Sine wave explaination?

[marrstians]

what's the real definiton of a sine wave? how much does it differ from from the typical wave that most pedals generate? what effects use sine waves in them?

[Paul Marossy]

Check out the Distortion 101 section at http://www.geofex.com
That will explain a lot.

[Tim Escobedo]

In audio terms, a sine wave has no harmonic content, consisting only of the fundamental frequency.

I can't think of many real instruments that produce sine waves. "Clean" guitar sounds are often erroneously thought of and referred to as sine waves, especially in places like Harmony Central. However, the cleanest plucked guitar note is very rich in harmonic content for almost all of it's duration, until perhaps the note has faded almost completely away.

RG's distortion article covers the common distortion modes used in fx circuits. For simplicity sake, the examples given are often sine waves, so you could "see" what happens.

[Paul Perry (Frostwave)]

I can't think of many real instruments that produce sine waves.

Flute is not too bad, if you need a rough sine as a test signal and have a keyboard that has 'flute' setting. Running it thru a low pass filter (set just above the freq) will clean up harmonics that remain.
The mains are NOTHING like a sine now, due to switchmode supplies etc. :evil:

[niftydog]

y = Asin[ω(x − α)] + C

A is amplitude, ω is angular frequency, α is phase shift, C is vertical offset.

Does that help?  

sorry... I just feel the need to inflict this torture on others... I hated this topic at school!

In it's purest form, a sine wave has zero average power (perfectly symetrical) and zero distortion. Sine wave distortion is often hard to recognise.

how much does it differ from from the typical wave that most pedals generate? what effects use sine waves in them?

You talking as in LFO waves or the actuall effected sound? Just trying to get at your motivation for asking this question.

The output of a pedal is only as good as it's input. Your guitar doesn't produce perfect sine waves, therefore it's a moot point when you're talking signal chain.

For LFOs and stuff, it's REALLY hard to HEAR distortions in the sine wave when it's modulating some other heavily distorted waveform.

Another interesting point; a perfect square wave is comprised of an infinite number of perfect sine waves!

[Yuan Han]

hmm just thinking, has anyone tried using diode-clipped sine waves as LFOs ? like you know like a distorted sine wave ?

I would think that you need to push up (and down) the limits of clipping...

hmm

Han

[Hal]

sine waves (and all trig functions) are somewhat of a mathematical freak/miracle.  Read some stuff about simple harmoic motion, and basic trig calculus.  Everything kinda fits together.  Its neat.

[Brian Marshall]

Ok... here is the simplest way to explain it....

sine waves are based on a circle

if you have an object traveling arround a circle at a constant speed, and meausure its position on one axis  (a better way to explain is to visualise the circle and then turn it sideways so that it looks like a straight line)  

measure the possition of the object over time  (time becomes your other axis as it moves along in on direction)  you have a perfect sinewave.

i actually remember that from calc class.... it seems like its almost useful now.

[niftydog]

thanks Brian... the concept of angular frequency (rotational velocity) explained very concisely!

[Boofhead]

Your question has a lot of ambiguity.  Effects pedals deal with many waves:  There's the input signal from your guitar, there's an output waveform which is the waveform the effect puts out, then there's possible a number of wave sources which are unrelated to the input signat - these would include clock waveform (eg for clocking a BBD device) and LFO waveforms (used as a modulation waveform).  Presumably you want to know about LFO waveforms such as those in modulation effects like Phasers, temolo's, chorsuses.

There many way to describe this mathematically but I should imagine these desciptions are of no use to you - otherwise you would already see the connection.  

A sine-wave is the most pure form of a wave because it only has one frequency *component*.    The sine-wave is very smooth it has no sharp steps at all.   A square-wave on the other hand has sharp edges.  A square wave can have the same frequency as a sine wave - that's called the fundamental frequency.  However, the square-wave has extra frequency components as well, these are at higher frequencies that are multiples of the fundamental frequency.  The sharp edges where the square wave changes are indications of higher frequencies being present.  If you listen to a 100Hz sine wave and 100Hz square wave you will be able to hear a buzz on the square-wave - this is your ear hearing the higher frequency components.  A triangle wave is kind of in between a sine and square wave: it's not as smooth as a sine wave but it isn't as abrupt as the square wave.

When you use sine, square or triangle waves in modulation effects your ear detects the smoothness or rapidity of the modulation.  In this sense a sine-wave will sound smooth whereas a square-wave will sound abrupt.  That's pretty much the basics.     The way your brain peceives things can make the conclusions slightly off from saying sine-waves are the most smooth.

