QUADRAPHONIC SYSTEMS

The first phonograph recordings were made with the vertical, or hill and dale method. This caused the groove made by the recording cutter to be modulated vertically. The groove became deeper and shallower as the sound waves modulated it. This causes the playback stylus to vibrate in a vertical direction, as shown by the violet arrow. Of course, the arrow is exaggerated in size - the stylus could not possibly vibrate more than a third of the depth of the groove without causing groove tracking trouble.

Later recordings (including most 78 rpm records, and all mono LPs and 45s) were recorded laterally. The stylus vibrates from side to side, as shown by the green arrow. This modulation is also used for sounds centered between the speakers in a stereo recording.

The head of each arrow shows the modulation direction on an increase in sound pressure. A decrease in pressure moved the stylus the other way.

Lateral can be played on any stereo phonograph, provided the proper size stylus is used.

To play vertical records, either a phase reversal of one stereo channel is needed, or the surround output of a Dolby Surround system can be used.

• Lateral = .71L + .71R
• Vertical = .71R - .71L

Capital letters indicate stereo channels. Lowercase letters indicate quadraphonic channels.

Stereo phonograph recordings use stylus motions at 45° angles to horizontal. With a V-shaped groove, the left wall of the groove (as seen from the front of the phonograph) carries the left channel. This is the wall closest to the spindle. The right wall of the groove (the wall closest to the record rim) carries the right channel. For sounds between the speakers, the modulations become shallower, becoming lateral for sounds centered between the speakers.

On the Poincaré sphere, the left channel modulation is on the far side of the sphere. The right channel modulation is on the near side. A small circle shows a modulation plotted on the near (right channel) side of the sphere. A larger circle denotes a modulation plotted on the far side (left channel) of the sphere.

Stereo records can be played on any stereo phonograph, provided the proper size stylus is used.

A "Three Channel" recording used three mics. The third mic (f) was fed equally to both channels of the record, producing a lateral modulation. This plays on any stereo.

• l = L
• r = R
• f = .71L + .71R

The Poincaré Sphere (also called the Stokes Sphere, the Foucault Sphere, and the Fresnel Sphere) was originally conceived by Henri Poincaré in 1892 to describe polarized light, and by Foucault to describe free-swinging pendulum motion. It was adapted by Peter Scheiber in 1970 to describe the phase relationships between the stereo channels of a recording, and was independently discovered by the page author for the same purpose. All modulations are on the surface of the sphere. The six orthogonal modulations are shown as follows:

• Lateral motion (f) is at the extreme right.
• Vertical motion (b) is at the extreme left.
• Left channel motion (l) is on the far side.
• Right channel motion (r) is on the near side.
• Clockwise motion (n) is at the extreme top.
• Anticlockwise motion (n) is at the extreme bottom.
• Odd angle & elliptical motions are in between.
• Small dots are on the near side of the sphere.
• Large dots are on the far side of the sphere.

Modulations 180° apart on the sphere have complete separation. Modulations 90° apart have 3 dB separation.

The stereo pickup can play back any modulation on the Poincaré Sphere. Some kind of decoder is then used to recover the wanted signals and route them to the proper speakers.

• l = L
• r = R
• f = .71L + .71R
• b = -.71L + .71R
• n = .71L + .71Rj
• z = .71Lj + .71R

This image represents the listener's head in speaker location diagrams.

In 1969, Peter Scheiber evenly divided up the spaces between the linear orthogonal motions already described, arriving at the modulations shown. No commercial recordings are known to be recorded in it.

By 1971, Sansui had independently developed what is essentially the same system, which they called QS. It has the second largest discography of surround material, including one movie.

In both cases, speakers are provided for the left front (lf), left back (lb), right front (rf), and right back (rb) signals.

The QS system encoder produced the n (nadir - straight down) modulation when equal signals were presented at all inputs. The z (zenith - straight up) modulation is also possible, but is not normally used.

• L = .92lf + .38rf + .92lbj + .38rbj
• R = .92lf + .38rf - .92lbj - .38rbj

A Dolby Surround system in the Surround mode plays these recordings, as does any QS or RM decoder. Actually, Pro Logic also does a nice job, as do any of the Dynaco or EV systems.

