Not phonetic but ___???

I'm looking for a term to describe a linguistic
concept having to do with pronunciation.  This is kind
of difficult to explain, so bear ith me while I try to
make my question understandable.

A phonetic alphabet is meant to describe what a
particular sound actually sounds like.  Thus a word
can be transcribed in different ways to represent the
different manners in which it is pronounced in various
dialects or with various foreign accents.  As a
result, someone transcribing their own speech into
some phonetic alphabet could possily transcribe that
word differently from someone else who spoke with a
different dialect or accent.  But what I'm looking for
is a variation on a phonetic alphabet that it
independant of dialect or accent so that even if two
people spoke with different dialects or accents they
would still transcribe the word in the same way.

For example, I might want to say that however YOU
pronounce the vowel sound in "fat", you should
pronounce the vowel sound in my conlang word "glap"
the same way.  Thus different people might pronounce
"fat" in slightly different ways in the absolute
sense, but each would pronounce "glap" in the same way
they pronounce "fat" and so they would all be said to
pronounce "glap" the same way in the _relative_ sense.

Thus the symbols of this "relative phonetic alphabet"
would not relate to absolute sounds, but to sounds
relative to how you normally pronounce other sounds in
your own dialect or accent.

I'm thinking about alphabets like "Shavian" where I
can read something written by a speaker of British
English and actually "hear" the British accent in what
is written.  What I'm looking for is a way for a
speaker of British English to transcribe a word so
that a speaker of American English or Australian
English would NOT "hear" the accent when he read it.

In other words, some symbol like '#' would NOT
represent some pure definition of a sound, but would
represent, to each individual speaker, a different
sound that was relative to his own native dialect or
accent.  I want to be able to say, in effect, I don't
care how you pronounce "glap" as long as you pronounce
it with the same vowel sound with which YOU pronounce
"fat", even if that's different from the way I
pronounce "fat".  Thus I'd have an alphabet that was
both "phonetic" and dialect-neutral, which can never
be acheived using an alphabet that defines absolute
sounds.  Am I making any sense with this?

--gary

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