The first American stereophonic discs were released by Audio Fidelity Records, in March, 1958. The four 33 & a third titles were..
The Stereo-Pak made the first practical car audio possible. The system used a continuous loop of tape that was enclosed in a plastic cartridge. The 4 tape tracks were played two at a time, with a tape head switching positions once. While playing, the tape head did not change programs automatically. This would have to be done manually (the 8-track format featured an automatic program-changing mechanism).
Image from https://www.discogs.com
In June 1969, recorded music advanced to four channels -or quadraphonic sound- with the release of the first"Q4," prerecorded open reel tapes. These were followed, in November 1970, by RCA's quadraphonic 8-track -or Quad-8- cartridge. Eventually, this 4-channel format would be promoted as simply "Q-8."
The Quad-8 cartridge debuted with "At Carnegie Hall", by Harry Belafonte. Unlike Stereo-8 tapes, that had arrived on the scene 5 years earlier, Quad-8s only switched tracks once..instead of three times. Quad-8s had a notch in their upper left corner that switched a Stereo-Quad player into the Quad-8 mode. Oh yes, the two 8-track formats were not compatible. If you played a Quad-8 on a Stereo-8 system, you would hear only half of the song at one time.
Image from RCA Records-http://www.8-track-shack.com
In March 1971, the first matrix quadraphonic LPs appeared, utilizing the ABC-Sansui QS system. Columbia-Sony countered with SQ matrix LPs in October 1971. These were followed by RCA-JVC's discrete quad format, known as CD-4 or Quadradisc, which hit stores in February 1973. Unlike the Quad-8 tape format, all three Quadraphonic LP formats were stereo-compatible. A few quadraphonic 45 rpm releases were pressed, with most being test records.
The Quad Revolution moved ever onward with the release of the first six 4-channel LP's, in early 1971. These Command Quadraphonic discs were produced by ABC Records. To hear a QS disc reproduced properly, one would have to own a sound system, equipped with a QS Vario Matrix Decoder.
Image and logo from ABC Records and Sansui Electronics (see media fair use rationale at end of article)
The first Columbia-Sony SQ LPs were released in late 1971. Similar to the ABC-Sansui system, SQ Full Logic created the illusion of four separate sound tracks by "encoding" each of the two rear channels into the two in front. It worked pretty well. In fact, SQ quad recordings -such as Santana's "Abraxas" album, Pink Floyd's "Atom Heart Mother" album (a British import) and Edgar Winter's "Frankenstein" song- demonstrated some neat, moving-around-the-room effects.
JVC/RCA's CD-4 or Quadradisc LP debuted in early 1973. CD-4 used an ultrasonic "carrier wave," which instructed a CD-4 Demodulator to divide the audio into four separate (or discrete) sound channels.
To convert from stereo to quad, one would need to either scrap everything and buy an entirely new sound system or else acquire an additional stereo amp, two more speakers and the appropriate decoder(s). For CD-4, one would have to have the CD-4 demodulator, a new "high capacitance" turntable and phono cartridge that could accommodate the additional frequency range of the carrier wave.
The sonic separation of CD-4 LPs was superior to that of the two major matrix systems...however, there was also a great deal of distortion with the CD-4 system that was not present when playing QS or SQ matrix quadraphonic LPs.
The three competing -and totally non-compatible- systems vied for prominence through the remainder of the 1970s, with none emerging victorious. Quad sound was gone and nearly forgotten by the advent of the digital compact disc, in 1983.

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