Hi,
The surefire way of getting 1:1 is of course using double the frequency and then divide it by 2 in a flip-flop.
Actually, it's not the hysteresis, but a thing happening when the threshold voltages aren't symmetrical around Vdd/2 (0V reference assumed).Schmitt triggers have hysteresis, that's why the unequal on/off times.
Just adjust the load until you satisfy the aboveI think there is a way to get an ~50% duty cycle with the one Schmitt NAND gate oscillator. I think you have two sets of feedback resistors/pots. A diode is placed in series with each set. the diodes point in opposite directions.
The surefire way of getting 1:1 is of course using double the frequency and then divide it by 2 in a flip-flop.