This has been discussed before... but quickly,
The FBS design sends a long pulse and then short pulse trains at two frequencies. The low freq is 3.125KHz and the High is 25KHz, which is a harmonic of the first and not as strong. There are many harmonics in the transmit signal, but they are not used (the detector only sense the low/high return signals). The idea that there are 28 freqs broadcast is true, but they are unused harmonics. Might as well say there are 100 or 1000 frequencies - again, true, but not used.
So, what does this mean? It means the detector is designed to find high conductors (which are usually valuable) and ignore low conductors (which you don't want, like iron trash). Low freqs drive deeper into the ground and do not excite low conductors well (low conductors need many pulses to drive eddies to return a strong signal, but you don't want them to do that, which is the problem with high freq detectors - they find tiny iron).
The Noise Cancel simply shifts the base freq (and all harmonics) about 10% to avoid interference with other detectors. It isn't going to give you significant target sensitivity changes, though some think it does.
A small gold chain, thin ring, small clasp, thin earring, etc. are all going to generate weak eddies when hit with low frequency transmit signal. The high freq helps but is weaker ... so, you probably aren't going to find these thin jewelry items unless attached to a pendant or some other conductive surface. Your best chance to find thin jewelry will be circular shaped targets that generate a composite eddy that circles the target (like a ring). A thin straight pin, or broken ring (broken circuit) is going to be very weak. The tiny individual links in a gold chain individually produce a very tiny eddy (it is not summed) and therefore are below the sensitivity of FBS machines. However, a high freq gold detector would light them up to a considerable depth.
The advantage of the CTX is it's ability to go deep in iron/mineralized soils and still retain reliable target identification. Other detectors can find smaller jewelry at greater depths but the higher the soil minerals become the more the advantage swings to the CTX (and E-Trac). There is no perfect detector.