Adventures in Surround Sound, from 7.2 to Quad 
(personal and historical notes, basics, and acoustic realities often forgotten)
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Matrix "Quad" Systems
RM vectors
The RM (Regular Matrix) System

To he first notable matrix encoding system that was suggested led directly to something that eventually became called the "RM" or Regular Matrix. In this case the name certainly fits. Above, when you click, you'll find a nice new scan of one of a trio of sheets I just located calculating the vector math of this particular system, and SQ and QS as well below. I can't go into the mathematics of it here and now, perhaps soon. I will point out that on the above sheet the fan shape is an overall vector diagram of the levels of each channel, how they are distributed with respect to the center front, which is exactly to the right, the "reference" angle. If you want a little extra detail, the box below will inform slightly more. I'll add a Bibliography soon for even better background information.

Some Slightly "Tech-Tawk"

On the SQ and QS sheets there are also basic schematic drawings of the general circuit used, which is somewhat more complex than the RM originally was, so needed clarification here. You can see at a glance that these are not particularly complicated circuits, at least leaving the Psi-Networks out of it. Even if you added those, there would be far less "stuff" that the average home gear of today: clock, tv remote, CD player, computer. It's from an old discrete component era for the most part, when even an elaborate receiver had but a handful of transistors, and only a few dozen resistors and capacitors and so forth. To the right of these circuits you can see other vector diagrams. Again to the right horizontally is the reference angle.
Backwards horizontally is the "out of phase 180 degree direction". Up vertically is 90 degrees CCW vector, while vertically down is 90 degrees CW, the exact out of phase opposite of the straight up CCW vector. Some of you will already be familiar with this kind of graphic solution, and will pick up what was going on here. There's a note to myself that with the addition of the all-pass filters (known as a 90-degree quadrature pair) or Psi Network (also called a J-Network), the RM can be converted exactly into a QS matrix. And vice-versa. Certainly "Logic" Circuits and enhancements for separation beyond the pitiful 4.8 dB maximum (that's at best, most of them had only about 3 dB separation) were needed, some "gain-riding logic" had to be provided to imitate the completely enveloping soundfield of glorious discrete surround sound. What really was needed was what we've only recently standardized: DVD-A multichannel audio disks!

RM enchanted me in a different way, though. Here was an extended plan which followed closely the simple fold-down method I have been using since the mid 60's to derive two-tracks of Stereo for final release, when most of my master mixes have been designed and realized as four channel surround sound. It was during the production of Sonic Seasonings that Rachel and I really got excited about this elegant way to collapse the soundfield into normal stereo. I've reported before, and so has Rachel in the liner notes, that at times we had to double-check what we were listening to, as the two channel reduction could often mimic true surround sound, when played back on the same setup. Anyway, RM represented the underlying pattern that our method was a subset of. Kinda cool, and the fact that at times you can be fooled like this suggests that there is more to this field that anyone has yet explored. I think it's time we tried, don't you?

sq vectors
The SQ (Stereo-Quad) CBS/Sony System

Since Ben Bauer came up with the ideas behind the SQ matrix starting in the late 50's, it's hard to date the final system historically. I'll simply place it after the Regular Matrix since the final configuration that the system became know for was decided upon at that time. In any case, this is not intended be be an historic document, and there is some overlapping in the designs, which obviously were treated rather secretively at first. Once again, this is one of the three drawings that I had neatly recopied for my own analysis, of what to expect when using the CBS system. You can see the simplicity of the basic networks in their purest form. (Note: my silly use of "exact" for numerical values in these charts merely meant: "more exact," what I used to calculate my tables and charts.)
So-called "logic" circuits added a lot of additional circuitry to the decoder (the encoder remained the same, except for the additional kludges CBS Labs designed to allow at least some way to do the "forbidden" of SQ encoding. These got fairly elaborate. Perhaps I'll add a couple of examples in a future update, if there's enough interest. The original CBS Logic Decoder was a pretty compromised affair, we thought. It pumped and glitched, and created an appalling instability around the room. I usually ended up just turning it off, going with the basic matrix. Of course there was only 3 dB's of separation now between rear (they didn't know about side channels) and front. Essentially that's like no quad at all. Is it any wonder these schemes failed?! Really, isn't there a lesson or two to be learned here?
Finally, at the last gasp of SQ, a new kind of logic circuit showed up, called Tate Logic. It was released only in the Fosgate 101a, to the best of my knowledge. This new design didn't ride gain, but shifted the matrix's coefficients while decoding so that the strongest signal was channeled correctly, the adjacent leaking channels receiving some of the opposite phase signal added in instead, canceling the crosstalk. So these secondary sounds sort of "scurried" into another channel for a moment (still only two simultaneous sounds at a time could be steered) which yielded a minimum amount of leakage from the dominant channel. It all happened very quickly, readjusting from second to second. There were few swoops during the attacks of new sounds, and since we tend to judge direction by the attacks more than steady portions of a sound, it could create a much better simulacrum of true discrete sound.
Again it depended on the program material, and that kind with a minimal amount of polyphony, with clear solos darting from speaker to speaker, not too much in between, not too much ambience or reverb, both of which would drift, it was not bad. Tate logic chips then were licensed to Dolby Labs. Friends in high places there told us about it, and we all agreed this was the ideal marriage for both. Film soundtracks usually impose simpler demands than music, not too much happening at once, unless it's meant to create an overall effect, a blur all around. Tate logic is adept at this trick, as has been proven by the several thousand films mixed that way since 1977's Star Wars unveiled the welcomed new system.

