Bloody hell! Lot of vitriol flying around here. One problem with amps and loads is that there are two distinct types of amplifier in the guitar world (where I might claim a tiny bit of experience?) valves and transistors*.
Valve OP stages (gitamps) have a relatively high source impedance. An AC30 say might have an 8R tapping but its OPZ is closer to 30 Ohms. This has quite an effect on how the amp delivers power to a speaker. Valve must never be run into an open circuit and it is best to stay within one 'move' of 'mismatch' (though we don't ever 'match' anything in audio) So, set amp to 4R and hook an 8R speaker. Pretty safe even if you drive the bllxs off the amp. BUT! Some designs are rather feeble and you might damage valves and, in rare cases OP transformer. 4R into 16R is even less safe but again, power matter. For home plinking/a tune up, no harm. Running a valve OP stage into a LOWER load, 16R tap into 4R, worst case will not destroy the amp but again, high volumes can cause red plating, fuses to pop an possible valve failure. N.B. Not ALL valve amps have HT fuses (get 'em fitted!) and so valves easily be buggered.
Big, 50W+ fixed biased valve amps tend to use a bit of Negative Feedback and this lowers the OPZ but even so it is rarely less than 10 Ohms so load will still influence 'tone' to a degree.
Transistor OP stages are the opposite. They are happy to drive any load (but not an open circuit) so long as it is at or above the stated minimum, usually 4R but some older tranny amps might state an 8R minimum. If a sstate amp has jacks available to connect a speaker then one can assume it is protected to a degree from low loading and shorts but don't bet on it! Extended drive into a lower than minimum load can cause slow heating and a sudden 'thermal runaway'. Might just pop a fuse. Usually forks 18 transistors.
Tranny amps USUALLY have a near zero OP resistance but some guitar amp designs have used feedback to attempt to emulate the OPZ of valves.
Doubling the load on a tranny amp will not halve the power because most use unregulated supplies so the lower current demand means the available voltage will be a bit higher. An amp rated at "100W into 4 Ohms" can be expected to deliver 70-80W into 8R...But! Just the fact of rating the power output of amplifiers is a discussion all of its own!
Power rating of speakers is again fraught. For a valve amp the speaker should be rated at at least 50% over the stated amp power, better 100% because valves do not have a 'sudden death' clip point, they keep putting out power at ever increasing distortion. Note too that many speaker brands are very 'optimistic' and punchy about their ratings. I find Celestion tend to be conservative. Put a 60W celly in a 50W valve amp and you are unlikely to break it. Other makes, not to sure.
There is BTW a simple formula for SPL (at 1mtr) ref watts: SPL= Log W.10+s where W is power in watts and 's' is the sensitivity of the speaker shown as "dB/W/mtr" That is a VERY rough ball park calculation but does give you a starting point.
I do not subscribe to the 'massive OTT power into lower rated speakers idea for anything. If you are designing a PA system for a given venue say, you first decide on the SPL you need at the punters bum positions. That tells you the SPL needed 1mtr from the speaker and thus you look for speakers that can deliver that, their sound quality will be decided by budget. The chosen speakers will have a sensitivity and from that you can determine the power output needed. Nice to have a bit of headroom but even just 3dB is another amp! Pricey.
*Class "D" amplifiers tend to be very load sensitive i.e. power fall off very quickly outside rated load, usually 4 Ohms.
Just my conclusions garnered over a few decades.
BE NICE TO EACH OTHER!
Dave.
