Just some idle pondering on my part. I know it would not be practical, but would it be possible? How many tubes would be required?
You don't even need active components. An R-2R ladder is a DAC. You might want one tube for an output buffer.
https://en.wikipedia.org/wiki/Resistor_ladder
Many decades ago I heard that the first flash ADC converter used vacuum tubes.
https://en.wikipedia.org/wiki/Resistor_ladder
Many decades ago I heard that the first flash ADC converter used vacuum tubes.
Bell Labs used special cathode ray tubes as ADCs. In fact the USA used digital voice encryption in WWII. Shortly after the war (1948 and 1951), publications about digital telephony and even closed-circuit digital television appeared in the Bell System Technical Journal. See https://archive.org/details/bstj27-1-1 and https://archive.org/details/bstj30-1-33 Of course it was no coincidence that the first publication about information theory was also just a few years after the war, https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf
An audio DAC becomes a lot simpler when you use an oversampled and noise shaped single-bit digital signal. I've made a DAC like that, see https://www.diyaudio.com/community/threads/valve-dac-from-linear-audio-volume-13.308860/ , but as it only uses valves for the analogue/mixed-signal functions and semiconductors for everything else, it doesn't quite meet SoaDMTGguy's requirements.
By the way, the 1948 article about digital telephony includes the simplest multibit DAC design I've ever seen, invented by Shannon himself. When you transmit the data serially with the LSB first, a first-order RC low-pass filter with a time constant equal to a bit time divided by the natural logarithm of two can serve as a DAC. You have to sample its output at the end of the MSB bit time. It is not suitable for high resolutions because of the difficulties of making the time constant very accurately equal to a bit time divided by the natural logarithm of two.