Connecting Klipsch Cornwall to Rotel RA-1062

Make sure the front-panel speaker selector (on front of amp) is set to "A". Connect the left speaker to "A" left speaker terminals on back of amp (Red wire usually means "+" and Black means "-"). Do the same for the Right speaker using "A" Right speaker terminals on back of amp. If this doesn’t work, read the manual.

If your speaker cables terminate with four individual connectors at the amplifier end, Connect the HF speaker cables to the appropriate left/right channel of channel “A” on the amp.  Connect the LF speaker cables to the appropriate left/right channel of channel “B” on the amp.

More common are biwired speaker cables that combine to just two connectors, plus and minus at the amplifier end.  In this case, both speakers can be powered by channel “A” .

The speaker cables have four connectors at the speaker end and two connectors at the amplifier end. If I connect both to A or Both to B on the amp only one speaker plays. 
I only get sound out of both if left is plugged to A on Amp and right is plugged to B on Amp. 

Something is wrong. Check your wires/speaker connection and make sure there is no short.

There should be four binding posts on the back of your amp - two for speaker "A" red + black -.
                    two for speaker "B" red + black -

On the front of the amp set the speaker selector to EITHER "A" or "B" and connect to whichever you set it at.I suspect you are using the wrong binding posts.The posts may be lined up vertically OR horizontally. It's easy to get one on correctly and the other on the incorrect post.

I have your Luxman SQ-N150 amp, love it.

It is a 10 wpc tube amp. It has the standard one stereo pair of speaker connectors: 4 speaker wire posts: L + and -; R + and -, expecting 'normal' speaker wires.

No internal crossover, no bi-wire or bi-amp options, no pre-out, just hook up 1 pair of EFFICIENT stereo speakers.
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Your 'bi-wire' speaker cables, only 2 at one end, 4 at the other end:

I SUSPECT you have these:

https://www.amazon.com/Copper-Braided-Bi-Wire-Speaker-Gold-Plated/dp/B0755VZK6Y/ref=psdc_3236443011_... 

(you need a PAIR of these to connect a SINGLE pair of speakers).

Those 2 to 4 speaker wires:

There is no difference between the two reds, it is simply split into two within, there is no difference between the blacks, similar internal split. there is no difference in wire construction of any leg.

WHY? I suppose they are designed to connect to a single speaker that is 'expecting' to be truly bi-wired or bi-amped (the speaker would have two pairs of connectors). Those type speakers have separate crossovers inside, each crossover designed to disallow highs or disallow lows. Disallowing: thus only the flow of the frequencies each wire construction is specialized for occurs.

NOT bi-wire (each side, L or R: two separate pairs, 4 at each end, ONE AMP), each pair of wires a different construction, one pair for high frequencies, other pair for low frequencies). They would be separately identified at each end.

NOT bi-amp (each side, L or R: two separate pairs, 4 connectors at each end, two amps) 1 pair from one amp, (i.e. your 10 wpc tube amp) for the speaker's upper frequencies input; one pair from another amp, (i.e. a brute) for the power intensive bass to the speaker's lower frequencies input.

Your Cornwall Speakers are the type ’expecting’ either bi-wire or bi-amp. (allowing, things cannot expect can they?)

These type speakers provide external removable ’jumpers’ so that:

Jumper in place, a single pair of speaker wire can be used: the jumpers connect the upper and lower speaker wire connectors, you can connect to either upper or lower pair, the jumpers are an 'external' 'removable' electrical bridge to the other pair of connectors.

OR, the jumper removed, thus the upper connectors and lower connectors are independent, allowing bi-wire or bi-amp.

So, the Rotel RA-1062 Amp I was using was faulty. I had only used it with headphones (long story) so was unaware the speaker connections were not working. The Audio store loaned me an Amp until my Luxman comes in and it works perfectly. 

That said, I love the way these threads take on a life of their own. Good stuff.