The timing window calculations for ADOFAI are quite complex! While I think all the information about it is already out there, it seems like a good idea to keep a canonical explanation of it available to prevent any confusion.

Fundamentals

At their core, the timing windows are based off of the angle difference between the planet and the tile when a key is pressed. For $d = (\text{planet angle}) - (\text{tile angle})$, we have the following judgments:

• $d < -60\degree$: Early!! (too early)
• $-60\degree \le d < -45\degree$: Early!
• $-45\degree \le d < -30\degree$: EPerfect!
• $-30\degree \le d \le 30\degree$: Perfect!
• $30\degree < d \le 45\degree$: LPerfect!
• $45\degree < d \le 60\degree$: Late!
• $60\degree < d$: Late!! (too late)

To put it more simply:

• Within $\pm\, 30 \degree$ results in a Perfect!
• Within $\pm\, 45\degree$ results in an EPerfect! / LPerfect!
• Within $\pm\, 60\degree$ results in an Early! / Late!
• Anything else results in an Early!! / Late!! (too early/late)

As a visualization, this is the where the timing windows line up:

Factoring in BPM

With the angle based calculations, it means the faster the BPM the smaller the hit windows. We can convert the angle windows to millisecond windows with the following formula:

$$ \text{angle\degree} * \frac{1 \text{ beat}}{180\degree} * \frac{1}{\text{BPM}} * \frac{60 \text{ s}}{1 \text{ min}} * \frac{1000\text{ ms}}{1\text{ s}} =\frac{\text{angle\degree}}{\text{BPM}} * \frac{1000}{3} $$