I was recently working with an ESL student from India on pronunciation. When I asked him if there was a song he might like to sing to practice American English pronunciation and accent, he said "Bobby Gill." Or at least that's what I thought he said. But he was saying "Barbie Girl." I misunderstood because of the lack of the American "r" sound.
In British English they also don't have a strong 'r' sound: when Brits say "Barbie" it sounds more like "Bobby" in American English, although the vowel might be longer (in the British word). However, if an American "hot" sounds close to British "heart", the British "hot" is not the same as the American: when Brits say "hot" the corners of the mouth come closer together; when Americans say "hot" the corners of the mouth are completely relaxed and passive and the jaw may be more dropped.
As far as "girl", Brits don't pronounce the 'r' sound, but the vowel of 'girl' would not come out 'gill': it would be somewhere between American 'gill' and 'gull'. These differences inspired me to come up with a list of words that use these different vowel sounds. Please say them out loud to practice your American 'r' sounds :) You can also use it to practice vocabulary; note: some words have more than one meaning.
Compare the vowel sounds in the two columns (if more than 1 syllable, refers to part in bold). The words in the left column have the vowel sound ɑ in IPA - the international phonetic alphabet. The vowel in the right column is the dipthong ɑɚ in IPA (there should be a ˘ above the ɚ - couldn't find that font...)
Note that many different letter combinations may form the same vowel sound.
hot heart
cop carp
ought art
lock lark
tot, taught tart
God, god garden
yon yarn
con carnivore, Carnegie
pawn Parnassus
fawn farm
bonfire barn, barnacle
bod bard
loss larceny
toss tarnish
gosh garnish
bought barter, bar
jot, john jar
knock narc(otics agent)
bock, balk bark
box barks
shock shark
stalk, stock stark
mock mark, Mark/Marc (name)
pock park
pom-pom parmesan
dock dark
clock Clark (name)
sock sarcasm
hawk hark, hearken
ox arks, arcs
bob barb
top tarp
posh partial
pall, Paul, Polly parlor, parlay
pot part
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Note that the vowel sound in gill is a pure vowel (only one sound), represented in IPA as ɪ; the vowel in girl is also represented as the pure vowel ɝ in IPA. I tried to use all words that end in 'l' for similarity. At first I thought it was a dipthong, but it's not; I was just getting confused by the 'l' sound...
gill girl
pill pearl, purl, plural
bill burl
mill Merle (name)
twill twirl
will whirl
kill curl
nil neurological
hill hurl
ill earl
fill unfurl
This is still a work in progress!...
Stay tuned for technical tips on how to pronounce the "r" sound.