Just guessing here, because my pronunciation is the same as yours... Dai = Day Die = Die If you make an "ay" sound, then transition to an "i" sound, you can

Just guessing here, because my pronunciation is the same as yours... Dai = Day Die = Die If you make an "ay" sound, then transition to an "i" sound, you can feel that the sounds are continuous. So maybe that inbetween sound OP is talking about literally the sound you make with your tongue between "ay" and "i".