Hi Brian,
Brian Davies:
I fail to see how anyone noting at the rate of ten per second can achieve any kind of tranquility,could you elaborate? Regards Brian Davies.
Noting at 10/s and tranquility: Without wanting to go into hair-splitting, here's a simple conceptual model I find useful:
1. Concentration is not the same as tranquility. Concentration is, well, concentration, focus, narrow beam. Tranquility is smoothness and stability. Tranquility can arise when concentration is held very stable over the long term.
2. "Momentary concentration" is what powers the 10-per-second noting practice. Think of each notice as a flash of concentration. You're right, this is not tranquil. When tranquility arises from noting practice, the noting has likely become a smooth, rhythmic thing without any noticing going on. This is why a drumbeat can be the object of concentrated, tranquil states, even if it sounds so discontinuous.
There are many ways to play this. Straight noting practice will forego the tranquility, result in these quick, harsh bursts of highly concentrated flashes, and while a fast way to proceed can be very unpleasant.
Another way is to get all tranquil and concentrated (whether by entering jhanas, or just powering stable concentration on something), then let it go on its own for a while (maybe abide in the jhana for some time, or just let the concentration sustain itself if you're not into counting jhanas), and pay close attention to what happens when the thing ends, perhaps do some noting practice at that point. Very pleasant, but it can be a bit seductive to just enter the nice, smooth state again without looking too closely at the icky shifting things it broke apart into.
Another way is to not enter any very hard concentration state, but instead to be on the constant look-out for drawbacks even to the most refined states. This requires one to stay "out" of the states most of the time, at door-frame, peering in, so to speak.
Really, experiment. Often, practice will take you one way or another in this spectrum between tranquility and insight. A good teacher will be able to guide you; or you might go the gung-ho route and do noting practice like there's no tomorrow, or you might rely on your intuition.
Often, I think that the most useful model is: whenever one is doing *something*, that *something* stays done (which translates into "trust the process").
Just as often, though, I like the more refined and geeky models better

Cheers,
Florian