Let me explain better.
The first chart here below shows the equal loudness of the three frequencies (in the X-axis we see the phon, in Y-axis the corresponding dB: per each phon we have the same loudness at different dB for each frequency.
EDIT: more accurately, the first chart shows the difference in dB between the tone and the equally loud tone @1000hz.. this is why we see a rise from 0 phon to 10 phon. However, nothing changes in our reasoning, as the distance between the curves is equal). As we see, the difference in dB between frequencies varies between the different phon levels (second chart): as we know, at lower phon the perceived loudness varies most, while at higher phon the perceived loudness is more similar between different frequencies).
Basically, we need to know the difference in dB to equal perceived tones at the three different frequencies.
I run a test on my headphones, playing at a certain fixed Windows volume level 80hz at -60db (almost inaudible), -40db (fine), -20db (LOUD
) and, at each level, I found the corresponding equal loudness level for 40hz and 160hz (compared to the 80hz). Here are the results (the first one, -16hz, should read as follows: playing 80Hz at -60dB is perceived equally loud as 40 Hz at -44 dB, of course on my headphones and at this certain Windows volume level. -13,7 dB, the second value, implies that 160 Hz has to be played 13,7 dB lower than the 80 Hz (-73,7dB)... so, yes, signs are inverted because I'm showing 80Hz-40Hz and 160Hz-80Hz).
The run was interesting because playing 160Hz @ -73,7dB made the harmonic distortion well noticeable.
Anyway, what is the result? The first run was (80hz@-60dB) close to 20 phon (let's say 22 phon), the second (80hz@-40dB) somewhere around 50 phon and the latest (80hz@-20dB) maybe around 75 phon. Please note that the blue datapoints are just the ones plotted as blue and orange line in the second chart above, just that here I plotted in XY instead of lines.
Theoretically, we should have the result distanced by 20phon (
EDIT: not quite, that would have been true if we were referring to 1000hz, since 1 phon equals to 1 db, in fact the difference in decibel between 0 phon and 100 phon @80Hz it's just 83 db), while I got 22 phon - 50 phon - 75 phon. Moreover, orange points should lie just between the blu ones, while the second and third runs somehow were not so accurate, at least when we look at the difference between 40 and 80 hz. I guess the best I can say is that picking equally loud frequencies is not so easy (as Peter wrote), anyway I think it's safe to assume the second run (80hz@-40dB) is somewhere around the 50 phon curve. So, if I were to decide (at that loudness level) which phon curve to use, I would pick the 50 phon.
Probably having more points and more runs might result in a more accurate estimate, at least now I have a rough idea on how loud my headphones are playing