Thanks Samuel for your reply.
The reason is theorical, just to be consistent with the dim chord meaning (bb in 7th)...

On the other hand my main purpose is to build a series of the five chords (Major, dominant, minor, half diminished seventh and dim7), to practice and to be able to follow the notes.

Do you have any idea how to build that in BIAB?
By now just start with F, and found the bb issue... (that as you said, could be replace by next natural). The thing is what do you recommend to practice those chords with BIAB. I am new with the software...
Thanks for any help.
Best regards
Claudio