• lf = .92L + .38R
• rf = .38L + .92R
• lb = -.92Lj + .38Rj
• rb = -.38Lj + .92Rj

In the BBC trials, the basic QS matrix was Matrix A, and the QS Variomatrix was Matrix C.

In 1970, Dynaco developed a passive matrix decoder, using only the way the speakers are connected to the amplifiers to do the decoding. It uses the four linear orthogonal motions listed above. The Dynaco Diamond is the simplest and cheapest system available. Anybody can build one with nothing but speakers and resistors.

The major disadvantage at the time was the location of the speakers on the faces of the listening room walls, instead of in the corners. This caused conflicts in room decor and in positioning speakers so they sound best.

Several commercial recordings are known to be recorded in it. The Dynaco Diamond is actually better suited to classical music than most of the other systems. The page author used it in 1971 to produce a set of sound effects for a stage theatrical production.

• L = .71f + l - .71b
• R = .71f + r + .71b

A Dolby Surround system in the Surround mode plays these recordings, as does any Dynaco Diamond, QS, or RM decoder. Pro Logic also does a nice job, as do any of the Dynaquad or EV systems.

• l = L
• r = R
• f = .71L + .71R
• b = -.71L + .71R

In 1970, Leonard Feldman and Jon Fixler developed what would become the Electro-Voice Stereo-4 system. This was the first system to use different sets of coefficients for encoding and decoding. (Most other systems have decode coefficients that mirror the encode coefficients.) It was originally developed as a way to make headphones work with surround sound. Afterward, it was extended to work with speakers.

This is a front-oriented system, because it emphasizes front separation and front-to-back separation, at the expense of rear separation. This makes it better suited to classical music than most of the other systems.

Many commercial recordings are recorded with it. It has the 5th largest discography. I have normalized the equations, so all of them have the same amplitudes (the original equations did not).

• L = .96lf + .29rf + .89lb - .45rb
• R = .29lf + .96rf - .45lb + .89rb

A Dolby Surround system in the Surround mode plays these recordings, as does any Electro-Voice decoder. Pro Logic also does a nice job, as do any of the other Regular Matrix decoders.

• lf = .98L + .20R
• rf = .20L + .98R
• lb = .78L - .62R
• rb = -.62L + .78R

In 1971, Dynaco changed the Dynaco Diamond into the Dynaquad system, which has the speakers in the corners of the room. It is still a passive system. This system also uses different sets of coefficients for encoding and decoding. This is a front-oriented system, because it emphasizes front separation and front-to-back separation, at the expense of rear separation.

Few recordings were made in this system. It is better suited to classical music than most of the other systems. I have normalized the equations, so all of them have the same amplitudes (the original equations did not).

• L = .97lf + .24rf + .89lb - .45rb
• R = .24lf + .97rf - .45lb + .89rb

Dynaquad Quadaptor

Dynaco sold a $20 decoder called a Quadaptor, to be connected between the amplifier and the speakers.

A Dolby Surround system in the Surround mode plays these recordings, as does any Dynaquad decoder. Pro Logic also does a nice job, as do any of the other Regular Matrix decoders.

Quadaptor equations

• lf = L
• rf = R
• lb = .86L - .5R
• rb = -.5L + .86R

In 1971, Benjamin Bauer, Columbia Records, CBS, and Sony developed the SQ system after experimenting with systems similar to QS and UMX. The system preserves left-to-right separation, at the expense of front-to-back separation. It is not well suited to ambiance recordings of concert halls. This system is unusual in that the back channels are recorded with circular stylus motions.

CBS SQ has the third largest discography.

There are two encoders, pan-potted and 4-corners, each with different modulations for sounds from the sides.

There are two decoders. The 10-40 decoder is cheap, with no logic. The expensive decoder uses the main modulations with signal-steering logic.

