Sorry for the disguise: Q1.15 is equal to Q15 definition found in Wikipedia
It defines 16 bit fixed point format with one sign bit and 15-bits fractional part
-1^B15 x Sum(2^-Bn)
where B15 is MSB and B0 is LSB
So the range for this format is [-1, 0.99996948242188] or which is represented by hex coded numbers in the range [0x8000, ox7FFF]. For simplicity this range is typically referred to as -1 to 1.
If you are curious try this in Matlab
q = quantizer([16,15])
hex2num(q,'7FFF')
hex2num(q,'8000')
num2hex(q,1)
num2hex(q,-1)
num2hex(q,2)
num2hex(q,-2)
Regards
Mowgli