I saw [a̟] in PHOIBLE and thought "okay, it's an advanced front vowel-- hold on, it's already in the front." Is it an error in PHOIBLE or an error in my linguistic knowledge? What effect does the advanced diacritic have on front vowels?
Co-editor of PHOIBLE here. In the feature system used in PHOIBLE,
a is considered to have features
-back — i.e., a (low) central vowel, not a (low) front vowel. Therefore you would think that
a̟ should be considered as a low front vowel (as your instincts suggested). However, that featural specification is already in use for
æ. This illustrates that the PHOIBLE feature system is incomplete, precisely because of thorny issues like this one (read on to see just how thorny...).
There are doculects in PHOIBLE that contrast
a̟ː (e.g., Tewa, inventory 93, glottocode tewa1260), and others contrasting
a̟ː (e.g., Hopi, inventory 95, glottocode hopi1249). Both of these were ingested into PHOIBLE from the Stanford Phonology Archive (SPA), which had its own, fairly careful scheme for representing things like vowel quality or consonant place of articulation. For example,
a̟ː is called "a-front-long" in SPA. You can view the mapping from SPA's system to the corresponding representation in PHOIBLE. Note that SPA also has "ash-long" and "a-long", thus creating the conundrum of how to distinguish these three in a feature system that will make sense to most linguists.
Another thorny problem is that the "combining plus below" diacritic can mean different things (i.e., change different features) depending on the glyph it is added to. This makes it hard to automatically assign features to phonemes that contain it (which is why line 176 of this file is blank).
Part of ongoing work on PHOIBLE is resolving the various places where the feature system is unable to fully accommodate the contrasts present in the doculects. Another ongoing effort involves correcting places where the data in PHOIBLE don't match the description of the sound in the describing document. Please feel free to open issues on the PHOIBLE GitHub page if you find cases where the phonological inventory in PHOIBLE does not match the textual description of the sounds in the associated grammar/dissertation/journal article, or if you have suggestions for how to improve the feature system to better accommodate contrasts that are currently not encoded. Better yet, submit a pull request that fixes the problems you find!
It isn't clearly established whether there are any phonetic categories of sounds, and it's possible that what exists in the phonetic component is all continua (that is certainly the case with physical realization, which is the other way that people think about "phonetics"). The term "front" is a phonological categories, with a phonetically-inspired label attached to it. The IPA letter [a] refers to a range of productions, which can be divided into "more front" and "more back". The IPA diacritics indicating "more front", "more round", "less round" and so on, are modifiers relative to an ideal standard. When a vowel is more front than that standard, or any other deviation from the standard, it is appropriate to use the diacritic to indicate that fact about production of the sound. It might be that in some language, the vowel is generally more front than the standard, or it might be in a specific context (an allophonic rule).
It is probably not an "error" by PHOIBLE, but you might check the original source that PHOIBLE relied on. If you can locate samples of the particular language, and if you can locate expert IPA reference performances, you might be able to judge that the vowel is actually higher, not more front, so that would be an error of judgement (assuming it's the original phonetician's error and not yours).