• L = lf - .71lbj + .71rb
• R = rf - .71lb + .71rbj

Only an SQ decoder or an EV-Universal decoder can decode this right. Dolby Surround and RM decoders decode all but the rear corners correctly. They place the rear corners in the middle of the room.

• lf = L
• rf = R
• lb = .71Lj - .71R
• rb = .71L - .71Rj

The 10-40 decoder has a 10% blend between the front channels, and a 40% blend between the back channels.

In the BBC trials, the basic SQ matrix was Matrix B, and the SQ Full Logic was Matrix D.

In 1972, D. H. Cooper, T. Shiga, and Denon released the UMX (Uniform Matrix) system. It is not compatible with any other matrix system, and has some stereo compatibility problems. It was used in Japan and eastern Asia, but practically nowhere else.

This was originally billed as UMX. In 1974, Denon divided it into the 2-channel BMX, and the carrier disc UD4, which plays BMX without the decoder.

Peter Scheiber offered the same matrix as an alternative, and CBS studied it as one of the "New Orleans" matrix ideas before settling on SQ.

I normalized the equations, so all of them have the same amplitudes (the original equations did not).

• L = .65(lf+lfj+lb-lbj) + .26(rf+rfj+rb-rbj)
• R = .26(lf-lfj+lb+lbj) + .65(rf-rfj+rb+rbj)

UD4 carrier contents (limited to 3 KHz bandwidth):

• L_car = .65(lf+lfj-lb+lbj) + .26(-rf-rfj+rb-rbj)
• R_car = .26(-lf+lfj+lb+lbj) + .65(rf-rfj-rb-rbj)

Three 3 ways to play this correctly:

1. Use a UMX or UD4 decoder.
2. SQ decoder: reverse lb speaker phase, move speakers.

   	lb
   lf		rf
   	rb

3. Matrix H decoder gives suboptimum results.
    

• lf = .65(L-Lj) + .26(R+Rj)
• rf = .26(L-Lj) + .65(R+Rj)
• lb = .65(L+Lj) + .26(R-Rj)
• rb = .26(L+Lj) + .65(R-Rj)
   

In the BBC trials, the basic BMX matrix was Matrix F.

In 1971, JVC announced a discrete system for phono records that recorded ultrasonic carriers in record grooves. RCA used it in 1974. It has the following disadvantages:

• It requires special CD-4 pickup, wiring, and demodulator.
• Playing the record without a special pickup damaged the carrier permanently.
• A damaged carrier sounds like sandpaper, naming CD-4 "sandpaper quad" and "seedy four".
• Dust makes crashing sounds instead of clicks.

It has the 4th largest discography, but most extant discs are unusable, due to groove damage. Suggestions were made to matrix discrete discs, using RM, SQ, UMX (UD4), and H (UHJ). None except UD4 and UHJ were ever released.

• L = .71lf + .71lb + carrier(.71lf - .71lb)
• R = .71rf + .71rb + carrier(.71rf - .71rb)

Suggestions on playing these:

1. Don't.
2. Use a CD-4 pickup, wiring, and demodulator, and hope for the best.
3. Use a CD-4 pickup and play it as a stereo record.
4. If the carriers are already ruined, cross off the CD-4 on the label, and play it in stereo.
    

• lf = .71L + .71L carrier
• rf = .71R + .71R carrier
• lb = .71L - .71L carrier
• rb = .71R - .71R carrier

In 1973, Electro Voice signed an agreement with Columbia, and produced the EVX-44 Universal Decoder. The idea here was to make a decoder that can play the EV, QS, and SQ records mixed on a record changer without having to change decoders. They later suggested the same coefficients as an encoder, but no records were ever produced.

The decoder has a front-oriented automatic variable blend that reduces rear separation when center front material is present. It can also be set to be blended all the time, or never blended. The lb and rb dots farthest apart on the sphere are not blended, the ones closest together are blended. The Metrotec decoder is the EV universal decoder without the blend in the "synthesized quad" position.

• L = .98lf + .20rf - .63(lbj+rb) + .25(lb+rbj)
• R = .20lf + .98rf - .25(lbj+rb) + .63(lb+rbj)

Records were never released in this format.

