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Given C♭♭4, for example, is that enharmonic with B♭3 (because you start at C4 and flat it twice) or B♭4 (because octave number 4 means octave number 4)?

Asked another way, how do you write the note below in scientific pitch notation?

Staff showing C-Double-Flat on ledger line below treble clef staff

I'm just wondering from a theoretical perspective.

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Follow the note name. Add the accidentals later.

Begin by acknowledging that this pitch is some type of C4. Then add the accidentals to show that it's C♭♭4.

This is a little strange, because (as you say) C♭♭4 is lower than B3. But that's really no more odd than saying any C♭♭ is lower than its nearest B.

And the same is of course true going the other way: B♯3, despite being enharmonic to C4, is nevertheless identified in the "3" register.

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    Makes sense. Guess you don't really need double accidentals to have this question. – trw Jan 18 '19 at 19:15
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    I think it helps the question to have the two pitches sounding the same. If it's only C♭, it's still above B♭, so the question of "why is 4 higher than 3?" isn't as problematic. – Richard♦ Jan 18 '19 at 19:21

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