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A rectifier coverts AC wall current to DC for the amp to use. Most modern amps use a solid state circuit to do this, but the Mesa Recto series uses old skool tube rectifiers.
The main point being that tube rectifiers behave differently that solid state rectifier diodes when there's a heavy current draw. For example, when you suddenly lay into the guitar real hard, the amp calls for more current to reproduce the dynamics.
Solid state diodes are more efficient than tube rectos, thus they have a harder attack, whereas tube rectos "sag" or have a spongier feel. Some like it, some don't.
The solid state diodes are far more reliable and less expensive and keep costs down for manufacturers, so that's probably the main reason why tube rectifier amps are so exotic (erotic?) or whatever now.
Many amp gurus feel that the cheap diodes that come stock in most amps are too harsh and tube rectifiers are too "soft", so one compromise is to replace the stock diodes with FREDs (fast recovery epitaxial diodes) which are supposed to smooth things out.
I've done that myself, and I would describe the difference as subtle at best. It's pretty much something that only a player familiar with their amp would notice, but I would do it again if I got a new amp with the cheapies in it.
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