The decoder plays:

1. EV and Dyna recordings quite well.
2. SQ records quite well.
3. QS records, but not as well.
4. UMX records if the speakers are rearranged and phased as above.

• lf = .98L + .20R
• rf = .20L + .98R
• lb = .63(Lj-R) + .25(L-Rj)
• rb = .25(Lj-R) + .63(L-Rj)

In 1974, the BBC started investigating matrix broadcasting. They tried several matrices, which they labeled with letters, and settled on matrix H. One requirement was that it have full mono compatibility, which it does. But the matrix does not match any other matrix.

Few recordings are "officially" released in Matrix H, but the page author has some that behave as though they were recorded in matrix H, and several more that behave as though they were recorded in matrix H with the rotations reversed (named HR by the page author)

A small unofficial discography exists in H and HR, and BHJ and UHJ (see below) are also derived from H.

• L = .85(lf-lbj) + .35(lfj+rf+lb-rbj) + .15(rfj+rb)
• R = .85(rf+rbj) + .35(lf-rfj+lbj+rb) - .15(lfj-lb)

For HR, reverse the signs of the j terms, reverse the rotations of the stylus motions, and flip the Poincaré Sphere image over vertically.

The upper left Poincaré Sphere positions for the left and right pair are panpot positions; the lower right ones are 4-corners encoding.

Without an H decoder, the best way is to combine an RM and an SQ decoder with six speakers, placed as follows:

RM lf	SQ lb	RM rf
RM lb	SQ rb	RM rb

Reverse the phase of the SQ lb speaker.

For HR, trade the SQ speakers.

An RM decoder works, but with less separation.

• lf = .85L-.35(Lj-R)+.14Rj
• rf = .85R+.25(L+Rj)-.14Lj
• lb = .85Lj+.35(L-Rj)+.14R
• rb = -.85Rj+.35(Lj+R)+.14L

This was mentioned by Peter Scheiber, but never used. The page author built an encoder and a decoder, but never produced any recordings with it. By the time it was operational, Dolby Surround had become the standard matrix.

The idea was to design a matrix with equal separations between all channels.

• L = .95lf + .30rf - .67(lbj-rb) + .21(lb-rbj)
• R = .95rf + .30lf - .67(lb-rbj) + .21(lbj-rb)

Only a few experimental recordings ever existed in this format. They no longer exist.

• lf = .95L + .30R
• rf = .30L + .95R
• lb = .67(Lj-R) + .21(L-Rj)
• rb = .67(L-Rj) + .21(Lj-R)

This was originally developed to make "Star Wars" under the name Dolby Stereo. It quickly became the preferred surround system for movies. Home movies were encoded in it, as were many phonograph records, cassette tapes, and CDs. Most soundtrack recordings are encoded in Dolby Surround because the movies they came from were so encoded. There are more recordings in this matrix than any other.

One difference from other systems is that the decoder adds a delay in the back channel before it goes to the speakers, and that back speakers (called surround speakers) are placed on both sides. This removes the problem of localizing the side images that other 4-corners matrices have. Also, applying identical signals to all of the inputs produces the nadir (n) modulation.

• L = l + .71f + .71bj
• R = r + .71f - .71bj

New Dolby Surround decoders are widely available. Other regular matrix decoders do an acceptable job.

• l = L
• r = R
• f = .71L + .71R
• b = .71Rj - .71Lj with a delay

This was patented and announced, but it makes no sense. This was intended as an alternate way to encode for Dolby Surround, but it looks like nothing but a way to get around patents. It does have a resemblance to the Stereo 180 miking system's output. But there are some discontinuities in the encoding patterns as a sound is panned all the way around the listener.

• L = lf + .71f - .71lbj + .50rb
• R = rf + .71f - .71rbj + .50lb

A small discography exists in this format.

It is intended to be decoded with Dolby Surround.

SQ can be used with the lb and rb speakers traded.