qs vectors
The QS (Quad-Stereo) Sansui System

In point of fact, Sansui's QS matrix came out of the Regular Matrix (and later, vice-versa, too). The first versions of RM had some less desirable properties in regard mono compatibility, and maintaining an adequate channel separation between any adjacent speaker pair. QS attacked these with the introduction of similar Psi-Networks as Ben Bauer had developed to enhance the SQ matrix. There were quite a few differences, and certainly it would be a stretch to suggest that the resulting recordings were compatible in any way. RM and QS maintained the compatibility of their origins, but SQ stood out against them both. I think Bauer had been thinking mostly of classical masters he had heard early on at CBS records, which invariably used the one speaker in each corner "obvious quad" configuration.
So these masters usually had the orchestra or smaller ensemble recorded in the usual way up in front, and two distant mikes much further back picked up the hall sound for the rear two channels. For this notion the SQ matrix is a clever idea, and perhaps is the best one could hope to come up with given the restraints of only two actual channels of final output. I've heard it sound pretty all right under those conditions, nothing to write home about if you've heard the real thing, but something mildly interesting that might attract the attention of a small user base who listen to only a certain restricted kind of recording.
Sansui came up with its own excellent separation enhancer, called "Vario-Matrix." It sounded surprisingly decent, the images wandered a little, but you were not aware of any annoying pumping, especially of the front-rear variety (the circuit instead varied the playback matrix's sum and difference coefficients, thus its name). The Tate system described above for SQ is quite similar to Sansui's Vario-Matrix: both alter the matrix values from moment to moment to keep the dominant sounds, primarily their attack portions, located near their correct positions, and the leakages are canceled out as well as can be accommodated at the same time.
Sansui QS variation of RM, is probably the best of the matrix systems. It arrived a bit too late to make much of a dent on the progress of surround sound in the 70's. By 1974 either the SQ system had been adopted by CBS-loyalists, or the true quad (discrete) QuadraDisk had become the favored choice of the RCA wing. Some small independent companies went with the QS matrix (not wishing to side with either CBS nor RCA!), and a couple even experimented with several systems, going so far as releasing alternative versions in competing systems. But that was rare -- while artists had the least choice of all. Sad to admit (it's mentioned in my second letter to Billboard), the QuadraDisk was often not the highest in fidelity, certainly not at first, and if misplayed the ultra high frequencies could be damaged: goodbye quad. It took care and a some engineering savvy both to cut and later extract the most from the complex JVC system. I had a lot of fun with it, learned to coax it into working fairly well, and longed to release some of my music using CD-4. We had some test QuadraDisks cut for us by JVC, but CBS balked. The QS matrix would also have been preferable, compared to SQ's unwelcomed limitations on recording and mixing. CBS said no. With the provisos on lack of robustness and slightly compromised fidelity, the QuadraDisk remained our first choice of available systems in 1974, as it was the most honest. And now so is the DVD-A.
I think it might be appropriate here to point out that the way I ended my second letter is still true in 2001, and forms the basis for the first section of this webpage. Let's get the speaker arrangements optimal from the get-go. If we had adopted some of the sophisticated circuits and concepts that were generally wasted in effort to make pseudo quad good enough to fool an audience, we would be creating much better stereophony and surround sound masters today. With the ultra fine audio quality and phase coherence of CD's and even better DVD-Audio disks, these old ideas ought be looked into again. Several early 20th century ideas also ought be reintroduced, like Blumlein sound-shufflers, neat arrays of spaced coincident microphones, or newer digital devices for mimicking the effect of binaural over loudspeakers (pioneered by the excellent Lexicon CP-1, CP-3 and DC-1 series). We can do some very KEWL things with such collections of tools! It's an exciting opportunity, let's work together on it. If no one's interested, you can bet I'm gonna try, anyway. And I'll report back to you here if anything interesting comes along! :^)

