Noob here - waveform question.

[Audiorain]

Hello everyone, I'm Michael, I'm 18, and I just signed up. Ok so I've just started a course in music technology, and so far I'm coping ok, but still having trouble understanding some things. The module I'm doing right now is 'Instrument Technology' and right now I'm learning about the basics of waveform, timbre, pitch, harmonics, etc.

One of the things that confused me was when talking about the different harmonics in a waveform.
As I understand it, the lowest component of the waveform is known as the fundamental, or first harmonic.
The other harmonics have a number corresponding to the multiple of the fundamental frequency (in Hz).
So the second harmonic is approximately twice the fundamental, the third harmonic is thrice the fundamental, etc etc. I understand this concept but am just confused as to why exactly this is? Why does this multiple occur?

This hurts my brain. Can someone please explain in plain English? Hertz are a measure of frequency/pitch right? That means how high or low the tone is, right? How does that fit in so precisely with the waveform multiples?

 

[AlChuck]

It's kind of difficult to explain, but it has to do with the idea of a standing wave. The classic demonstration of this concept involves holding one nd of a string that's tier to a doorknob or something at the end. Hold the string tight and wiggle it up and down, slowly at first, then gradually speed it up. At some particlular speed of wiggling (frequency), there suddenly appears a beautiful curve that looks like a single peak of a sine wave moving up and down together. This is called a standing wave. The idea is that the frequency is such that peak of each disturbance you introduce into the string lines up exactly with an earlier peak, and the amplitudes add. The fundamental has a wavelength that's exactly the length of the piece of string.

If you exactly double the frequencey, you get a double standing wave with two crests and troughs. Same with tripling. It has to be an integral multiple because it's tied to the length of the string and how many waveforms can evenly be divided up along the string.

Any high school or college intoductory physics text probably has this example nd a much better description than mine...

 

[tedluk]

Hello everyone, I'm Michael, I'm 18, and I just signed up. Ok so I've just started a course in music technology, and so far I'm coping ok, but still having trouble understanding some things. The module I'm doing right now is 'Instrument Technology' and right now I'm learning about the basics of waveform, timbre, pitch, harmonics, etc.

One of the things that confused me was when talking about the different harmonics in a waveform.
As I understand it, the lowest component of the waveform is known as the fundamental, or first harmonic.
The other harmonics have a number corresponding to the multiple of the fundamental frequency (in Hz).
So the second harmonic is approximately twice the fundamental, the third harmonic is thrice the fundamental, etc etc. I understand this concept but am just confused as to why exactly this is? Why does this multiple occur?

This hurts my brain. Can someone please explain in plain English? Hertz are a measure of frequency/pitch right? That means how high or low the tone is, right? How does that fit in so precisely with the waveform multiples?

Ok, this is probably way too complicated to explain well here, but a couple of things are worth mentioning.

First off, the second and third and other harmonics are not necessarily double and triple the fundamental though they certainly could be. One method of analyzing a complex sound is to break it down in to components. You are correct that the First harmonic is the fundamental and usually the lowest component (but it IS possible for there to be harmonics below the fundamental). The other component of the fundamental is that it needs to have the most energy. In other words, if there are lower frequencies present that have less energy, then those are sub-harmonics. The other harmonics can be of any frequency, they only must be of lower amplitude and higher frequency.

It is this structure of harmonics that make up a sound's timbre and why different instruments sound different playing the same pitch.

You are describing "octaves" in your example of frequency doubling. Each time you double the frequency, you raise the pitch by one octave. I don't think I can explain how we perceive pitch here very well. I'm certainly not an expert on the subject. Suffice to say that tones whose frequencies are in the ratio 2:1 (an octave) are considered harmonically equivalent.

Here is a link to a paper that attempts to explain octaves and why we perceive them as we do.

Hope this makes some sense and doesn't confuse the issue more.

Ted

 

[Rock Star 87]

not sure if im right here, jamez, correct me if im not, but i just aced theory, so here goes. when u play a note, say a G3, that G is the fundamental. but there are also things called overtones. when u play a G3, the overtones are say, A4,C#4,F#, and five other following notes. there's a formula, but i can't remember it off the top of my head. these notes sound barely very distinctly from the fundamental, and this helps develop the timbre of the note. the timbre is why a C4 sounds different on an acoustic piano than on a honky-tonk piano. any more questions ask, or any corrections, just let me know

 

[Cloneboy Studio]

Overtones are just another way of saying harmonics.

Everything other than the frequency of the note can be looked at as an expression of a mathematical ratio of the fundemental... both over and underneath the fundemental. Not all harmonics are necessarily an equal expression of an even or odd harmonic, nor do they remain constant.

On a day to day basis it isn't applicable to find out these things, but to be effective in the recording world you should know about them implicitly, as it can help you understand certain phenomena or the effects of different types of gear or process and what to expect.

Example: a lot of tube devices, when sufficiently pushed, introduce distortion into a signal by amplifying the 2nd harmonic (fundemental freq x2)... pushed further (or certain types of tube designs) you can end up with 3rd harmonics. Say you have a "saturator" plugin that allows you to increase the 2nd and 3rd harmonics you would know what to expect when adjusting those parameters in addition to the effects on the sound.