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Default 2nd, 3rd harmonic distortion

quote from Empirical Labs Distressor web page: Helpful in the pristine
but unforgiving digital world. Three audio modes provide user
programmable, warm harmonic distortion. Emphasized tube-like 2nd
harmonic in clean and Distort 2 mode. In Distort 3 mode the distortion
becomes dominated by 3rd harmonic (similar to tape).


So tape is 3rd harmonic and tubes are 2nd harmonic distortion?


also,
let's say you play an A-440. is the 2nd harmonic the A one octave
above (880hz), or the E a 12th above (1320hz or whatever)? I always
think of the first harmonic as the first overtone above the
fundamental. But I'm starting to get the feeling that the fundamental
is called the first harmonic, and then the octave above the
fundamental is called the 2nd harmonic, etc.
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