Electronic – Defined LM339 behavior when the (+) input is floating

Look at chapter 5 under line regulation.

For the 5V regulator at \$V_{IN} = 7 V\$, then you will typically see a \$3 mV\$ ripple with varying load, up to \$50 mV\$ worst case. At \$V_{IN} = 8 V\$ this reduces to \$1 mV\$ typical and \$25 mV\$ worst case.

So you'll need at least \$2V\$ head room, but \$3V\$ has less ripple (which is better)

Another parameter to look at is Dropout Voltage, which is just little below the line regulation. The dropout voltage is the voltage required for the regulator (between output and input) to be able to do its job properly. In the same table is stated typically \$V_{d} = 2V\$. But if you want to design a robust circuit, you should always use the worst case which is here \$V_{d,max} = 2.5 V\$ value to ensure the circuit will work with all regulators.

The DJ mixing desk device (mentioned by F. Bloggs) used to be called a "ducker" as it 'ducked' the music level below the voice level. If you can't find a ready-made device, you should be able to find a suitable circuit on a web search. You'll also find terms describing how quickly it ducked - too sudden doesn't sound too nice - and the release time - how long the silence has to be before the music starts to fade back up - and the release rate - how quickly it fades up once it has started.

The ducker is also a feature on many building PA systems to mute the music during paging.

https://en.wikipedia.org/wiki/Ducking may help.