Here are a couple quick tunings thrown together:
- Slot 63: Inverted C4=E3 12T
Added this one after the initial post so that the E4 key sounds as a C3. So, it really is just mirrored in terms of number of black and white notes as your traverse down the keyboard (with the sounds going up).
- Slot 64: Inverted C4=C3 12T
Since his ARP2600 keyboard was just voltage inverted going from C to C, this one should be similar in that the C notes still sound as C. And C# is B. The key C4 sound is the frequency of a C3 in 12-Tone Equal Temperament. MIDI notes 121 to 127 are the same as original, though.
- Slot 65: Inverted 12ET
Simply inverted the expected MIDI notes so 0 is really the note that 127 would be and 127 is now 0.
From very limited testing, it seems to work for the Oscillators and when using Sample Stretch on the samples.
Without Sample Stretch, only the upper half or so of the keyboard seems to be descending in tone. It's possible I missed something or there's an assumption in how the sample keymaps are handled with alternate tunings that doesn't allow the inversion to work. I haven't fully explored the keyboard, yet.
If you want them in another Alt. Tuning slot, then change byte 5 (counting the first byte as byte 0) from 63 (or 64) to some other number from 1 to 64. The value stored in the SysEx file for the tuning program position is 1 less than the value shown on the Prophet X/XL display.
Just for technical reference: It's possible the checksum value is ignored. Historically, different manufacturers have calculated it differently. And all the checksum values in the 64 Alternate Tunings that Robert Rich put together have a 0 checksum value.
Hope that helps for some exploration.