We've a Yamaha A-S700 and the loudness control works OK down to about 9 o'clock. Certainly it provides that little bit of wiggle room when the main volume dial can't really be turned any lower else everything sounds like crap. Kind of get the feeling the speakers are at least being moved, then dial the loudness back to just take the edge off the volume.
I must say that it is only used hen the volume is at low levels, where voices ever so slightly raised, can have a conversation over it.
I should shove an ADC into the headphone out, turn off the speakers and just play some white noise through. Turn the loudness dial down and measure average RMS or average dB at 1kHz, then plot the graphs. Alas amp is in one room, ADC and PC in another...
A-S300
Have you ever been interested in what the Loudness Control knob does on Yamaha A-S301 amplifier exactly? It is used to compensate for perceived loudness in some way according to the equal loudness curves (after D.W. Robinson and R.S. Dadson, 1956) when listening to music at lower volumes...
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An old Yamaha amp from the 70s
Looks to me like a bell/peaking filter ~ 1 kHz and a high shelf filter. The trick is getting them to tie together at the right ratio.