sounds like you have a filter ehich has a attenuation slope of 6dB/octave (doubling of frequency). Assuming you want to keep the -6dB per octave slope, you want to shift you nominal cutoff frequency such that the frequency you are interested in is in the middle of the octave (half octave -> 0.5*-6dB=-3dB). half octave is Factor 3/2, so the starting point is at 2/3 of the specific frequency.
example you have -6dB at 100Hz, so at 50Hz der should be the last frequency with 0dB and at 200Hz you have -12dB.
if you want -3dB at 100 Hz: last point at 0dB would be 2/3 * 100Hz. the middle if octave is then 1.5 * 2/3 * 100Hz=100Hz and you have -6dB at one octave= 2*2/3*100Hz=133.33Hz
