I’m constantly reassessing the Crescendo algorithm. This morning I took a closer look at the innermost body of code where we estimate the power in each Bark bandwidth at quarter-Bark spacing. I found I could slightly improve the speed of the conversion process between Bark and Hz frequency space.
Efficiency in these code fragments is important because they get executed more than 200,000 times per second while Crescendo is running. I went from an operation cost of 2A+2M down to a cost of 2A+1M. That matters. Not as much is it once did, but it still matters.
But I also looked again at the conversion formulae. Corrections have been developed atop Traunmuller’s original 1990 paper where he showed the conversion formula from Hz to Bark space.
Those corrections apply at very low bass frequencies, which are of little importance to Crescendo, but also at high treble frequencies, beginning above 5 kHz. And those high frequencies are very important to Crescendo.
So I made sure those correction factors were included in the conversions from Hz to Bark, and back again.
Here is a graph showing the situation:
The green curve is what had been in use by Crescendo. The red curve shows the new formulae now in use.
When I listened to the results of the new corrected transforms, the high treble became almost silky smooth compared to previous listening sessions on the same material.
But, always distrustful of my own impressions with my poor hearing, I sought out an expert opinion from an artist client. His hearing is much better than mine, with his vTuning down below 35 dB, compared to mine at 60 dB. He confirmed the improvements.
I am amazed that such a slight change made such a huge improvement. But in retrospect maybe I shouldn’t be. The old uncorrected transforms were placing too much audio power in the lower end of the highest Bark bands, and starving the very highest bands of power. The result in Crescendo is an underestimate of the gain needed in those lower high bands, and too much gain in the very highest Bark bands.
The distance we have come from the earliest days of Crescendo development to what we have now is nothing short of breathtaking. There is nothing else on this planet that can make music sound so incredibly good to people like us with hearing impairment. It is enthralling…