Any suggestions? (On running two programs within one Arduino maybe)
Small excursion:

You are right to observe that the Arduino with its 1 core can only execute one instruction at any given time. However, there are ways with which we can achieve that the Arduino "does things in the background". We can e.g. use interrupts from hardware timers, which will interrupt the main CPU core to quickly execute a interrupt service routine, and then continue where it let off originally. 

This is also how an RTOS (real-time operating system) works. You can only execute one thing at a time, but if you set up a timer interrupt every 20 milliseconds in which you switch between the executed functions, you get a "emulated" multi-task system. These are the basics of any operating system.

References:


https://www.sparkfun.com/tutorials/326 
https://www.youtube.com/watch?v=QtyOiTw0oQc
https://arduino-info.wikispaces.com/Timers-Arduino
https://www.freertos.org/implementation/a00002.html


You will also notice that your Arduino Uno can't play music directly -- for that, you would need a digital to analog converter to produce the needed analog audio voltages, together with a audio amplifier for headphones or loudspeakers. 


https://www.youtube.com/watch?v=Y2OPnrgb0pY


Fortunately there are many Arduino shields that do the job. Some of them are:


Seedstudio Music shield (documentation, library)
Adafruit Music Maker shield, with either headphone or loudspeaker output


Here, the work of playing music (from a file on an inserted SD card, for example), is offloaded to an external synthesizer chip. We do however need to supply the chip with the to-be-played music data in the background.

When you look e.g. at the library reference for the Adafruit Music shield, you'll see that it offers a function that will use interrupts to play a file from the SD card in the background. 



Using the library in this interrupt mode will of course use an interrupt source (either timer or pin), which may conflict with your EMG code if it also uses that timers. In that case you will have to move either the EMG code or the music code to a different available timer.

In short:


Learn more about what interrupts and timers are
find a suitable shield (e.g. the adafruit shield above) and understand its library capabilites and limitations