Locate a pitch on the key's ladder of scale tones.
Anything counting in scale degrees has to put a pitch on this ladder and back
again afterwards. Keeping the chromatic offset apart from the rung is what
lets a note between two scale tones survive the arithmetic as the note it was:
without it a shift by any number of degrees — including none — would first
flatten every chromatic pitch onto the scale.
In C major, C# sits on the tonic's rung with an offset of one semitone.
Layer-internal: the generators count degrees with it, and callers reach the
same arithmetic through the transforms that use it.
Locate a pitch on the key's ladder of scale tones.
Anything counting in scale degrees has to put a pitch on this ladder and back again afterwards. Keeping the chromatic offset apart from the rung is what lets a note between two scale tones survive the arithmetic as the note it was: without it a shift by any number of degrees — including none — would first flatten every chromatic pitch onto the scale.
In C major, C# sits on the tonic's rung with an offset of one semitone.
Layer-internal: the generators count degrees with it, and callers reach the same arithmetic through the transforms that use it.