--Wendy Carlos

(We've come a long way!
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The matrix systems depicted above, as we've seen, rely on what's called a "Psi-Network" (or "J-Network). It's a real shame that this concept was so closely tied to the pseudo-quad brigade, that when those compromises faded, so did most other interest in these circuits. So let me make take a moment here to set the record straight. Things are confused by another name for this all-pass filter audio tool, the "Hilbert Transformer" (a fine, if technical description, in this case implemented digitally (with C-Sound) can be found at this link). I've also encountered one more name: "Dome Filter," a somewhat older term from the days of analog circuits. (I've not yet been able to obtain a copy, but I note a tempting paper that describes dome filters, that's available through NTIS.) Whatever the name, they show up in unexpected places. I ought mention a wonderful sound transmogrifying device I've been using since the mid-60's: the "Klangumwandler," or Frequency Shifter. Only recently I learned that inside one of these you'll find a few psi-net circuits.
Harald Bode, an skillful pioneer in the engineering of electronic music (i.e., the Bode Melochord), designed and invented several unique Klangumwandlers. In the early 60's Vladimir Ussachevsky (electronic music pioneer and Professor of Music at Columbia when I got my MA in composition) asked Harald to construct a couple of them for the Columbia-Princeton Electronic Music Center. That's where I first saw one, and made good use of it on the first music score I ever composed, for Bob Shaye's clever, amusing early short film, Image. It was screened in November 1999 at the Whitney Museum of Modern Art's retrospective of 20th Century art and film. I attended that with Bob, and smiled to hear the "sins of my youth," including some venerable old frequency-shifted harmonica melodies Bob played himself for me. Truly kewl!
Later Bob Moog constructed for me a wonderful custom analog Klangumwandler from Harald's designs, which I've used for years. (You can hear it nicely on the slow, rich tutti sections of my 4th Brandenburg realization, mvmt. II -- it's in the new boxed set.) Anyway, these units took one kind of advantage of what can be most accurately described as "90-degree Constant Phase Difference Networks." Now THAT's a mouthful! (But descriptive...) Other neat musical uses were suggested by Benjamin Bauer, prior to his including two pairs of them in the SQ matrix (see the Bibliography below, the first two papers listed). It was a clever way to design a pseudo-quad system, as without them the results are even more disappointing. Ben's first ideas, overlooked in the quad hyperbole of the 70's, are still valuable today.
If you pass a mono signal through a psi-net pair, and patch the outputs through stereo speakers, you'll hear a widened image, completely filling the space in between the two speakers. That's pretty special already, so bear with me. To finesse the effect you need another classic audio tool, called a Sum and Difference network. Those are used to record with classic MS (Mid-Side) stereo microphones, the earliest stereo LP cutters, current FM stereo radio transmitters and receivers, Dolby Stereo soundtracks, stereo TV/video, and many other audio processes we now take for granted. Quite a list, for this popular audio "swiss army knife!" If you combine psi-nets with swiss arm..., I mean, sum/difference networks, and some other stuff I can't go into here, you'll be able to work some minor miracles in stereo sound. I've used similar methods a lot in my own work, in lot's of ways (listen carefully to Tales of Heaven & Hell). It's a rich resource for our newest DVD-Audio multichannel surround recordings.
I'd love to go into the details, but have already become far too technical in this section for a general web page essay (apologies). I need not say that experimentation is necessary, since it takes a subtle, experienced "touch" to get the most benefits. It's not quite "plug and play," and for that reason alone it may remain delegated mainly to the more adventurous surround sound investigators. But there truly are worlds to explore here!

