Questions about half-pedaling.

The dampers in the bass range are also heavier and wider than in the upper range, hence the damping duration ratio is not as high as it could be expected from a first approximation. If you check the ratio damping duration(no pedal)/damping duration(half pedal), you will observe it is approximately the same from bass to treble. Hence bass lasts a little bit longer with half pedal, in the same way as they do with no pedal. It may be more evident to observe it when disabling the sympathetic resonances which modify the decay globally. There is also a tricky effect to take into account: single and double wedged dampers have an accelerated dampening effect when they start falling down between the strings, contrarily to the flat dampers in the medium and upper range.

I am not sure half pedalling can work as an efficient sostenuto substitution, because if you really want a bass note to last a few bars, then the related damper needs to be almost away from the strings, and so will be the upper range dampers too. But I may be wrong.

The book describes it thus...

"Half Pedalling

The term does not mean that a pedal is to be brought half way up. It refers to the correct use of the sustaining pedal to achieve effects that would otherwise require a sostenuto pedal. The thicker, heavier strings of the low notes require a greater amount of damping than do the lighter treble strings. The loud pedal must be fully raised for a fraction of a second and then fully depressed again so as to obliterate the higher notes and allow the lower ones to continue sounding. As an example of how half pedalling works, with your left hand strike very firmly an octave G, its top note being an octave and a half below middle C, while directly pedalling it. Take your hand off the keys and, with a quick flick of your ankle, raise and lower the sustaining pedal so swiftly that the octave is slightly, but not completely, damped. Continue raising and lowering the sustaining pedal, again with quick flicks of the ankle, and see how often you can do it before you damp the notes completely. Do this exercise a few times to get the feel of the process.

Now play a chord of G, your left hand filling out the octave you have just played with a B and a D, and your right hand playing a similar G chord starting an octave and a half above middle C. Strike the complete chord using both hands simultaneously while directly pedalling it. Take your hands off the keys and, with a quick flick of your ankle, raise and lower the sustaining pedal so swiftly that the sound of the upper chord is damped, but most of the lower chord’s sound sings on. Keep on practising this until you can cut the upper chord quickly and completely while still allowing the lower chord to sing on. As mentioned earlier, sections of Rachmaninoff’s famous Prelude in C sharp minor and many similar passages in other works will benefit from accurate half pedalling."

Someone on a good evenly-regulated acoustic piano could give this technique a whirl and see if the book's description is right. I am not sure how important it is for regular playing, but having a way to keep the bass line humming while the treble side quiets out might have some merit. (It could be the author's piano was adjusted so the bass dampers drop a little later, thereby creating the desired effect.)