I just got into a conversation on one of the FB conlang groups that made me
realize that I have no idea how to define a phoneme in Aeu, one of my
sketchier langs.  The problem I have is figuring out where to draw the line
between phoneme and suprasegmental.

There are 9 unrounded vowels:

/i/  /ɨ/  /ɯ/
/e/  /ə/  /ɤ/
/æ/  /ɐ/  /ʌ/

I am certain these 9 are all phonemes.
Each of the above can be rounded as:

/y/  /ʉ/  /u/
/ø/  /ɵ/  /o/
/ɶ/  /ɞ/  /ɔ/

I also confidently assert that all of those are phonemes in Aeu.
That makes 18 phonemes.

Every one of those can be short, half-long, long or over-long. (I know at
least three of theese will be in the language, but I might not decide to go
for all four.  I've waffled back and forth over the years.)  Length is
lexically important. A A; A: and A:: are all different lexical items.
Should I count length as phonemic?  It normally is in cases like this.
That would make anywhere from 54 to 72 phonemes.

I'm fairly confident up to that point, but then we get to the "voicings."
I'm not using phonations, because, as I understand it, nasalization is
normally not considered a phonation, but in Aeu, it forms a class with the
phonations, since a vowel of any rounding or length (or tone though we
haven't gotten to that yet) may be either naslized or not, but a vowel that
is creaky voice, may not be nasalize nor may it be breathy or rough.  A
vowel may be plain, nasalized, creaky, breathy or rough, but it may not,
under any circumstances, be more than one of these simultaneously.  Now
nasalization is often concidered phonemic, but what of the other "voicings"
in my list.  Should/can I count breathy-/e/ as a distinct phoneme from
creaky-/e/.  They are just as lexically important as the roundedness or the
length. This would mean that Aeu has anywhere from 270 to 360 phonemes.

Now we come to the 11 tones, and here I am really unsure how to describe
Aeu.  Each of the tones may apply to any of the vowels, round or unround,
at any length, with any voicing (though there are bound to be holes here
iand there in the actual vocabulary where a given *possible* syllable is
not an *actual* word), and again tone is as lexically important in Aeu as
it is in Chinese, so should I count the tones as phonemes?  In that case
Aeu has between 2970 and 3960 phonemes and essentially every possible
syllable is a unique phoneme.

Or should I say Aeu has 9 vowel phonemes, 2 rounding phonemes, 3 or 4
length phonemes, 5 voicing phonemes and 11 tonal phonemes and every
syllable requires exactly one phoneme from each category such that eveery
syllable is 5 phonemes.

Or should I be looking at some hybrid?

Or some entirely different analysis.

Adam