Csound Csound-dev Csound-tekno Search About

Re: How to generate subharmonics

Date1999-06-11 22:45
FromTobias Kunze
SubjectRe: How to generate subharmonics
> I´ve seen Unicorns. I´ve heard Unicorns ;-)

Then i take it you've shaped your brain waves, haven't you?  :)


> Do you mean it is not mathematically possible? I´m interested in a
> practical implementation. Maybe distorting the signal applying the
> inverse of a Chebishev polynomial (but this adds lots of DC and other
> unwanted components), maybe with a sort of FFT resynthesis or simply as
> a psichoacustic effect, by generating harmonics of the low frequencies
> to reinforce their presence.

well, depends on what you mean by "subharmonics".  The--original,
I believe--meaning of the term stems from music theory (another
sad chapter in the long history of failures in this field) and
refers to an inverted series of overtones _below_ the fundamental, 
that is at 1/n f.  Clearly, the fact that such a spectrum is still
harmonic as long as n has a finite limit did escape the theorists
who came up with it.  Besides, no such spectrum exists in "nature",
which puts them in the same category as unicorns.

In a more practical sense, I guess you could term "subharmonics"
anything that's low enough not to be perceived as pitch and high
enough not to be perceived as rhythm, so at around 12-16 Hz.  The
first example in Music History I can think of is the first act
of Verdi's "Othello" which has an C00/C#00/D00 organ chord underlying
the maybe first 15 minutes of the act to illustrate the storm.
The result is, well, close to noise.

But, as any double-bass player will jump in to deny immediately, 
_any_ low frequency will do as long as it is low enough.  Witness
said double-bass player tune his/her instrument, for example.  :)

So, no need for advanced DSP...