--Wendy Carlos

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Here are a few good resources and references, in no particular order, for those of you who'd like to investigate these related topics further. Some of the following papers are rather technical, others not so much. I'll try to update the list occasionally as I locate other sources and pertinent references. These all shed light on some of the important background material that goes into Surround Sound of many kinds. Since this web page is certainly not a "paper in a scientific journal," I've tried to remain more informal, anecdotal, and have not dotted the text with many footnotes and qualifications. What I've tried to do is help you learn about the "bottom line," conclusions implied and to be drawn from well documented material. Any mistakes, memory lapses, or omissions are my own error, and I apologize for them.
You may be surprised that some of these topics happen to go back quite a few years (note Blumlein). This certainly isn't virgin territory, even if the technology for wide-dissemination of high quality surround audio is recent. I believe most of this material has simply been forgotten or ignored in the newest rush towards surround sound and music. Many self-proclaimed (ahem) "Master Surround Sound Mixers", don't seem even vaguely aware of what's really going on here. Yet they've gotten some excited press, speaking as superficial "experts," and are responsible for a lot of confusion, misunderstanding, and plain rubbish. Hey, people, it's Caveat Emptor, like deja vu, all over again! ;^) Enjoy!

Resources and References

1. Bauer, Benjamin B., "Phasor Analysis of Some Stereophonic Phenomena", J. Acoust. Soc. Am., vol. 33, no. 11, pp. 1536-1539 (Nov. 1961).
2. Bauer, Benjamin B., "Some Techniques Toward Better Stereophonic Perspective", IEEE Transactions on Audio, PART I, pp. 88-92 (May-June 1963).
3. Bauer, Benjamin B., Gravereaux, Daniel W., Gust, Arthur J., "A Compatible Stereo-Quadraphonic (SQ) Record System", J. Audio Engineering Society, vol. 19, no. 8, pp. 638-646 (Sept. 1971).
4. Griesinger, D., "New Perspectives on Coincident and Semi Coincident Microphone Arrays", J. of the Audio Eng. Society, 82nd Convention, Lon-don (1987) Preprint # 2464 (H-4).
5. Eargle, John M., "4-2-4 Matrix Systems: Standards, Practice and Interchangability", J. Audio Engineering Society, vol. 20, no. 8, 7 pp. (Dec. 1972).
6. Bishnu S. Atal and Manfred R. Schroeder, "Apparent Sound Source Translator" - U.S. Patent Disclosure, Patent No. 3,236,949, Feb. 22, 1966.
7. Bauer, Benjamin B., Gravereaux, Daniel W., Allen, Richard G., Budelman, Gerald A., "Quadraphonic Matrix Perspective -- Advances in SQ Encoding and Decoding Technology", J. Audio Engineering Society., vol. 21, 9 pp. (June 1973).
8. Blumlein, A.D., British Patent 394,325, 14 June, 1933, reprinted in J. of the Audio Eng. Society, Vol. 6, pp. 91-98, 130 (April, 1958).
9. Griesinger, D., "Theory and Design of a Digital Audio Signal Processor for Home Use", . of the Audio Eng. Soc., vol. 37 pp. 40-50.
10. Inoue, T., Takahashi, N., Owaki, I., "A Discrete Four-Channel Disc and Its Reproducing System (CD-4 System)", J. Audio Engineering Society, vol. 19, 8 pp. (Aug. 1971).
11. Bradley, J.S., "Contemporary Approaches to Evaluating Auditorium Acoustics", Proc. of the AES 8th International Conference, 1990, pp. 59-69.
12. Griesinger, D., "Multichannel Matrix Surround Decoders for Two Eared Listeners", Preprint from the Los Angeles Conference of the AES, Nov. 1996.
13. Griesinger, D., "Spaciousness and Envelopment in Musical Acoustics", Preprint from the Los Angeles Conference of the AES, Nov. 1996.
14. Lipshitz, S., "Stereo Microphone Techniques -- Are the Purists Wrong?", J. Audio Engineering Society, vol. 34, no. 9, pp. 716-744 (Sept. 1986). Also a special "Stereo Mic Technique Demo", Dolby C (or B) Cassette is available from AES and the author. (
Very recommended -- WC)

--Wendy Carlos

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