Jeff
1KHz = 2^3 x 5^3 Hz and
440Hz = 2^3 x 5 x 11 Hz
so the difference is? 5^2 and 11.
This gives rise to x11 then 1/25 to produce 440Hz. That is all you need.
The multiplication by 11 from 1 KHz square wave to 11 KHz is very much better than trying to multiply 10Hz to 110Hz, an 11 KHz tuned circuit of good Q is much easier, cheaper and smaller than a 110 Hz tuned circuit. The division by 25 is very simple, either two locked multivibrators ( two double triodes or two blocking oscillator dividers and one double triode to do 1/5 and 1/5 to get down to 1/25 and 440 Hz.
You would loose your bet, two or three? double triodes would complete the job and should be quite stable. A very good crystal oscillator , oven and divider chain AND the 1K to 440Hz? synth would easily go into a single thin rack panel or a small box in the 1950's.
There is something much more interesting than 440Hz about musical notes. A good enough equal temperament scale can be produced by dividing a frequency around 2 MHz by integers to produce top notes then dividing by octaves. The sequence:-
239? 253? 268? 284* 301? 319? 338? 358? 379? 402? 426? 451 gives a workable set of approximations to the ratio of 1.059463094 between adjacent notes.?? 284 is for A,? the exact drive frequency is 1999.360 Hz for 440 Hz but 2 MHz is close enough.? 12 different dividers were contained in one I.C.? and replaced 11 L-C oscillators in electronic organs in the 1970's. The idea is earlier, Hammond organs used gears to multiply up and down from a synchronous motor driven by mains frequency. Gears are more versatile than dividers, machinists have used some clever gear combination for over 200 years to cut specific threads however the last Hammond did use top octave dividers instead of gears.
But distant Musical History now but very little to do with Test Equipment apart from the frequency synthesis aspect.
Regards, Alan G8LCO
