Harmonic analysis is a creative reductionism and not a mechanical operation. There's no single valid harmonic analysis. Different scholars perform harmonic analyses differently, and disagreements arise everywhere:
- V7 or viio, ii6 or IV, IV6 or vi
- I64 or Cad64 or V64 or a functional labelling of passing chords
- cadential I(247 - 35) - triple suspension, a reddit discussion
- should we mark passing harmonies?
- should we mark common-tone chords?
- what's a root of a non-applied diminished seventh chords, eg. io7 or #ivo7?
- what if a third/a fifth is missing, or there are three consecutive pitches? pic source
- can root be missing/implied, eg. use V7 in place of viio?
- are we overgeneralize Roman numerals as functional analysis labels in ambiguous cases?
- what to do with quartal chords? pic source
See "On the relative openness of syntax" in Mark Gotham's paper
As a single example, below are three different analyses of the beginning of Beethoven's op. 2 no. 1 mov. 1 (🎥 audio on YouTube):
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And how it's annotated in William E. Caplin's book:
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Christopher White, "The Music in The Data", chapter 3 on harmony
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AugmentedNet paper - also follow other cited works from there