We want to perform a gradient PCR for our primers whose suggested Tm's are between 49.6°C and 50.7°C. We want to test with temperatures ranging from 47 to 55°C. Is this setup correct?
I would try from 45 to 54 because it is important to get some amplification then you can see how it cleans up with increasing temperature but these are very low temperatures and if you could design primers annealing at about 60c they would be more specific and easier to work with
Like mentioned, I would definitely try it broader, even from 40 to 60 degrees. Generally you want to see a curve from 1) aspecific amplification (at around 40), through 2) optimal amplification (no misamplification, specific band, some primer band at around 50) to 3) no/limited amplification at around 60 degrees (weak specific band)
Start with a temperature 5 degrees below the lower primer Tm. The range you can cover in a gradient PCR depends on the brand of machine you are using but are typically up to a difference of 10 degrees across the plate so a good starting place is to try a range centered on your lower Tm. If no amplification is observed try increased magnesium and high GC content melting conditions.