I'm also not convinced. That said, the author is suggesting that large intervals tend to get their power when we identify smaller intervals emerging from the br

I'm also not convinced. That said, the author is suggesting that large intervals tend to get their power when we identify smaller intervals emerging from the broader composition. For example, when hearing an arpeggio of a chord progression, the literal intervals are large, but we easily identify the "higher level" small intervals appearing between chords, and those smaller intervals become melodically important in the listener's mind. This might occur more subtly in your examples.