Need help reproducing graph (audiogram) with log axis with very specific ticks/gridlines

I’m trying to reproduce a graph known as a tone audiogram. It has some peculiar requirements:

1. vertical (decibel) axis is inverted with specific major grid lines.
2. horizontal (frequency) axis is in fact a log axis but its ticks are linear, and should only show the ticks/gridlines 125, 250, 500, 2000, 4000, 8000 (note the doubling of frequency values).
3. the aspect ratio should be such that a the area bounded by 20 dB and a frequency doubling (say 250-500, or 4000-8000 Hz) is square.

1 is not a problem in Bokeh. 3 could be achieved (more or less) by fiddling with the plot size.

2 is the real challenge.

Any hints? TIA