I have learned figured bass only using well-organized reduced excerpt.
Above picture shows a real excerpt with figured bass.
Does '8' respond to the red circled 'Eb', and '7' to the 'Db'?
What makes you choose Eb and Db and write 8-7 when there are many other notes? why are Eb and Db chosen to represent the chord?(what makes Eb and Db stand out among other melody notes? Is it because Eb and Db are the only pair with 2nd apart?)
What makes you choose Eb and Db and write 8-7 when there are many other notes? why are Eb and Db chosen to represent the chord?(what makes Eb and Db stand out among other melody notes? Is it because Eb and Db are the only pair with 2nd apart?)
Wait, did you learn figured bass? I'm not sure you're clear on some of the fundamentals. Keep in mind that, before it was used for theory analysis, it was used as instructions for performance. In baroque music, you might see only one note here, the bass dotted-half E flat, and the figures. The continuo player would know that they're meant to play an Ebm chord, and that one of the E flats (not the bass one) will move to a Db.* That's all the information they have. It's up to them to create all the other notes other than the bass one (or "realize" the figured bass), in any way that meets these criteria.
Figured bass is not made to explain "melodies" or the "many other notes." In fact, that's why it's a good tool for harmonic analysis; you're analyzing the motion of big building blocks and don't care about all the other gobbledy-gook. From a functional harmonic perspective, this excerpt is no different from this:
The numbers are present because the only note that's not part of an Ebm triad is the Db, and the 8 is here to talk about the motion to that seventh.
* Maybe I'm mistaken, but I would have thought it would have need a "b7" to indicate D flat in performative figured bass, as the figures follow the key signature literally...
This isn't figured bass; it's Roman numeral analysis. If it were true figured bass, the figure at the beginning of the measure would be ♭. This indicates that the third of the chord is lowered. The 5 and the 8 are implied. The end of the measure, as Andy Bonner noted, would be ♭7 because, well, the seventh is lowered.
Roman numeral analysis uses figures derived from figured bass primarily to indicate inversions, whether the chord is a seventh chord, and sometimes suspensions and other non-chord tones, but it isn't really proper figured bass. The implementation of RNA figures is somewhat different from actual figured bass that you might find in a 17th or 18th century bass part.
In Roman numeral analysis, we don't need to have the ♭ figure for an altered minor chord (as in this example), because the case of the Roman numeral indicates whether the third is major or minor. Here we have a lower-case i, which along with the signature of three flats indicates that the piece is in E major and we are analyzing this chord as the parallel minor.
The fact that the seventh is a minor seventh is implicit -- the seventh chord with a minor third and major seventh is not a feature of common-practice period tonal harmony -- so it's not necessary to write an explicit flat sign on the figure 7 here, again because this is RNA rather than true figured bass.
Your question is really a prompt for a complete overview of figured bass and that is beyond the scope of Q&A at this site.
Personally, I think this page https://robertkelleyphd.com/home/figured-bass/ gives a good overview, and encourage you to read it.
Figured bass gives numbers representing intervals above the notated bass. Those tones can be in any octave provide it is above the bass. The figures are short hand instructions for a keyboard play used to improvise chord based accompaniment in their right hand while the left hand plays the notated bass.
The figures 3/5 are often omitted. From that you can say the "default" way to harmonize a bass tone is with a root position triad (not seventh chord), and no special figures are need to prompt a player to do that. You can call such omissions "unfigured", and "unfigured bass."
So, very roughly, in practice when you see the numeric figures, it's a sign that the chord is an inversion, a seventh chord, or both. The interval numbers involved include a lot of 2, 4, 6, and 7. Other figures and symbols are included to alter tones from the diatonic key signature.
Review the overview I linked.
Look for some "realized" figured bass examples. You can often find that in the accompaniment keyboard part for classical (probably more properly Baroque) music. Looks at songs, arias, and sonatas for soloist with keyboard accompaniment. I helps a lot to read a realized and notated out accompaniment along with figured bass.
Does '8' respond to the red circled 'Eb', and '7' to the 'Db'?
Yes, but there are details to discuss.
In your question the 8 would normal be omitted, because the first chord is simply a root position triad, no figure is needed.
Including the 7 for the second chord would be normal, because that tone extends the chord beyond the "default" root position triad.
There are some additional concerns about the key signature and your Roman numerals. Figured bass normally includes accidentals and other symbols for any intervals that are altered from the key signature, which you have done. If you are really doing a mode switch from Eb major to a tonic of Eb minor, the first chord would get a figure, but it would be simply a ♭, which is a short hand to say "minor third" in a root position triad. The 7 should also get a flat as ♭7, because it is an alteration from the key signature.
The score shows figured chords, Ebm for the first two quarter notes (I assume the eight notes are triplets), then Ebm7 for the last one. So the "other notes" are just figured chords.
Number 8 is normally omitted, just as 3 and 5 are in root inversion. Here it is written to emphasize the motion from 8 (eb) to b7 (db), which is also emphasized in the score, with eb moving to db on the third quarter note. 8-7 is a typical marking for such pattern.
