As recently discussed, one of the breakthroughs which led to the
advance of solenoid operated pianos was the development of pulse width
modulation (PWM).  Instead of controlling the pull of the magnets by
adjusting the amount of steady current, this is achieved by rapidly
switching the full current on and off.  The ratio between the 'on' time
and 'off' time determines the overall force from the solenoid.

So what's new?!  The concept is well described in this extract from an
unidentified technical report written at least 85 years ago describing
the Telektra player piano :-

  ".. the current for the operating magnets is varied by vibrating
  contacts, the rate of vibration being regulated by the music record.
  At zero vibration the full current passes, and as the rate of vibration
  increases the value of current decreases in direct proportion to the
  time of contact.  The control of the number of vibrations is so
  perfect and so nearly instantaneous that a practically unlimited
  number of degrees of expression may be produced."

Richard Stibbons
Cromer England