AD9850 always uses the 125Mhz MCLK (or whatever Mhz is going in there) as the source for the accumulator. No random division going on, just straight up 125Mhz (again, or whatever a person is using for the MCLK).
125Mhz input, 32-bit "tuning word", which is the value that is added to the 32 bit accumulator, the upper 10 bits of which are fed to a sine wave loop up table, which in turn feeds the 10 bit output DAC.
Start off with zero's in everything...
You've got this 'tuning word', which is the adder, set it to a value of "1", just 1, not 0x01, just 1.
MCLK pulse comes in, add the value of the tuning word to the accumulator, accumulator = 1, nothing in the upper 10 bits yet (won't be for another 4MiB pulses)
Keep adding MCLK pulses at the rate of 125 million per second and this 32 bit accumulator will overflow in 34.359738368 seconds (125Mhz / 32bits), giving you an output frequency of 0.02910383045673370361328125 Hz.
Change the tuning word to 2,147,483,648 (2^31), the upper bit of the accumulator flips every MCLK pulse (it's an add, not a multiply, not a look up, just an add), the accumulator overflows, the overflow is thrown away. But, the upper bit, 31, is also the upper bit of the 10 bit DAC. Therefore, only 1 bit of the DAC is being used, the MSB. Therefore, the output value only flips between 2 possible values, high and low.
Change the tuning word to 1,073,741,824 (2^30), the upper 2 bits of the accumulator change on every MCLK pulse. The upper 2 bits, 30-31, also the upper 2 bits of the DAC. Only 2 bits of the DAC is being used. The output value only flips between 4 possible values.
So on down the line...
If the tuning word is less than 2^22 (total accumulator size - upper 10 bits, which again are the 10 bits of the output DAC), then and only then can you possibly get all 1024 values output in the DAC. And with an MCLK of 125Mhz, that will only happen when a desired frequency of less than 122,070.3125Hz has been selected. Any higher than that, all POSSIBLE values in the DAC won't get hit each and every time thru the sequence. They might get hit eventually, but not on each cycle of the outputted sine wave.
What miguelvp said in the last post about being tuned to 30Mhz with a 125Mhz MCLK and every 25th wave being identical sounds about right, although I think it'll actually be every 6th wave will have identical characteristics...the other 5 waves will be fundamentally 30Mhz but with different distortions, harmonics, etc.