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As I want mine to be polyphonic, each note would need to have its own oscillator and a set frequency. I could do a monophonic type with just one oscillator but it seems a waste to have 2 octaves and not able to play anything
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OK, well its an awful lot of circuit. With valves you will also be needing a pretty big PSU. LC oscillators seem a popular solution, I presume because they can be made with low drift – but that's a load of big chokes to make too.
You might want to do the maths and calculate the cost before deciding to use ICs.