Absent any other context, if you play Root, b5, b7 there's just as good a chance you're implying a whole-tone environment.
(Emphasis added.) Very true.
It'd only be within that minor II-V progression that you would be able to suggest a half-diminished chord without playing the b3.
(Emphasis restored.) Well, there and in a couple other cases.
- The half-diminished chord, as the viiø in a major key, works as a dominant chord, resolving directly to the tonic a half-step above, especially in classical music, as an alternative to the diminished seventh chord;
- it is also not uncommon as a passing chord between the Imaj7 and the ii, and
- between the IVmaj7 and the V (or the second inversion of the I).
In all the above cases, it certainly can be analysed as a rootless dominant 9th chord (respectively: a V9, a V9/ii and a V9/V), but it will more often than not be played rootless by everyone.
- Finally, at times you'll bump into the third of the above sequences of chords, but in reverse order (IOW, the half-diminished used as a passing chord between the V, or the I in second inversion, and the IV: think the last chord in the verse, pre-chorus, in "God Only Knows").
In all of these scenarios (except maybe for the last), a root-flat five-minor seventh arpeggio - with no explicit third - would be correctly parsed as an outline of the half-diminished chord, precisely because of the immediate (preceding) context.
...Which is, my nitpicking notwithstanding, the main takeaway from your post, especially valid for the OP:
@basslayer - I'm sure ear-training online tools exist for chord recognition. I'm a bit behind in this respect, myself. However,
chord syntax, as pointed out in this exchange and in other posts above, gives you a lot of mileage, and is arguably more important: one needs to
expect the changes, and to know where they they're likely to lead to. In order to do that, you need to learn a lot of standards, and to study harmony, so that you learn to identify and conceptualise the recurring patterns in those standards: e.g. this is the two in a cadence, this is a secondary dominant (V) of vi, and so forth.
Once you get started, you'll be forgiven for occasionally failing to follow the exact voicing of a dominant chord as chosen by the original arranger or the main comping instrumentalist in the jam, in a ne'ertofore seen piece; and you'll be ready to dip your toes into less predictable waters (pieces with lots of tonicizations, i.e. quick, temporary modulations, and overall unexpected changes). You can further your ear-training in the meantime - the two things are by no means mutually exclusive.