I worked around the problem and it seems OK!
Music from my player is just nice, I'm listening to it right now (music from Lemmings 2)
I just call
AHI_ControlAudio(actrl, AHIC_Play, FALSE, TAG_DONE);
AHI_ControlAudio(actrl, AHIA_PlayerFreq, frequency, TAG_DONE);
AHI_ControlAudio(actrl, AHIC_Play, TRUE, TAG_DONE);
With the neighbourhood of the 2 perimeter functions setting the frequency doesn't produce noises. All right, now the production of Diamond Player 2.0 can progress further
It is currently a program written in C++ with the use of its many interesting features. MOD and MED modules are for example the childs of abstract Music Module class, also audio output is a template in Music Player class, so there is a possibility to use different audio output methods like audio.device for example or AHI like it is now.
The workaround doesn't cause any problems (only there is a tiny, almost unnoticably break when changing frequency). Cheers.