There are many ways to transcribe English into phonemic transcriptions and, because there are various schools of thought and traditions, not all linguists agree on how it should be done. (At times, it may even feel as if there are as many conventions as there as dictionaries!)

As mentioned, the goal of this chart is to teach the sounds of American English. To do a good job of it, I had to decide what to focus on and just what to include.

Here are some of the decisions that went into the making of this chart:

/ʌ/ vs. /ə/

You will not find /ʌ/ (as in “dust” /dʌst/ or “STRUT” /stɹʌt/) in this chart. This may be the most controversial choice for some teachers, who have long been taught that “a schwa can never be stressed.”

My point of view is that, from an American perspective, /ʌ/ can be construed as a mere /ˈə/, i.e.: a stressed schwa:

• This is consistent with how a dictionary such as CMU (and its 100K+ entries) handles it, or how the Kindle's dictionary (The New Oxford American Dictionary) does it (e.g.: “someone” = /ˈsəmˌwən/) or how Dictionary.com handles their transcriptions too. In the end, this seems to agree with how many Americans perceive the sound.
• At the end of the day, the question was: what makes things simple to teach, but no simpler than they should be? And the only argument for keeping in /ʌ/ was tradition; it made no sense to keep it and I decided not to include it.
• Compare the sounds found in those words: "someone", "awesome". Should we have three phonemes just because we have three levels of stress? This makes no sense. Transcribing those words /ˈsəmˌwən/ and /ˈɔ·səm/ works fine and no phonological information is lost.
• If you'd like to contribute to the debate, please see this discussion: American English : are [ə] and [ʌ] different phonemes?.

As a teacher, you may want to teach the symbol anyway. As a learner, you may still want to know it exists and is pronounced as a stressed /ə/, i.e.: with more intensity and energy, longer.

/ɹ/ vs. /r/

This chart uses the proper /ɹ/ symbol for the (prevocalic) R sound. Many dictionaries simplify it as /r/ because it's easier to type.

/ɝ/ (vs. /ɚ/)

This chart uses /ɝ/ (as in “purple” /ˈpɝpəl/ or “NURSE” /nɝs/) for the R-colored vowel.

Some dictionaries may detail further, using this symbol in the middle of a word, but /ɚ/ at the end of a word (e.g.: “brother”). On the other hand, other dictionaries may simplify /ɝ/ as /ɜr/, or /ɚ/ as /ər/.