Ab vibrates at 51.91 cyc. G vibrates at 48.99 cyc. However, if we add the sum total of the tubes used when depressing the 1st and 3rd valves. Low F vibrates at 43.65 cycles per second. It is this shortness of tubing, when using valves in combination, especially in the lower register that the compensating system overcomes.
Extra tubing is utilised when the master valve is used in combination with another valve.
The master valve on a 4 valve Sovereign Euphonium is the 4th valve. The performer can concentrate on the music, without the complication of having to move slides during performance. At most, the performer is only using 4 valves. This is a difficult system to understand, but the benefits of using it are enormous. In short the only analogy I can think of which might simulate its use, is the difference between driving a manual gearbox car and that of driving an automatic.