"When using 4 ohm speakers you draw twice the current from the amp. Voltage times ampere are watt and at 4 ohm you will only need half the voltage to produce the same watt as compared to double the voltage using 8 ohm speakers. When the voltage is dropped from the power supply when selecting a 4 ohm setting it has to drop to half voltage to produce the same watt from a 4 ohm speaker as in a 8 ohm setting using 8 ohm speakers, but it is only reduced some 35% so it will be more power available in the 4 ohm setting when using 4 ohm speakers. When using 6 ohm speakers in the 4 ohm setting it will produce the same watt as in 8 ohm setting and 8 ohm speakers.
That does not sound logical! If you reduce the voltage by 35%, you will get less current and therefore less "power" whether the load impedance is 8 ohms or 4 ohms.
So in reality the only important thing that change with the speaker impedance setting are how the protection circuit operates
That could be the case, but in the case of your AVR-X3700H, it is obvious that impedance setting of 4 ohms will limit current, and power naturally, again regardless of 8 or 4 ohms.
www.avsforum.com
Those guys seemed to know their math, but also seemed like they are a little confused, making it hard to follow their thoughts.
So essentially in Denons switching to 4 ohm stops protection triggering too early, and allows thus producing more power for 4 ohm speakers.
Again, that could be possible in theory, but bench tests after bench tests show that it is not the case, so setting to 4 ohms will limit "power" severely, but if you don't need that much power then of course you will be fine, or more than fine, using the low setting.
If you are experiencing performance issues in your specific use case, then I would suggest you investigate further, as there could be other reasons. To be clear, if the poorer performance you mentioned, such as weaker bass, was due to protection triggering too early, then you will know because Denon's protection scheme will trip the unit, not just limiting the current and continue to operate that way. Some recent Onkyo models might (not 100% sure) in fact do what you described but certainly not Denon's X3700H.