Yes, there are many formulas that people have used. However, a lot of the reason for this is that Murrey has figured out that the start date is key to using the method. Therefore, he doesn't want everybody to know what it is really based on without coming to the class, or paying for his software. But it is really based on Gann himself so that is where the real answer lies.
Because of this, Murrey says in his book that it is the "first frost date", then he says Harvest Moon in his EMails, then he claims it is on his birthday ( Oct 7 ), then later it is based on the 3rd quarter of the bond market, then it is based on 4 calendar day periods from the harvest full moon , then it is based on 4 trading day periods from the harvest full moon, etc.
To settle the ambiguity, I went back and backtested from 1970 to present using some sample DJIA stocks like AA, BA, CAT, AXP, etc. and looked at what was working best over the whole period.
The net result of that is that the best answer for me was that it is based on 4 trading day periods from the harvest moon with appropriate rounding such that the start date is always rounded back to the previous trading day whenever it lands before mid-session of the trading day ( 12:45 ET ). This is because a market that turns before the turning point day is most annoying, much more so than one that turns 1 day later. I did this to minimize the chances of enduring nasty gap openings on the turning point days which results in either missed trades or poor entry points.
Correct turning point dates should show some major turns or major acceleration days ( long trend days ) on 0/8, 2/8, 4/8, 6/8, and 8/8 of the 32 bar, 64 bar graphs.
I have attached a graph of QQQ for the first 32 bar frame in 2003 using a start date of Oct 3, 2003. As you can see, there is a perfect hit on the 2/8 timeline = Oct 15, 2003, and 1 day off on 4/8 timeline = 10/27/2003, as well as decent topping behavior on the 6/8 timeline = 11/6/2003. So, it works for me. The next interesting date is the 0/8 of next frame = 11/18/2003.