● The pressure gradient and the phase

Fact: The pressure gradient is ahead of the sound pressure at 90°.

Phase of the S signal at the microphone with figure-eight pattern in
opposite to the M signal at the microphone with omni-directional pattern?

 See: "Soundfield Quantities of a Plane Wave – The Amplitudes": http://www.sengpielaudio.com/SoundfieldQuantitiesPlaneWaveAmplitude.pdf   When looking at the curves of displacement, sound pressure, sound velocity and pressure gradient there comes a question:   If the pressure gradient is always 90° ahead to the sound pressure, why is MS stereophony with an omni-directional pressure microphone and a pressure gradient figure-of-eight microphone no problem?   Answer: The frequency response of the pressure gradient increases with frequency at 6 dB/octave. To compensate for this, these microphones are "tuned damped". In the electrical analogy,this represents an RC pad above its transition frequency causes a drop of 6 dB/octave, and shifts the phase constant at −90°. In the whole area in which the "pressure gradient figure-of-eight microphone" has a constant frequency response, thus, the phase is equal to the "pressure omni-directional microphone".

 "Schallschnelle und Druckgradient sind nicht das Gleiche": http://www.sengpielaudio.com/SchallschnelleIstNichtDruckgradient.pdf   "Mechanische Abstimmung von Mikrofonen 1 - Schall-Druckempfänger http://www.sengpielaudio.com/MechanischeAbstimmungSchalldruck.pdf   "Mechanische Abstimmung von Mikrofonen 2 - Schall-Druckgradientenempfänger http://www.sengpielaudio.com/MechanischeAbstimmungDruckgradient.pdf   "Membranabstimmung des Mikrofons (Mikrofonabstimmung) - Wikipedia" http://de.wikipedia.org/wiki/Mikrofonabstimmung   "State of the membrane resonance in dynamic microphones and condenser microphones" http://www.ak.tu-berlin.de/fileadmin/a0135/Unterrichtsmaterial/Skripte/Bore_Peus_Mikrofone.pdf#search=Tiefabstimmung