Substitute
This issue Richard Barrett debates the use of numbers and slashes in chord naming, and acknowledges that there’s no correct answer…
Like all systems, chord theory occasionally struggles to itemise every single possibility in harmony. Just as mathematicians have no universally accepted way to write repeating decimals such as 0.333333, musicians often have various ways to describe a chord in our own language – all of which may be different but no less correct than each other.
In situations like this, it’s useful to employ a bit of logical thinking. For example, in what context does the chord appear? An A/G chord (an A major triad over a G bass note) could be referred to was an A7 3rd inversion (7th on the bottom), but if this then resolves to a D/F# (D 1st inversion/3rd on the bottom), it seems logical to go with A/G and acknowledge the descending bass.
Listen to The Beatles’ Dear Prudence for a nice example of descending bass notes creating a secondary melody within a chord progression. I have picked out what I feel are a few good examples here, so see if you agree with the names I’ve chosen!