I think I’ve settled on a tuning system for my Bionic Ear Institute piece. It’s a tricky thing. I’m trying to build up pitches based on overtones of a fundamental frequency. Each electrode in a cochlear implant is designed to respond to only a certain bandwidth of frequencies. The range of bandwidths used mean that certain parts of the scale will be received and interpreted differently, depending on which octave you play in.
Luckily, Robin Fox has sent me an implant simulator, which I am now using to test out different harmonies and combinations. Of course, the interaction of overtones with the cochlear implant becomes more complex still when differentiating between different instrumental timbres.
Varying the resolve-to-tuning with frequency makes a lot of sense. An interval like the wide septimal major third (9:7) is, with simple harmonic spectra, going to be be consonance (from the sensory consonance point of view) when it’s above the treble clef, but dissonant below. Likewise, a major third below c (second line bass clef) will be rough. This suggests a scaling approximating that of critical band width. I assume that you have some procedure for varying the tonic, so that everything is not construed as partials of a single fundamental. One other thing you might consider is add the possibility of subharmonic structures, at least the /4, /5, /6 triad, and maybe the tetrad adding /7 (which gives a “half diminished| chord, like that found on ii in minor, or in the “Tristan chord”.)
Thanks for the advice! The subharmonics are probably a good way to go. The lowest electrode in the implant has a range of about 180-320 Hz, which suggests that subharmonics may be necessary in any case. This is also because I’ve been trying to stay on the same tonic (it will be only a short piece) and see if it is possible to differentiate harmony and timbre. The bandwidths of the electrodes don’t follow a pattern consistent with actual overtones, just to keep things interesting.