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I understand that unlike chords from learning materials, in the real world there are not many pristinely organized chords.

Two chord tones are enough to establish a chord, non-chord tones are to be ignored, etc.

In the picture above, in m.1 at 2nd downbeat there are C F B D, C F B G led by preceding I chord.

Would you ignore the pedal tone, C? and assign vii diminished even if it might be an auxiliary sonority?

And Would you ignore embellishing set of notes in m.2, m.3, and in m.4?

Would you in m.4 assign ii6 for F and D and V6/V for F# and D, and V for G and B?

It's quite difficult getting a grasp over what's accepted and what's not because it seems very subjective.

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  • It can be helpful to work "big lens to small lens": start with the broadest, Schenker-style analysis and then fit the details into that. The story of this excerpt is "4-bar half cadence." (No doubt it's part of an 8-bar phrase with a full cadence at the end.) We can then fill in the smaller details without fear of analyzing ourselves into a place that doesn't make sense. Commented Jun 10 at 15:44
  • Also, it matters to know why we're analyzing. In school it's often "because we were assigned it" or "to practice analysis," but in the wild, we might stop at a certain level of detail depending on our goal. If we're trying to find the architecture of the piece, or broad harmonic motions, then we can stop at a large level; we might go finer if we're inspecting melodic figures or interesting ways that specific chords use voice leading. Commented Jun 10 at 15:47

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This is the interpretive (i.e., subjective) aspect of analysis, and different people might come up with competing, but equally reasonable answers.

I would look at the excerpt this way:

m. 1: The C is a pedal tone, and the second half of the measure is the V7 chord, even though the G doesn't occur until the final note.

m. 2 & 3: I would ignore the embellishing notes, since they don't serve to change the aural perception of the harmony.

m. 4: I agree with the given analysis of ii6 -> V6/V -> V

Ultimately, an analysis should reflect the heard experience of the piece. Since hearing itself is inherently subjective, so, too, is analysis.

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In bar 1, the 1st half is firmly C, so I. The second half is G7, so V, but with that C underneath as a pedal tone, rather than the usual suspension.

Bar 2 - all back at C (I), the fast run down not changing anything.

Bar 3 - G, with lots of diatonic notes of key C, but sounding like a G7 run, leading to the last quaver - a C 'chord', a little earlier than anticipated.

Bar 4 - G7, with V/V (D) modulating to key G.

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