Frequency Detection Circuit Design
You don't need a DSP or other fancy solutions -- in this case a straightforward analog circuit does the trick.

It sounds what you need is a classic light organ, aka color organ.  They originated in the 1970's, and were used to drive spotlights instead of LEDs.

Jameco sells a kit for this.  They also publish the schematic on-line for those that want to DIY.  It takes the audio input, runs it through an op-amp pre-amp, and then divides it into three frequency bands.  The outputs are used to drive banks of LEDs.

I've built two these (for stereo) and they work well.  I have no connection with Jameco.  You can get similar kits elsewhere.