[gmjoe]

Is this a cultural thing?

I was always taught there are 12 notes, while any standard scale contains only 7 of them. (The chromatic scale obviously being the exception which contains all 12.)

Accidentals are just for notation -- obviously B-flat and A-sharp are the same "note", just as F-sharp-sharp and G are.

Our entire turning of equal temperament is based on 12 equal intervals, not 7. So I'd argue parent commenter is correct -- notes are base 12, not base 7.

[SwellJoe]

Scales are based on ratios, and our equal tempered scale is a compromise to get equidistant steps that can be used to closely approximate those ratios. The idea being to be able to use the same instrument to play in any key without retuning the instrument and adjusting the intonation.

So...one could argue for either or both interpretation and explanation. The note names, sharps and flats, is what is most arbitrary about it.