can my amp cope?

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I am running a line out signal from a 10w guitar amp to a cheap Chinese 100w 4 ohm mono amp module connected to a 16 ohm 12" organ speaker rated at probably around 20w.

Running the 16 ohm 20w speaker from the 4 ohm 100w amp module seems fine for home use. I don't detect any overheating and the power output is quite subdued this way so the organ speaker seems in no danger.

I have also fitted an external speaker jack for live use that when connected to a separate speaker cab of 8 ohms renders the load to about 5 ohms altogether, close to what the amp module is supposed to be designed for, at much higher volume with most of the power going into the separate speaker cab so as not to overpower the 20w organ speaker with the 100w amp. So far this seems to work just fine.

My question is whether it's healthy to run the 100w 4 ohm amp at home with the 16 ohm speaker for extended periods.
 
I am assuming that your "cheap Chinese 100w 4 ohm mono amp module" is solid state and if that's the case then 100 watts into 4 ohms will equal 25-30 watts to a 16 ohm speaker. This is because of ohms law. So, in reality, the 100w amp module into a 16 ohm speaker load shouldn't harm your speaker unless you turn the volume all the way up.
Your amp module won't suffer either as it will be idling along driving your 16 ohm speaker.
 
Yes the Chinese module is just a little solid state thing I bought very cheap. I chose this particular one because it could be powered from the existing output of the toroidal transformer I already had in a dead Stagg BA60 amplifier so the whole resurrection of that dead amp into a generic powered speaker cost peanuts. Meant to beef up my 10w practice amps for live use, which it does very well.

But what I found was that the 12" 4 ohm speaker in the Stag cabinet sounded awful for my use. All midrange and flat. Probably OK for a punchy bass guitar sound but no good for my purposes.

I came across a few old organ speakers and after trying them in that amp they all sounded really good but I knew they weren't designed back in the day to take much power. There were three 8 ohm speakers and one 16 ohm which I decided to use because common sense told me that one SHOULD average out to 25-ish watts which was within reason for this old organ speaker.

I fitted an extension speaker jack so I could add another speaker cab for live playing and the idea seems to have worked great. The amp on it's own running 16 ohms is more than fine for home use at 25-ish watts and if I add another 8 ohm speaker cab to it the output goes to around 5 ohms and becomes much louder without noticeably taxing the organ speaker. A nice dual purpose amp.

It was just that I couldn't find any real information about running as much as a 16 ohm speaker from a 4 ohm amp for extended periods but logically it seemed to make sense. Anyway it appears to work very well.

These old organ speakers sounded so good I didn't want to blow them up as they're actually getting harder to find, so for live playing I can just bung on any old modern 8 ohm speaker cab for extra volume.
 
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