Home Page Forums MAME MAME Correct Apple ][ clock rate?

Hi. I'm looking at MAME again after a couple decades (?!?) away from it.

Specifically the Apple ][ emulation: MAME lists the clock as 1021800 Hz. In the source, I see:

Per "Understanding the Apple IIe" by Jim Sather, sec. 3-13, I believe the ~1.02048 figure is the more correct "average" clock rate, taking into account the 16/14 stretch of every 65th cycle.

Can anyone explain why MAME is using 1021800 and how that was derived?
(I'm asking because of sound generation code.)

MAME's core is not currently capable of emulating the stretched cycle, so every CPU and video cycle is exactly 14 master clocks. The 1021800 adjusts the speed downward slightly to give the same slowing effect as the stretched cycles. I don't remember the exact derivation, but it was pretty straightforward.

It makes sense to adjust downward to average out the stretching. I'm not sure that 1021800 is the correct adjustment though?

If the master clock is 4x NTSC 14.31818 MHz, then / 14 = 1.0227271429 MHz. Adjusting for stretching, 14.31818 * 65 / (65*14+2) = average rate of 1.0204843202 MHz.

The ratio between 1021800 and 1020484 looks like like the difference between 60 Hz and the actual Apple ][ vertical refresh rate (65 cycles @ 63.695 us x 262 scanlines = 17030 cycles @ 16688 us; 1000000 / 16688 us = ~59.923 Hz, according to Jim Sather.)

Perhaps the derivation assumed the vertical refresh rate was 60 Hz?