Numerous empirical rules have been established in order to rightly choose the number of stator and rotor slots and limit the audible magnetic noise level radiated by induction machines. However, these rules never take into account the stator natural frequencies neither the fact that the motor is run at variable speed. In this article, a fast simulation tool of the variable-speed magnetic noise emitted by induction machines, based on fully analytical models, is presented. On the ground of these models, the analytical expression of main magnetic vibrations due to slotting reluctance harmonics are derived and experimentally validated, confirming the prime importance of slot combination in magnetic noise radiation. Some simulations are then run on a 700 W squirrel-cage motor in order to quantify the noise emitted by all possible combination of slot numbers in two and three pole pairs cases, including odd slot numbers. The obtained database efficiently replaces the old emperical rules on slot combination numbers and helps designing quiet induction motors. Similar database can be built for other power ranges.