• l = L
• r = R
• f = .71L + .71R
• b = .71Rj - .71Lj with a delay

This is a modification of the matrix H, used by the Ambisonic system. BHJ is the 2-channel matrix. UHJ is a 3 or 4 channel version for DVD that increases separation. The 4-channel version adds a height dimension. For the Dolby Surround channel positions, the BHJ matrix is:

• L = .83l + .12r + .56f + .38b + .09fj - .43bj
• R = .21l + .83r + .56f + .38b - .09fj + .43bj

A small discography exists.

Various decoder configurations exist. The following work:

• Use an Ambisonic or H decoder.
• Use an SQ decoder. Feed the rb channel to both back speakers.

  lf		rf
  rb		rb

• Dolby Surround or RM does a partial job.
• Combine Dolby Surround with the SQ decoder method above, with 2 sets of back speakers

This was a modification to Dolby Surround used for a few movies. It adds a third dimension of height, using the zenith (z) and nadir (n) modulations. It is also encoded into the soundtrack albums of those movies. The name is the page author's suggestion, because no mention of it by name is known. Some versions trade the n and z modulations.

• L = l + .71f + .71bj -.71nj + .71z
• R = r + .71f - .71bj -.71n + .71zj

A few movies and records were released in this format, but not labeled.

It is decoded with Dolby Surround and an SQ decoder. Use Dolby Surround normally, SQ lb for n, and SQ rb for z.

• l = L
• r = R
• f = .71L + .71R
• b = .71Rj - .71Lj with a delay
• n = .71Lj - .71R
• z = .71L - .71Rj

This was suggested in several articles, but never used. The page author built a decoder and used it to play the Hexaphonic Tridee system with 4 speakers. It is basically the UniQuad ES system with the speakers rearranged (the rb speaker is hung from the ceiling in the back (zb), and the lb speaker is placed on the floor (nb). So the only difference is the speaker designation. Some versions trade the nb and zb modulations. To save download bandwidth, the UniQuad ES illustrations are used.

• L = .95lf + .30rf - .67(nbj-zb) + .21(nb-zbj)
• R = .95rf + .30lf - .67(nb-zbj) + .21(nbj-zb)

A few records were released in this format. The SQ 10-40 or the EV Universal can be used with the same speaker rearrangement.

It plays the Hexaphonic Tridee system.

• lf = .95L + .30R
• rf = .30L + .95R
• nb = lb = .67(Lj-R) + .21(L-Rj)
• zb = rb = .67(L-Rj) + .21(Lj-R)

This was not an encoding matrix. It was developed so that QS, EV, and SQ quadraphonic records could be intermixed on a record changer. It is a better match for all three matrix systems than that of the Electro-Voice Universal decoder.

Since there is no encoder, no encoding equations are shown.

No recordings exist in this format, because it is not a recording format.

• lf = .98L + .20R
• rf = .20L + .98R
• lb = .71L + .5Lj - .5R
• rb = .71R + .5Rj - .5L

Utah Studio-4

This was not an encoding matrix. It was a device to fake a surround sound experience. It did not do a very good job. It was essentially the same as the Dynaco Diamond, except that the speakers were placed in different places.

This provided a strangely folded listening field. It surrounded the listener with sound, but produced no useful instrument localization.

Since there is no encoder, no encoding equations are shown.

By moving the speakers, the owner of a Studio-4 could use it as a Dynaco Diamond decoder.

The following passive decoder variants circuits were made by the page author. All of them required only two channels of amplification:

UniQuad HP-1

HP-1 was made from wire and 8 RCA jacks, for 6 speakers from compact stereos. It provided the Dynaquad arrangement, plus center front and center back speakers, for hexaphonic sound.

UniQuad UQ-1

UQ-1 had a variable width blend control on the front speakers, variable depth control on the back speakers, AutoVary separation enhancement, and a disco bass booster.

UniQuad UQ-44

UQ-44 is the only passive decoder ever made that decodes all of the regular and phase matrices, including SQ. It has switch positions for preset and adjustable matrices, AutoVary separation enhancement, a disco bass booster switch, and a headphone surround circuit. The disadvantage was the box larger than one foot high, wide, and deep needed to house the parts.

Quadruplex, Composer, Quadrasizer, Etc.

