The fundamentals of acoustics don't go away if you try to ignore them ...
Sanken doesn't design or market their shotgun microphones for music recording. They deliberately attenuate the bass and boost the upper midrange because that improves speech intelligibility for dialog recording. This is in keeping with most other manufacturers of shotgun microphones (as well as most super- and hypercardioid microphones generally).
I know of only two manufacturers (no surprise: Schoeps and Neumann) who have seriously designed their shotguns for music pickup as well as for speech. I own both brands, and the difference in the naturalness and attractiveness of the sound quality between them and any other brands I've ever tried is striking.
Still, wherever possible I wouldn't use shotguns for music recording at all. Good supercardioids sound much better, particularly in reverberant recording environments. This is largely a function of the smoothness of their frequency response at ALL angles of sound incidence, which in turn is tied to their keeping the same directional pattern throughout their entire frequency range--exactly what a conventional, single-capsule shotgun microphone can't do (see below).
Sanken offers some shotguns (the best one being the CS-3e) that have multiple capsules, combined electronically in a way that gives them a narrow pattern across most of the audio range. But at the price point of this new 4" model, I think it can only have one capsule. That, in combination with its shorter-than-usual interference tube, means that its pattern will have a "crossover" frequency in the upper midrange; below that frequency it will function as something like a supercardioid, while the narrower pattern will occur only above the crossover frequency [note added later: Yes, this is borne out by the polar diagrams that Sanken has up on their Web site]. With single-capsule shotguns, the shorter the interference tube, the higher the frequency of that crossover, and the broader the pickup pattern even at its narrowest. Longer shotguns have both a narrower pattern at high frequencies, AND a lower crossover to the region in which they have that narrower pattern.
--best regards
P.S.: The AKG C 747 which someone mentioned earlier in this thread is NOT a shotgun microphone nor did AKG sell it as one; it is just a directional microphone designed for speech pickup. It does that job well enough, though it's on the noisy side.