Did you listen to the wave file i posted?Christian Schüler wrote:You can hear the switch even in cheap headphones.
Yes but consider for a minute that the harmonics coming in and out are many dbs quieter than the overall volume of the wave. So the discontinuity is very small in respect to the overall volume of the wave. Hence for everything but the very highest notes that 12db rolloff starts > 30 or 40 dbs down, and mostly way up in the high end of the spectrum where people either cant hear it or at the least can't perceive it.Here's why:
The worst thing to do is dropping off the highest harmonic at any point in time - it will cause a discontinuity, which has an infinite spectrum falling off at 6db/oct with the center at the harmonic in question (for instance 18kHz).
When switching the harmonics at a zero crossing this is simply a higher order discontinuity, for instance a C1-discontinuty (the wave slope will change instantly). This falls off at 12 dB/oct, but is still an infinite broad spectrum discontinuity.
So even by the time some of it is aliased into a part of the spectrum where it might be noticeable it is already past > 60 or 70 dbs down.
I know that.. but what does it matter if no one can hear it?Essentially a ring modulation of the highest harmonic with a step function. The spectrum of the step function is shifted to where the harmonic is.
A ramp or window function has a much narrower spectrum than a step function, so when multiplied with the harmonic, the harmonic will be broadened but not as much as with an instantaneous step.
cheers,
chris


