I am seeing some wild misinformation in this thread. Much of it is due to misunderstanding.
1. There is no such thing as a phase shift unit that gives the same phase shift at all frequencies. It can't be done. What is needed is a set of two phase shift units with what are called psi shifts that produce a difference in the outputs of the two units that is the desired phase difference between them at all frequencies in the audio range. So you might get psi+0 (psi) and psi+90 (psi j) as your two outputs. But if you compare one of these psi outputs with the original input, the phase is frequency dependent and goes all around the phase angle clock as the frequency changes.
I have built several psi units for my quad experiments. One set of four units works with a speaker matrix (SQ for Dyna?)
The SQ interior encoding mode uses the original input of a front sound and the psi shifted back sound to cause pseudo randomization between the sounds.
2. The encoding is not dependent on the actual phase angle, but on the relative phase angles between the left and right encoded outputs. Thus the following are true:
All four of these pairs produce an in-phase encoding (center front for most matrix systems):
L = a, R = a; L = -a, R = -a; L = aj, R = aj; L = -aj, R = -aj
A decoder can't tell them apart. All 4 are sent to the same location.
All four of these pairs produce an antiphase encoding (center back for most matrix systems):
L = a, R = -a; L = -a, R = a; L = aj, R = -aj; L = -aj, R = aj
All four of these pairs produce a left channel encoding (left side encoding in different places for various matrix systems):
L = a, R = 0; L = -a, R = 0; L = 0, R = 0; L = -aj, R = 0
All four of these pairs produce a clockwise 90 degree encoding (left leads right - left back in SQ):
L = a, R = -aj; L = -a, R = aj; L = aj, R = a; L = -aj, R = -a
All four of these pairs produce an anticlockwise 90 degree encoding (left lags right - right back in SQ):
L = a, R = aj; L = -a, R = -aj; L = aj, R = -a; L = -aj, R = a
Which of the four pairs for each encoding is chosen for an encoder design is based solely on a desired phase relationship between different encoded inputs in the final recording. But the decoder can't tell the pairs for the same encoding apart as far as where it sends the sound.
Selection of the different encoding pairs from each list is what makes the different kinds of SQ encoders Columbia used.
3. The purpose of the phase shifts in the QS system is to be able to encode a 4-channel tape, get all of the phases out the same when decoding the matrixed recording, and to not lose any sounds placed between the speakers when encoding (the Scheiber system lost center back sounds). But if you are encoding individual sound sources having no crosstalk using my panpot mixer method, a QS encoding can be made without any phase shifts (other than +a and -a). I have done it many times. Dolby Surround has the phase shifts for the same reason. They encode sounds in the back without cancellation of related sounds in either side.
4. Dolby Surround is based on the original Dynaco diamond matrix, with phase shifts to avoid cancellation in the back (not to change the encoding direction). The Dolby Surround with different back encodings and decodings for two back speakers are similar to the QS back speaker encoding and decoding, but with different separations (closer to Dynaquad than QS).
5. To get SQ back corner encodings, the signal must have a j in one encoded channel but not in the other.
6. Circlesurround is essentially SQ with the two back channels traded.
7. Recordings made for Dolby Surround, QS, the original EV, and DY are all very similar to each other, and can be interchangeably played on any of these systems. The only difference between the playbacks are slight side image shifts forward or backward and the addition of corrected side imaging (hearing sounds between the speakers on the side when facing forward) when the Dolby decoder is used with any of them.
8. RM generally refers to any matrix with front encoded inphase, sides in left or right channel only, back encoded antiphase, and no circular phase encodings except for overhead.
SQ generally refers to a matrix with the left channel encoding left front, the right channel encoding right front, center front encoded inphase, center back encoded antiphase, and circular phase for left back and right back.
9. Japan Phonograph Record Association (JPRA) and the Electronic Industry Association of Japan (EIAJ) created several standards for quadraphonic systems:
RM EIAJ Matrix EIAJ definition of QS (Regular Matrix) - equal separations for adjacent channels (Scheiber and QS)
QM EIAJ Matrix EIAJ definition of front-oriented matrix - greater separations in front than in back (EV4 and DY)
PM EIAJ Matrix EIAJ definition of SQ (Phase Matrix) - circular encoding of back channels (SQ, EVU)
UM EIAJ Matrix EIAJ standard for Uniform matrix - circular encoding of front-back position (BMX, UD4, H, UHJ)
This is where RM and PM came from.