Hello again chrish! I am pleased to see that you have posted again, and with some new findings at that! I am sorry that I did not respond earlier, but I now have the time to give you some feedback.
Your Mewtwo would be Method 1, as Mewtwo is one of the few Pokémon that is consistently generated via said method, as outlined in the original post. Now, this is excellent that you were able to produce some results... this was indeed a cartridge run, correct? If so, I am pleased to see that we have now had a cartridge player hit the same frame twice; clearly we are making some progress. Now, I have a few constructive comments concerning this latest experiment.
Please allow me to save you a bit of time by saying that the time at which you press A when "Wild MEWTWO appeared!" is not relevant. The game chooses the frame (and by extension, the PID of your Mewtwo) as soon as the screen fades to black before the battle. As such, the last step is irrelevant to RNG manipulation, so you do not have to worry about it hereafter. On a similar note, I think it may be significant to note that the first three times would presumably have an effect on the seed (0 to 80 beats), whereas 160 and 170 would concern the advancing of the frame.
If I may, I would also like to make a suggestion as to a research question to sort out. If you can, try the following: go into your game (no special steps required) and wait for some amount of time (this may be completely arbitrary). Then, save your game and shut it off. Then, proceed with your experiment once again, and see if you are able to hit the same seeds as you were previously. If the seeds are the same, we may be able to eliminate the playtime of the file as a variable ("time in-game" may refer to the way the frames advance; loadingNOW's old comment on the savegame affecting the seed could be outdated). If they are different after a substantial amount of trials, then we have good evidence that the playtime is indeed a factor that influences the seed.
As something similar to try, you may wish to toy with the button presses on the title screen/menu to see if we can confirm NeoSyrex's theory of button presses affecting the seed. However, these other things may be tested after you are comfortable with the "vanilla" test results, and whenever you have the time.
I would like to thank you again for your enthusiasm concerning this project, and for the amount of time that you have likely been putting into this research. Thank you for your research, and I eagerly await your continued efforts!
Your Mewtwo would be Method 1, as Mewtwo is one of the few Pokémon that is consistently generated via said method, as outlined in the original post. Now, this is excellent that you were able to produce some results... this was indeed a cartridge run, correct? If so, I am pleased to see that we have now had a cartridge player hit the same frame twice; clearly we are making some progress. Now, I have a few constructive comments concerning this latest experiment.
Beat Count (cumulative) at each step (game event)
------------------------------------------------
0 Switched the game on in sync with the metronome
70 Pressed the Start button on the title screen
80 Pressed A on the Continue screen
160 Pressed A in front of Mewtwo
170 Pressed A after "Mew" is displayed
190 Pressed A after "Wild MEWTWO appeared!" is displayed
(...)
3) We will vary each interval in turn in order to try and determine which intervals are relevant.
Please allow me to save you a bit of time by saying that the time at which you press A when "Wild MEWTWO appeared!" is not relevant. The game chooses the frame (and by extension, the PID of your Mewtwo) as soon as the screen fades to black before the battle. As such, the last step is irrelevant to RNG manipulation, so you do not have to worry about it hereafter. On a similar note, I think it may be significant to note that the first three times would presumably have an effect on the seed (0 to 80 beats), whereas 160 and 170 would concern the advancing of the frame.
If I may, I would also like to make a suggestion as to a research question to sort out. If you can, try the following: go into your game (no special steps required) and wait for some amount of time (this may be completely arbitrary). Then, save your game and shut it off. Then, proceed with your experiment once again, and see if you are able to hit the same seeds as you were previously. If the seeds are the same, we may be able to eliminate the playtime of the file as a variable ("time in-game" may refer to the way the frames advance; loadingNOW's old comment on the savegame affecting the seed could be outdated). If they are different after a substantial amount of trials, then we have good evidence that the playtime is indeed a factor that influences the seed.
As something similar to try, you may wish to toy with the button presses on the title screen/menu to see if we can confirm NeoSyrex's theory of button presses affecting the seed. However, these other things may be tested after you are comfortable with the "vanilla" test results, and whenever you have the time.
I would like to thank you again for your enthusiasm concerning this project, and for the amount of time that you have likely been putting into this research. Thank you for your research, and I eagerly await your continued efforts!