site, in one thread, a mention was made of "not a pure sinewave" output, but that is the only case I can find.

It just seems to me to be fundamentally quite important to know if you get that "pure circular" sinewave or just some "sinewave" that does not meet the purity.
Cheers

Tom

 

[brewnog]

I'm not sure I understand your definition of a sine wave that isn't "pure" or "circular". Perhaps you could expand?

 

[tomelex]

Hi brewnog,

Yes, the second sentence of my first post shows the definition of a sinewave from a book published in 1976.

Fundamentally, we all know what a sinewave is, but to match up with the sin button on a calculator, or sin tables that have been published, the phasor has to be rotating through a circle, ie the amplitude is of a circle, and hence, sin 90 is 1, etc. A pure sinewave to me is this one, a cirlce. It is the one always shown in electronics training.

look at the nice moving graphic of the circle sinewave here:

http://en.wikipedia.org/wiki/Sine_wave



Per definition of sinewave in post one, as long as we apply opposite over hypotenuse, we can call almost any sort of a waveform a sinewave...yes, I know we have some names for some other waveforms, triangle, square, sawtooth, etc.

That is how I see it anyway.

Thanks for engaging me on this one! I hope somebody learns something here..and I hope it is me!

Tom

 

[Feldoh]

Along these lines, can someone explan if an RC filter, for example, (what ever filter actually, bandpass, blah blah) when it decodes from a complex waveform, a waveform that it is "tuned" to, is that decoded waveform a "pure or as I call it circular" sinewave?

When we put a complex sine wave (i.e. square wave) into a passive low pass filter the signal that we get out is what's called the convolution of the two. Mathematically in this sense, you will not get a pure sine wave you will get a modified signal which is determined by the convolution.

I hope this helps?

 

[tomelex]

Hi feldoh,

Thank you for your input.

If a square wave is input, that is all odd orders, what if a signal that had even and odd were input, still a convolution and not perfect sinewave?

Thanks