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I'm looking at the Arpabet page on Wikipedia, and note some entries like this:

Arpabet | IPA | Word Examples
  ER    |  ɝ  | her (HH ER0); bird (B ER1 D); hurt (HH ER1 T), nurse (N ER1 S)

Now, I'm trying to convert this Arpabet "ER" into X-SAMPA. But, I don't see ɝ anywhere in the X-SAMPA specification. Instead, my reading leads me to see that character ɝ (and some others, like ɚ) are "R-colored vowels", which I think means they can be decomposed into two separate characters instead of written in one digraph character.

My question, in short, is: are these equivalent?

ɝ => ɜr
ɚ => ər
ɑ˞ => ɑr
ɔ˞ => ɔr
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That isn't the claim behind the rhotic-hook diacritic. It means that the vowel has the characteristics of the main vowel symbol, but with some kind of r-like raising of the tongue during its production. The sequence [ɑr] means "low back vowel followed by alveolar trill". Apart from the difference in timing (simultaneous vs. sequence) there is a substantial difference in the nature of the r-ishness. If you use the sequences [ɑɹ] etc, they would be more similar (r-coloring is superimposition of "ɹ" quality, not "r"). What might confuse matters is that in English, so-called r-colored vowels are derivable from a sequence of vowel plus consonant ɹ.

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    Ah ok, I see. There is no "decomposition", because these are not "composed" of two characters to begin with. Adding ˞ only modifies the vowel, it does not indicate a second character. And as you mention some languages may not distinguish (as in English, ɝ and ɜɹ would be allophones). BTW, the X-SAMPA page does mention how to make these ligatures: it's the backtick (`), as in "3`" or "@`". I just didn't look hard enough : ) – Greg Kennedy Mar 17 '16 at 5:50

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