GenericNameHere wrote:
And I thought sin[e] waves don't have much in the way of harmonics...
Not quite right. They don't have any harmonics. That's the definition of a
'sine' - 'wave'. A
sinusoidal oscillation, in this case one existing in the audible frequency domain. It describes the nature of the fluctuation in the pressure coefficient of the medium (air in this case). In layman terms it is a singular vibration. Any harmonics would be separate vibrations adding to the sum. In practice, that would be separate sine waves stacking above (and/or below) the fundamental frequency.
GenericNameHere wrote:...and thus, if two sin waves were played in sync, two octaves apart, there would be no phase cancellation, right?
Again, not quite right. 2 sine waves with the same phase running
at the same frequency would cause no cancellation. In your case though the 2 octave discrepancy would cause cancellation, as the standing waves are fluctuating at different absolute frequencies. This would lead to a difference in the position of the amplitude peaks of each wave along the time axis, leading to cancellation in the sum.
In this example
Red is the fundamental,
Green is the first harmonic; and
Blue is the sum. Note the phase cancellation. Keep in mind that this image expresses a fundamental and the
first harmonic. A picture of the second harmonic would look almost identical, except you would have 2 small equidistant dips in the sum instead of one, as the peak amplitudes of the harmonic would cancel the opposing force of the fundamental when they are </180/> degrees out of phase (but obviously in a smoothly iterating fashion, you can picture it in your head I'm sure.)
The Overtone Series of a fundamental are a series of
fixed integers, as expressed in
Laplace's Equation in fluid dynamics and
Harmonic function. They are the building blocks of
timbre in psychoacoustics. Any element
other than the fundamental sine wave oscillating at the base frequency of a sound, is essentially timbre; and all sounds in nature
are made this way*, inescapably. A square wave, for example, is simply a series of stacked sine waves with a specific equation applied to the amplitude distribution of consecutive harmonics.
*Read the part on Spectrum
GenericNameHere wrote:Don't tell me it's one of those theoretical, " in isolation, and only if it's a pure wave," shit.
So when you say this it's kind of difficult to give you a proper response because you're actively disregarding the correct answer. Everything is both never, and always in isolation, in as much as even things seemingly whole can be broken down in to their constituent parts. And in this respect sound, as built from
pure sine waves, do always theoretically exist in isolation; yet are also part of a sum that is never purely sinusoidal in nature. This is the nature of sound and it simply is something you're going to have to become accustomed with (theorizing over it's make-up in terms of isolated, interacting parts) if you wish to master the subject.
GenericNameHere wrote:I tried using seven cutoff/low pass filters on a deep/low end sin wave, qnd check what happened under a parametric EQ, and it looks like there are some "phantom" harmonics present in a "normal" sin wave. Is this theory even right?
Using a filter on a sine wave is the same as moving the amplitude fader on your mixer, a filter attenuates or boosts the frequencies at a given point on the spectrum. As a sine wave is expressing something at a single frequency (an oscillation vibrating at a given speed in Hertz). The point at which the filter begins to effect the sound will simply be attenuating the amplitude in the same way as decreasing the signal's amplitude via the track fader, in essence it is exactly the same thing.
By 'checking under a parametric EQ' are you referring to a frequency analysis function on the EQ's GUI? In which case any harmonics you may be seeing could be coming from a number of places.
- The type of EQ you're using could be introducing distortion to the audio signal depending on what type of filtering the EQ the unit is modeled on.
- The filter could also be performing a similar function as the EQ possibility.
- The source oscillator creating the sine wave in your synth could be mathematically incorrect. The VSTi 'Curve' by cableguys is known to have this problem, among other synths. This causes faint harmonics to be generated along with the fundamental meaning it is not a true sine wave, which you will be seeing in your Frquency analyzer.
- There's a small chance the analyzer it's self might have an issue.
The point being that no, there shouldn't be any 'phantom harmonics' in a 'normal' sine wave. If you're seeing harmonics it is down to human error; and understand that a sine wave is a theoretical mathematical function, which is expressed often quite imperfectly at front end. The important thing to understand though, in terms developing an understanding of the nature of sound, is that a sine wave should always be 'pure'. A singular vibration at a specific frequency.
GenericNameHere wrote: Also do cutoff filters alter the source on both sides? What I mean is that it's common knowledge that a low pass filter attenuates the frequencies above the cutoff point, but does it boost the frequencies below the cutoff point as well?
Read this
GenericNameHere wrote:How do you guys feel about using square waves for basses? It could make a bass you could feel and hear, right?
Squares for basses work well
)