If you are looking for an interesting piano mic system (admittedly a bit off-topic here in a virtual piano forum ), check out the Earth Works "Piano Mic".

http://www.earthworksaudio.com/77.html

Listen to the audio files -- quite amazing for such an unobstrusive piece of gear. Sounds almost the same with lid closed which is great to reduce bleeding. And oh, it's cheap -- just some 4.000 bucks

p.s. Carole was 29 in 1971 -- don't forget, by then she had been writing hit songs like this one for 10 years!

From what I can see, there are just two mics--the vocal mic and the one that's pointed to the upper treble of the piano. They may be the same make of mic--but I can't really see the head of the piano mic. The vocal mic, in any case, seems to be omnidirectional, a ball mic head, and when she moves her head, the sound stays full. But I wanted more bass in the piano.

Am I right in understanding the mic configuration-- she has a strong alto-lower soprano  voice, so the piano mic feed (upper soprano) is reduced in volume on the board? But why no mic on the bass piano strings? (Since the treble notes of a chord have more presence than lower notes, logic would encourage putting her voice over a fuller bass.) Just using as simple a live setup as possible? With compression on the vocal but not on the piano, so she can play loud without the piano overpowering the vocal?

http://www.youtube.com/watch?v=Gi3cOw5iJ10