Bluetooth – What Are AT Commands and When to Use Them?

There are two ways to solve these types of problems. Either at the source and or hide the effect. Fortunately the whistling and clicking appears directly related to the RN42 and not the PWM's.

Note the HiZ inputs of the pickup coils are going to pick up everything. From Florescent Lights to the RN42 aliased noises. Typically a band pass filter is used at the point of observation or A2D. Where here your pickups are likely directly tied to the AMPs input. And a filter here is undesirable.

The RN42 is creating noise that is bleeding out onto the power supply and radiating to Pickup's. And shielding the pickup's is impractical. Rather one needs to filter out the noise from its source. My own experience with the RN42 has a lot of clicking in the audio connected circuits.

Recently Elektor's July & August 2013 had an article for Android Elektorcardi♥scope where it used an RN42 to send the result to the Android. Where it was littered with Filters on the power supplies to all the IC's. Below is the filter used on the RN42.

^{simulate this circuit – Schematic created using CircuitLab}

Where the 30R@100MHz was used on other supply inputs with different capacitance. At DC it typically is under .2 Ohms, but with spikes and noises that will rise dramatically and react with the capacitance to block the noises.

The baud rate 57600 is a pretty marginal on an AVR (the microcontroller used) at 16 MHz, normally OK with only a bit over 2% error but some modules can be picky. The site WormFood's AVR Baud Rate Calculator shows some good tables on error percentages for various clock / baud rate combinations.

Also I just noticed Majenko's comment and he's quite right the software serial you're using will be worse at that speed so for a start try it using a hardware UART.

That Arduino runs at 5 V logic levels so if you're not using a voltage divider to drop the transmit line to 3.3 V that might be worth try first. I've read a few mixed things about whether the HC modules are 5 V tolerant on the serial lines or not and it certainly won't do any harm trying it first to see if it resolves it.

But if neither of those steps work I'd recommend getting a USB to TTL serial converter, it seems for that module you should look for one with a 3.3 V logic level like this one for Sparkfun. They are also useful for a host of other things so are generally useful to have at your disposal.