Well, the actual scale is based upon SSAT scores from over three years. Practice books may have a scale, which may be precise, but it is difficult to really calculate a scaled percentile (at least to my knowledge). Also, it is difficult to estimate the degree to which a score will be scaled. For example, a reading score may only start scaling (from 1/sample percentile) at 420 and stop scaling (at 99 percentile) at 712. The rate at which it scales is also not constant throughout the curve.
That was an answer to your call for an "exact" (more likely, "precise") scale. Test experts (something which I am not), however, may be able to provide a somewhat precise scale to fit your needs. I know, also, that the scale is configured similarly to the CollegeBoard SAT. I have the PSAT scale somewhere, and I will see if I can create a rough bell curve, in accordance with SAT guidelines, for the SSAT (of course, I need to find my PSAT guide from October 14th first which, considering my lack of organization, will be difficult).
I am curious, though, why do you need a scale? Without a practice/prep exam book what do you hope to gain from it. I guess you could look at it an say I need "at least" this much to get this percentile but it's hard to even estimate the raw score.
Maybe I am mistaken about all of this. Let me know.