B# and Cb octaves: bug or feature?

Sample score?

Good dilemma. I think changing octave names is the correct way to do this, because the octaves are defined by where they are on the keyboard, not their names. When you press the B# key you are actually pressing the C key. So the jump up an octave for a B# is what I would expect. The same logic works for Cb.

This is not a matter of taste or what you think or I think. This has to be defined somewhere in some standard and there must be an absolute answer.

https://infogalactic.com/info/Scientific_pitch_notation
C-flat and B-sharp issues

There is some possible confusion regarding the assignment of an octave to C♭ or B♯. The convention is that the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals. For example, the symbol C♭4 means "the pitch one chromatic step below the pitch C4" and not "the pitch-class C♭ in octave 4", so C♭4 is the same pitch as B3, not B4. Similarly, at the other end of the fourth octave, B♯4 is the same pitch as C5, not C4.

The matter may be clarified by viewing "♭" and "♯" as denoting lowering or raising by a variable amount. In equal temperament, that amount is exactly 21/12 ≈ 1.0594631, or 100 cents, whereas in quarter-comma meantone it is precisely 57/4/16 ≈ 1.0449067, or 76.049 cents, taking other values for other meantone tunings. Hence "C♭4" is the same as "C4♭", which in equal temperament is 100 cents below middle C, and equal to B3. In quarter-comma meantone, C♭4 is 76.049 cents below C4 and 41.059 cents (ratio 128/125 = 1.024) sharper than B3, which is 117.108 cents (ratio 8/55/4 = 57/4/15.625 ≈ 1.0699845) below C4.