Hey Daniel,
406, 407, 456 and 457 all use the same bias setting. Bias is an inaudible high-frequency signal that is applied to the tape during recording. In layman's terms, it excites the magnetic particles so they can be more precisely manipulated by the recording process. The bias signal was discovered by accident in the early days of analog. It reduces unwanted distortion.
The thickness of tape has more effect on Azimuth, saturation, and tape-to-head contact. On many consumer decks and some semi-pro equipment, such as the Tascam 388, the thicker tapes (406 & 456) work, but are not ideal. The reason is that the tape is too rigid to physically conform to the heads within factory spec. The lack of a snug tape-to-head fit reduces high frequency response and overall clarity.
Another difference between 40X and 45X is the type and density of magnetic particles. 45X will accept 3 dB more signal than 40X. However, if your machine's electronics can't handle the higher signal without introducing distortion then the higher capacity of the tape is wasted. Depending on the machine, 406 and 407 will be favored over 456 and 457 because the pleasing effects of analog distortion are realized at lower levels. So while 45X can be hit harder, the machine in question may not have the capacity to hit it hard enough. Therefore many recordists have discovered mastering to 406 or 407 gives them the much sought after "analog effect" they are looking for.
So while all the above tapes are bias compatible they are not necessarily physically compatible.
It comes down to a balancing act -- trying to avoid distortion introduced by the electronics of a machine while benefiting from musical distortion from tape saturation. It's an art.
Whether it was Tom Scholz of Boston and his beloved 3M 226, or Steve Perry of Journey and his favored AGFA/BASF 468, back in the day, successful artists and engineers were quite serious about finding the "magic tape" to best capture their signature sounds.
I encourage anyone serious about mastering this art to experiment with as many types and brands of tape they can get their hands on. Especially now while new-old-stock tape by companies no longer making it is still available. Some day it will all be gone.
Tim
. I recall reading, on rec.audio.pro I think, that some called the 407's sound "neutral" and preferred it to the rather "glassy" sounding 456 .. so I see what you mean by capturing one's own "signature sound". Anyway, I'm looking forward to getting the 407. 