kvanto: in addition to the fading option as pointed out by frankz and Critterman, since you say changing to WASAPI/Asio solved the problem at your DAC's end, 5 will get you 10 that you also had the Windows mixer set to 44.1kHz as I would imagine Direct Sound is what you had your output set to previously.
I have exactly one AIFF in my collection but it is "really" a 44.1k sample rate; I left the original id3v2.4 tag on that it came with (Bandcamp), but MusicBee can read neither the tag nor the sample/bit rates in its Edit window, so yeah AIFF has its issues. AIMP and Foobar do read the original tag and rates on that one.