All of these were variations on an idea: a monophonic instrument employing a single oscillator, generating a harmonically rich waveform (usually a square wave, or close to it). Divide-down circuitry produces 3-6 octaves' worth of notes from this. Then, a set of 10-15 fixed high pass and low pass filters can individually be switched in or out of the circuit by stop tabs or other controls usually mounted on the front of the keyboard, below the keys. Various combinations created formants that could, if one listened with an optimistic ear, approximate various string, brass, and woodwind instruments. Other combinations could produce then-novel tones. (A few types also had primitive envelope generators. More often, a knee lever was provided for the player to control the envelope manually.) The filters were usually basic, single-pole passive RC or LC types. Combining them could result in a number of complex response curves. It is not clear how the different values of the filters were arrived at by the designers, and there is surprisingly precious little design data available on the Internet. Presumably the filter combinations were developed empirically, so as to approximate the tonal characteristics of the instruments being imitated, although they may have had means available to research body formants of those instruments. Or perhaps they just guessed. In any event, with no buffering, switching in various combinations would have caused the filters to interact, probably leading to a lot of cut-and-try guesswork.
The resemblance to a analog subtractive monophonic synthesizer can be seen. An oscillator generates a harmonically complex waveform, and filters remove parts of it to produce a desired tone. Of course, the filters are fixed, there is no voltage control, and no proper VCAs, so the analogy only goes so far. Nonetheless, these instruments did have another component which was to appear in synths much later: the low-frequency oscillator. It was hard-wired to vary the frequency of the audio oscillator, and only a few rates and 2-3 depth settings were available.
Of course, all of the circuitry was tube-based, transistors having not been invented yet. No doubt this limited what could be done, not only from a strictly technological standpoint, but also based on cost, portability, and what the customer was prepared to put up with. The fully polyphonic Hammond Novachord was no doubt an impressive technological achievement in 1940. Owing in part to the number of tubes it contained, it's probably also true that it was very expensive (in retrospect, it's rather remarkable that Hammond was able to sell 2000 of them), capable of heating a small house, and, most importantly, it probably only ran a few hours at a time. Given the average operating life of most type types in those days, multiplied by 146 tubes, it probably averaged a tube failure every 10 hours or so. This may have been what ultimately killed it, and perhaps explains why only a handful of Novachords survive today.
One obvious way to address all this is to make a monophonic version. For that, you only need a few tubes; it ends up being a lot more portable, and most importantly, a lot less expensive. The inability to play chords didn't matter so much if the instrument was intended to be an adjunct to a piano, and many of these instruments were designed so that they could be fastened to the underside of a piano keyboard, in addition to being played on their own stands. And this is most likely how several designers arrived at fairly similar instruments.
Generally, the keyboard came with a combo amplifier which was an integral part of the instrument, providing power to the keyboard as well as amplification. Further, the amplifier was designed to perform wave shaping and other types of distortion and non-linear frequency response to further shape the instrument's overall sound. The amplifier was usually designed so that it and the keyboard could be fastened together to make a single enclosed case, for transporting.
The Clavioline was featured on several early rock hits, in addition to the aforementioned "Runaway". Max Crook himself had several minor hits under his own name, performed on the Musitron, as well as using it on nearly all of Del Shannon's songs. Producer Joe Meek had a Clavioline, and he used it to play the distinctive keyboard melody on The Tornadoes' original version of Telstar. (Answer to a trivia question: "Telstar" was the first song by a British group to reach #1 on the USA Billboard Hot 100 charts.) Among the groups The Tornadoes beat out for that honor were The Beatles, who later featured the Clavioline on "Baby You're a Rich Man". Jazz musician Sun Ra made frequent use of the Clavioline. Meanwhile, Crook continued development of the Musitron. He started by adding a spring reverb, made from hardware-store springs. Later, he gutted a reel-to-reel tape recorder and used it to incorporate a tape echo system into the Musitron, which also provided some effects capability by means of varying the tape speed. Crook went on to devise a more advanced instrument with true percussion sounds as well as a real-time pitch bend capability. Additional development continued in other quarters. The Ondioline had its keyboard mounted on a mechanism that allowed left/right movement of the key bed; using a guitar-like finger vibrato, the player could add vibrato or other effects to the sound. Selmer in the UK produced a version of the Clavioline with selectable sub-oscillators. Harold Bode developed a range extension for the Clavioline, and later developed a polyphonic version dubbed the Tuttivox.
The advent of performance synthesizers like the Minimoog (1971) probably would have killed off the Clavioline and its kin, but it appears that they were already out of production by then. What may have happened was that players in the mid-'60s discovered that combo organs could cover the most useful territory, cost about the same, and had the advantage of being polyphonic and more reliable. ((This was ironic since the first successful product of the Jennings Musical Industries company was a version of the Clavioline called the Solovox. The company later went on to produce the iconic Vox Continental combo organ.) It does not appear that anyone ever built a solid-state version of the Clavioline: by the time such a thing would have been practical, there was no point, as Moog and Buchla had already gone beyond it with their early voltage-controlled oscillators and filters.
The Clavioline-type instruments filled a gap between the first electronic instruments, and the availability of musician-affordable synthesizers in the early 1970s. They may seem crude and cheezy now, but at the time they were regarded as radical by popular music listeners used to the familiar timbres of guitar, sax, organ, bass, drums, and strings. They helped popularize the idea of new and unusual sounds, and helped pave the way for the use of synths in rock, jazz, and pop music.