In the standard octave numbering scheme, is the interval between C[N] and C-flat[N] a diminished prime or a diminished octave?

In other words, does the flat modify C[N] or does it modify the next C up, i.e., C[N+1]?

More like an augmented prime since you have the same letter. Apparently you are mixing up primes and seconds. At any rate any accidental modifies the note behind it.

Strictly speaking C♭6 is in a higher octave than B♯5 even though it's a lower pitch.

• Thanks! I have already modified the title. Does there even exist such a thing as a diminished prime, by the way? – Kim Fierens Sep 5 at 21:57
• Since distances are named "in absolute" (there is no negative second or such) and prime is already 0, I don't think a diminished prime would make sense. – user63008 Sep 5 at 22:10

Melodic intervals are always measured from the lower note to the higher note, no matter which note comes first.

So yes, if the intervals between Cb and C is just a semitone apart, it’s an augmented prime.

• Cb to Cb: perfect prime
• Cb to C: one semitone bigger —> aug.

If the interval between Cb and C is one semitone greater than an octave, then it’s an augmented octave. :)