> you are describing a so-called Vbe multiplier
No. I think ruffrecords is describing the basic voltage-divider, applying a "fixed" voltage to the Base. The Emitter "follows", so knowing the voltage and a target current you know an emitter resistor.
The "10X" thumb-rule keeps errors around 10%, which is good enough for any small audio work.
Oh, and you want that emitter voltage to be "large" compared with Vbe (~0.6V) to get "reasonable" temperature stability. For room-temperature work, Vbe may drift 50mV. If the emitter voltage is 500mV normally, a 50mV change is only a 10% change of emitter current, which is good enough for any small audio work.
When you add all the possible errors, or work in extreme temps, you may want a higher voltage across the emitter resistor. Use cheap dirty Silicon (or Germanium!) at high temps, you may even want to increase the current in the base voltage divider.
But these are rarely issues in modern home audio. (I remember when bleeding-edge Ge needed half the supply voltage across the emitter resistor, just to work in studios....)
On the other hand, if you are measuring thermocouples or strain gauges, microVolts matter. Then (as you well know from your telescope days) you get into very different techniques than we normally need in audio.
And since it IS such a broad topic, from Volts to microVolts, I think xela_92 needs to speak up and say what he is doing, guitar-buffering or precision measurements.