Thanks. I found the Microtuning section in my DX7S manual. This is interesting, and looks like it could accomplish the task, albeit one would have to calculate and enter values for each note. My only hesitation is that perhaps the "fine" tuning could benefit from being slightly finer for a smoother fit to the Railsback curve.
When I bring up A3, my display reads as follows:
>Micro tune< A3
f: A3 + 0?? 5802
We are in "fine tuning" mode, designated by the "f". Clicking the data entry +1/ON button changes the second line to the following:
f: A3 + 1 ? 5803
If, from the same starting point, but in "coarse tuning" mode, designated by "c", the same action (incrementing the value by one) results in the following second line displays:
c: A#3 + 0 ? 5888
c: B3 + 0?? 5973
c: C4 + 0?? 6058
I am curious about the right-most number. The coarse appears to vary the right-most integer by 85 (but sometimes 86), and the fine appears to transition over the intervening increments. I can see that this matches the 1.17 cents approximation that you referred to. I'm guessing the large integer is the index column of a data table that encodes frequency.
I've not found a source equation or chart yet for the Railsback values. I've read estimates of 10 to 20 cents perceived stretching occurs even for the middle octaves, even thought the Railsback adjustment made there is smaller. I suspect that the adjustments made by piano tuners, which are less in the middle registers and more in the outer registers, reflects a compromise that derives from common use of those frequency ranges. Around middle C, we are more likely to use "close-voiced" chords, and in that context, beating between the notes might be more annoying, whereas at the extremes, where open-voicings are used (octaves, or at the least fifth), the "stretch" could be the more discomfiting factor.
