Josep M Comajuncosas wrote:
> 
> Hi,
> this is probably a question to be sent to the music.dsp group, but I´m
> sure some folks here may well know that. How can you generate
> subharmonics? Is it a sort of waveshaping the best way?

In the analog realm, subharmonics are generated using a flip-flop circuit. The signal from which
subharmonics are to be derived is put through a comparator, essentially turning it into an on-off
square wave. The resulting signal is then processed by a flip-flop circuit, which provides a divide
by N function; for every N times the input changes state, the output changes state once. The result
is a square wave which is 1/N the input frequency.

This technique is very effective when used with a perfectly periodic waveform. Synths like the
Roland SH-101 and MC-202 use subharmonic generation to get signals 1 and 2 octaves below the main
signal, which can then be mixed in with the original waveform. Electronic organs like the Vox
Continental and Farfisa Duo Compact would have 13 oscillators (12 for each note in a chromatic
scale, plus one for the bottom key), and run the output of each oscillator through a network of
flip-flops to derive all of the necessary pitches for an organ. In some "string synths" like the
Solina and ARP Omni, additional waveshaping would be used for each note to convert the pitches to a
pseudo-sawtooth wave, that would then be sent through several parallel delay lines (each with
independent LFO modulation) to produce the characteristic "ensemble" tone.

However, generating harmonics in this fashion proves to be more tricky when dealing with
non-electronic signals, such as that provided by any acoustic or electroacoustic instrument. Most
"real" instruments do not output a signal that can easily and consistently be divided in this
manner; minute changes in timbre can cause the tracking of the subharmonic generator to leap through
harmonics, seemingly at random. In addition, having two or notes playing at the same time wreaks
havoc on the process, causing the output to jump all over the place. Some effects devices, like the
Boss Octave OC-2, deal with these problems quite well, by lowpass filtering both the input and
output signals. Other boxes, like the MXR Blue Box, embrace the weirdness of the process as a
"feature" (it CAN be fun to play the leaping harmonics, if you are so inclined).

Another method of subharmonic generation is through self-modulation, such as an oscillator
modulating its own phase. As the amount of self-modulation increases, the harmonics increase as with
FM, but with a smoother increase in harmonics (i.e. none of the characteristic "sideband clusters"
of normal FM). With certain settings, a chaotic transition to subharmonic states, as well as noisy
states, can be seen. This seems to be similar to the evolution of subharmonics in acoustic
instruments. Not terribly controlable, but a pretty cool sound.

Sean Costello