Coefficients for half-order filter
Allan Herriman notes on the music-dsp mailing list that the filter, created by Paul Kellett and named the "instrumentation grade" pinking filter for white noise, is not optimal in (my words) minimum absolute error sense in the magnitude frequency response. I don't know if it should be, perhaps it would be more desirable for it to be that on dB scale. My guess is that the coefficients are handcrafted. Also I don't know if the filter tries to approximate a "half-order" filter or to have an approximately 10 dB / decade slope over the audio band for pink noise generation from white noise, probably the latter.