Here is my understanding:
A "MIDI quarter note" is 24 MIDI clocks. ("MIDI clocks" are small MIDI messages sent at a steady rate that help indicate the current tempo to other MIDI devices.)
A "notated quarter note" is presumably how your MIDI software displays quarter notes on the screen.
In a Time Signature event, the bb value supposedly lets you change the relationship between a "MIDI quarter note" and a "notated quarter note". However, in the MIDI software I have used, my tests changing the bb value had no effect on how the software displayed quarter notes. And in every MIDI file I have encountered, the bb value is always set as 8 indicating a "MIDI quarter note" and a "notated quarter note" are the same.
Does the MIDI Manufacturers Association or any other users here know of any MIDI software that uses the Time Signature bb value in any way?
If you were to set the bb value to something other than 8, then you have to carefully understand which items are defined in terms of "MIDI quarter notes" and which items are defined in terms of "notated quarter notes":
Tempo meta event: The specification says "Another way of putting 'microseconds per quarter note' is '24ths of a microsecond per MIDI clock'", indicating the tempo meta event value is defined in terms of "MIDI quarter notes".
Time signature denominator: The specification says "nn and dd represent the numerator and denominator of the time signature as it would be notated", suggesting the time signature denominator is defined in terms of "notated quarter notes".
Ticks per quarter note: When the quarter-note based division is used, is the "division" value in the header in terms of "MIDI quarter notes" or "notated quarter notes"? I guess it's "MIDI quarter notes", but the specification only says "ticks per quarter note".
As you can see, I have also wondered about the exact meaning and usage of the Time Signature bb value, but since I haven't found software that uses the bb value for anything, and the specification could be clearer about which items are defined in terms of "MIDI quarter notes" or "notated quarter notes", my current suggestion is to always set the bb value to 8 to specify "MIDI quarter notes" and "notated quarter notes" are the same.
In a Time Signature event, the cc value is intended to let you change the duration between metronome clicks. For example, if you use a 6/8 time signature, instead of each measure consisting of six metronome clicks, you might want each measure to consist of two metronome clicks (one click every three eighth notes). To specify that, you could set the cc value to decimal 36 (hex 24) and the bb value to 8.
However, in the recent MIDI software I have used, my tests changing the cc value had no effect on the metronome clicks. Most software always clicks the metronome nn (the time signature numerator) times per measure.
The last time I tested Synthesia, it ignored the Time Signature cc value, but did have special metronome behavior for the 6/8 time signature. As I remember, the default "1x" metronome setting clicked two times per 6/8 measure, and the "2x" metronome setting clicked six times per 6/8 measure. This is a reasonable default that I really like, but it doesn't matter what you set the Time Signature cc value to.
I might dig up some of the older MIDI software I have used and test it. I think I remember using sequencer software like Cakewalk and Voyetra Music Write 2000 that let me specify two metronome clicks per measure for 6/8 measures, but I can't remember if it saved and read the MIDI file Time Signature cc value to do that or if it was only saved in its own file format.
Does the MIDI Manufacturers Association or any other users here know of any MIDI software that uses the Time Signature cc value in any way?
Here's another thing I've thought about in regards to the cc value: Should the metronome clicks always align evenly with measures? What if the cc value indicates metronome clicks that don't evenly fit into a measure? For example, in a 6/8 time signature, if cc was set to decimal 37 (hex 25), should the metronome really click at a slightly longer duration than the notes?
If I wrote a MIDI sequencer I would probably only obey the cc value if: A. an integer number of metronome clicks fits into a time signature denominator note value, or B. an integer number of time signature denominator note values fits into a metronome click and an integer number of metronome clicks fits into a measure.