[gradofans]

I usually can't wait that long( like 40 minutes ) . Ten minutes is the upper bound for me ...

 

[mcandmar]

Everything Tomb said, and i'll add that at about the 1 hour mark the tube will be as hot as its going to get and its emission will have stabilized.  If you have access to a tube tester you can see this as the tube emission will rise as the temperate of the anode and plates rise.  10-15mins will get you 90% there, but there is a small but measurable difference after an hour or so.
 
Personally i power up and wait a minute before before plugging in the headphones and listening to avoid any DC spikes. The above is an interesting quirk of tubes, but lifes too short to worry about such things.

 

[BirdManOfCT]

  Despite the silliness of many posts in this thread, the real answer has to do with the nature of tubes.  They need heat to allow the cathode part of the tube to "boil off electrons."  It is these "free" electrons, that are added to the signal applied at the grid, that produce amplification.  The free electrons are "added" to the signal coming through the grid.  The "plate" of the tube accepts the addition of the signal from the grid with the added electrons coming from the heated cathode.  The result of the output at the plate is a much stronger, amplified signal.
 
All that depends on the heating of the cathode, however.  To reach a thermal equilibrium takes time.  Thermal equilibrium is an inexact condition, usually brought about by the passage of time that is much greater than a few musical songs.  Think how long it takes to boil a pot of water or heat an oven to 400 degrees to cook your pizza.  For a tube to be dependably linear (minimal distortion), that elevated thermal equilibrium must be achieved and it takes time.
 
As for running a signal through - as soon as the cathode is initially heated (30 seconds, give or take) - the tube is going to amplify and reproduce the music signal.  Whether or not a signal is present before or after makes no difference.  It will either produce sound or not.  The best sound will be reached when that thermal equilibrium has been achieved, however. 
 
 
P.S. There is an initial state, depending on the amplifier design, where the accompanying parts of an amplifier (DC-blocking capacitors) have not charged enough to block the DC needed to bias a tube.  That DC, if passed through the circuit, could damage your headphones.  Those things only last a half-minute or so, though, so as long as you don't attempt to listen to a signal in that brief moment after turn-on, everything stated above applies.  Many OTL tube amps are built with a relay-delay to take care of this specific, turn-on condition.
 
Some amps - output transformer-coupled amps, for instance - need no cautions about power turn-on spikes.

Thanks for the info. It included much of what I was doing a search for.

 

[gwaaron]

To reinforce what tomb so eloquently and thoroughly described, my Audio Research preamp (which is always turned on first) has a built in 30 second mute cycle, so that no signal, intended or otherwise, can be introduced into the system. My headphone amp is routed through my preamp to take advantage of all my source components.

 

[bequietjk]

I think my project horizon sounds incredible after it's been on for a couple hours. 's gotta be nice n' hot ^_^