For example, when you have pitch shifting devices like Flangers and Choruses the amount of *perceived* pitch shift doesn't quite follow the LFO, especially over larger sweeps - it's actually cause by tghe way you brain percives pitch (it's mor logarithmic).  For this reason smooth sounding Flangers don't use sine-wave they actually use a disorted form of sine-wave which undoes what you brain does to the pitch.

[Paul Marossy]

Square waves are also packed with odd order harmonics of the fundamental - 1st, 3rd, 5th, 7th, 9th, 11th, 13th, etc. The strength of each progressively higher harmonic decreases as you go up. In other words, a 3rd order harmonic will be much stronger than an 11th order harmonic.

Amps/dist. pedals that sound really buzzy basically take the original signal,  a "sine wave", and amplify the heck out of it, then whack it with really hard clipping. This results in a waveform that looks a lot like a square wave, but the corners are slightly rounded. The end result? Buzzy, harsh sounding distortion. It's really interesting to look at this stuff with a scope and compare the way it sounds to the way it looks.  

Here's an example: http://www.diyguitarist.com/Images/clippedwave.jpg

[Arno van der Heijden]

Square waves are also packed with odd order harmonics of the fundamental - 1st, 3rd, 5th, 7th, 9th, 11th, 13th, etc. The strength of each progressively higher harmonic decreases as you go up. In other words, a 3rd order harmonic will be much stronger than an 11th order harmonic.

An ideal square wave has an infinite series of odd order harmonics.
My textbook about mechanical measurements (Bechwith) has a nice picture to show this. When only the first 3 terms (including fifth harmonic) are taken into account, the square-wave looks somewhat like a clipped sine wave. When more terms are added, the wave gradually moves into a real square wave. An ideal square wave can never be realised in real life because it is impossible to generate an infinite series of harmonics.

[Paul Marossy]

Yeah, in an ideal world.  :wink:

[Mark Hammer]

Probably the single most important thing to know about sine waves is that they generally do not exist in nature, because they are mathematical products of steady state devices.  A signal generator or other type of oscillator can produce a sine wave because it is engineered to do so on a sustained basis.  

In contrast, all "natural" musical instruments (so I am excluding "instruments that actually ARE oscillators) produce sound through the momentary application of energy to a mechanical system which does not fully absorb that energy.  There could be a membrane, a string, or an air passage involved, but it is still the momentary application of energy/force.  The implication is that in responding to that force, the instrument will vary in how the applied energy translates into motion in the membrane, the string, or the air passage.  Much like a gun/bullet where the bullet is *always* falling/arcing once shot, no matter how much force is applied to it (though with more force the arc of trajectory is less evident), no instrument will produce the exact same waveform twice through multiple cycles, and especially if the decay is quick (analogous to a bullet fired at high power or just pushed out of the barrel).

What changes most about the character of the energy translated by the instrument is that multiples of the fundamental change more drastically in amplitude over time than the fundamental does.  As a result, when one reaches the sustain part of the amplitude envelope of any natural instrument, it starts to sounds more sine-like with less harmonic content, but it still isn't a "true" sine.  As noted, flutes can sound somewhat sine-like after the initial plosive content, and indeed wind instruments, which have a more extended decay cycle sound closer to oscillators (and conversely oscillators can do a more plausible simulation of them too), but granular inspection shows it still has varying harmonic content.

Perhaps equally important is the truth that presenting a steady state wave to an effect (and most esopecially anything that is dynamically responsive) is not the same sort of test of that effect's properties as is presenting a "burst" more typical of the dynamic properties of musical signals (including change in harmonic content, hence shifting waveform).

When it comes to controlling other devices with oscillators, the most prominent thing about sine waves is that they present continuously accelerating and decelerating rates of change.  If you have a voltage that starts to increase more quicklyand then starts to slow down in its rate of change, then speed up, etc., you have a sinusoidal control voltage coming out of your LFO.  For sweeping flangers and to some extent phasers it is helpful to have the rate of change be different depending where it is in the sweep cycle.  Imagine the best slow flanging sound you've ever heard.  Now, thinking through it, do you want it to move as quickly through the "low" part of the sweep as it does through the highest point in the sweep?  Likely not.  This is why some devices use what has been called "hypertriangular" and in other instaces "parabolic" LFO waveforms.  This is an instance where the highest part of the sweep is triangular, and the lowest part is sinusoidal, suich that the sweep moves through the "uninteresting" parts of the sweep faster, and the more interesting parts slower.