Definitely go with the output into 4.
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Saving a detailed explaination for others, suffice it to say tht when I have 4 ohm speakers (speakers with a nominal impedence of 4 ohms) I assume that they have a lower minimal impedence, and I look for SS amps, of what-ever power rating, that double their power output rating at 8 ohms, i.e. 200wts at 8 ohms to 400 wts at 4 ohms, 800 wts at 2ohms. This insures that the amps has sufficient current delivery to drive difficult loads. With a tube amp I look for amps that not only have sufficient wattage but that have 4 and 2 ohm output taps.
There isn't a universal answer. In my case, as per the manufacturer, the power recommendations are based on the standard 8 Ohm power rating for amplifiers, but, the manufacturer assumes that one is using a high quality ss amp that "doubles down" and suggests that if one is using a tube amp they choose one(s) with increased power output to compensate for the minimal impedance load. For example if the speaker has a 4 Ohm nominal/4 Ohm minimum impedance and the suggested power requiremnets are 50-250 Watts per channel, choose an amp that can provide between 100-500 Watts per channel into 4 Ohms. In most cases that would mean a high quality ss amp that "doubles down" rated at between 50-250 Watts per channel, or a tube amp rated at between 100-500 Watts per channel. FWIW, there is an old audiophile rule of thumb that suggests that one start with doubling the manufacturers minimum power recommendation.
Tonywinsc, Jim Thiel has told me himself that (at least with his older models) that his power recommendations are based on standard 8 Ohm amp ratings, and the assumption that the customer is choosing high quality ss amps that are capable of "doubling down". With your CS6's minimum impedance of 2.4 Ohms, I suspect your Thiels could handle well over your available 700 Watts into 4 Ohms. With that said, I'm sure your system sounds fine.
You may detect a sonic difference between the two taps, depending on the design of the speakers and your ears/expectations. You should try both taps and simply pick the one that sounds best to you playing the music you enjoy hearing. You won't damage anything by doing so.
Sometimes folks find that the 4 ohm taps can produce a more solid bass, some that the 8 ohm taps can produce better highs, but it all depends on how your speakers impedence curve matchs the amps output impedence. Speaker and amp impedence values are not fixed at anything as absolute as 4 ohms and 8 ohms. Those a just nominal numbers.
so after reading everyones comments "I" believe maybe i should up my power because "I" believe that maybe just maybe my Thiels will open up a bit more if I do 200 watts into 8 ohms. But thats also under the theory that in order to hear a difference I would need to double my current output, view my systems and you will see what i am talking about or in other words.
the followings numbers "wattage" are the points of difference:
50 100 200 400 800 - basically oh i have 100, oh i have 150 so then that means i am louder is that true, i believe not, i believe the next level of DB improvement would be 200 for the example given. Is that correct or no?
The difference between the power out put between 100 and 200 wts, everything else being equal, is 3db. If that is the threshold where you and distinguish clear differences in SPL's then you are correct. But if you have the ability to discern smaller changes (and I think most do - some even claim to her differences as small as .5db) then your conclusion wouldn't work. You might see how manufacturers treat this issue by looking at the different gradiations they use in the steps in the attenuators. Some use 1db, some 2db, and some use gradual decreasing step sizes as you 'apply more my volume'.
So everything else being equal, the difference between 100 watts and 200 watts is a mere 3db increase in SPLs. When you are listening to your system with the volume turned up, and your max'ing out your systems (including your room) ability to produce coherrent sound, a 3db increase in SPL may be relatively inaudible.
If you haven't already done so, buy a SPL meter and see what average/peak levels you listen to in your room and do the math. But don't be surprised when you find that with even moderately efficient speakers, that you rarely, if ever, exceed say 20wts, and even then only on peaks. And if you do, consider that if you are listening to music at that level it may not be a problem for long.
Nothing wrong with 'powering up' but the price go's up as well and its a lot to pay for something you may not need.
Not being entirely sure by what is meant by 'peaks increasing expotentially' and for the benefit of others facing a decision about how much power is needed, consider this as a rough guide.
Assuming you anticipate that the average sound pressure level of your music will have peaks 15db higher than the average SPL, not an unreasonable assumption, I think (nor is it absolute), if you are listening to pop, jazz, & classical music.
Assume your speakers have an efficiency of 86db's.
Assume you have a meduim sized room where I think an 85db SPL would be considered by most to be fairly loud but still within the ability of the room to respond without overloading. The following watts would be needed to producte the indicated SPL. This little chart contains no consideration of current needs, impedence values etc.
1 wt - 86db
2 wt - 89 db
4 4t - 92 db
8 wt - 95 db
16 wt - 98 db
32 wt - 101 db
64 wt - 104 db
128 wt - 107 db
256 wt - 110 db
512 wt - 113 db
1024 wt - 116 db
IF, and only IF, you found my 85db average SPL reasonable, and you add 15 db to that, you would only need 32wts. Now if you want 3 or even 6 dbs of headroom you would need no more that 60 or 120 wts (BTW all numbers are rough/rounded and meant for illustration).
I've got no argument with you'r table. One can easily see that there is quite an increase in power from 86dB to 104dB. IMHO, and this might be more so with ss than tubes, that one would probably be better off staying away from an amplifiers ceiling of power delivery to keep the sound as clean as possible. One way to accomplish that is to have extra power at hand.
The reason to have a more powerful amplifier is not to play the music louder, but to play the music more accurately. The soundstage "opens up" because the peaks can get louder while the valleys stay quieter. The music also sounds more real because, again, the peaks can get louder. The reserve headroom in the amplifier makes all the difference. The sharp, high peak of a whip crack or even just a smack can require near infinite power to duplicate.
My viewpoint is that playing the music either louder or quieter than the original session is a type of distortion- at least that's what I tell my wife when she wants me to turn it down.
I'm sorry for getting a bit off topic here, but in some instances a higher powered amp might sound better even at volumes that could be handled by a lower powered amplifier. In some class A/AB amplifiers designs the bias of class A before going into class AB increases proportionaly to the total power output..