These were variants on the Dynaquad Quadaptor. They had passive decoder circuits that were just enough different that they didn't infringe on any patents. They decoded any Regular Matrix recordings.

Reverb Systems

Several systems were sold to send synthetic reverberation to the back speakers. These can't decode encoded recordings.

Utah Studio-4

• lf = L
• rf = R
• lb = .71L + .71R
• rb = -.71L + .71R

Speaker placement of Dynaco Diamond signals in Studio 4 arrangement:

l                r

listener

f                b

UniQuad HP-1

• f = .71L + .71R
• lf = L
• rf = R
• lb = .86L - .5R
• rb = -.5L + .86R
• b = -.71L + .71R

Speaker placement of HP-1:

lf        f        rf

listener

lb        b        rb

UniQuad UQ-44

Switch positions on UQ-44

• QS
• EV-4
• Dynaquad
• SQ
• EV-U
• UniQuad ES
• Compatiquad
• UMX
• Basic Matrix variable
• Regular Matrix variable
• Compatiquad Variable
• SQ Variable

This was proposed by Denon, but never used beyond a few experiments.

The idea was that the two stereo channels always have the same amplitude, but different phase. The phase angle is equal to the direction the sound comes from.

• L = .71f + .71lj + .71r +.71bj
• R = .71f + .71l + .71rj -.71bj

All channels can be derived using an SQ decoder and resistor summing networks. Reverse the phase of the left speaker:

• f = .71 SQ lf + .71 SQ rf
• l = - SQ lb
• r = SQ rb
• b = .71 SQ lb + .71 SQ rb

Decoding equations:

• f = .71L + .71R
• l = - .71Lj + .71R
• r = .71L - .71Rj
• b = - .71Lj + .71Rj

The BBC ran a series of trial experiments using several matrix systems. They were lettered from A to H as follows:

• Matrix A was QS, no logic.
• Matrix B was SQ, no logic.
• Matrix C was QS, with logic.
• Matrix D was SQ, with logic.
• Matrix E was a tetrahedral matrix Peter Scheiber's proposed for high separation.
• Matrix F was UMX (BMX), no logic.
• Matrix G was UMX modified to reduce the phasey stereo image.
• Matrix H was Matrix G modified.

This was the other tetrahedral matrix proposed by Peter Scheiber. Other than for these trials, it was never used. It made the stereo image sound very "phasey".

• L = .820(lf+lb) + .339(lfj+lbj) + .425(rf−rb) − .176(rfj−rbj)
• R = .820(rf+rb) + .339(rfj+rbj) + .425(lf−lb) − .176(lfj−lbj)

The matrix decoding equations of all of the matrices in the BBC trials are the complex conjugates of the encoding equations.

This is a modification of Matrix F (UMX) intended to get rid of the phasey play in stereo and mono. It was never used for released recordings.

• L = .890(lf+lb) + .313(lfj−lbj+rfj−rbj) + .110(rf−rb)
• R = .890(rf+rb) + .313(rbj−rfj−lfj+lbj) + .110(lf−lb)

The matrix decoding equations of all of the matrices in the BBC trials are the complex conjugates of the encoding equations.

This is a modification of Matrix G, intended to improve separation. Matrix H is based on Matrix G. It was never used for actual released recordings

• L = .860(lf+lb) + .347(lfj−lbj+rfj−rbj) + .140(rf−rb)
• R = .860(rf+rb) + .347(rbj−rfj−lfj+lbj) + .140(lf−lb)

The matrix decoding equations of all of the matrices in the BBC trials are the complex conjugates of the encoding equations.

This is a modification of Matrix G, intended to improve play in stereo and mono. It is an early version of Matrix H. It was never used for released recordings.

• L = .926lf+.163lfj+.852lb−.397lbj+.145(rf−rb)+.310(rfj−rbj)
• R = .926rf−.163rfj+.852rb+.397rbj+.145(lf−lb)+.310(lbj−lfj)

The matrix decoding equations of all of the matrices in the BBC trials are the complex conjugates of the encoding equations.