As an intermediate English learner, when I talk to my American friends, sometimes they will misunderstand my [ɛ] and [e] sounds. For example, measure mistaken for major, pepper for paper, and for end ... etc.
What can I do to ensure that [ɛ] and [e] are easily differentiable?
The first thing to note is that the words major, paper, hate, mate have what is called a 'diphthong' in standard varieties of English. A vowel can be either a monopthong or a diphthong. A monopthong is a vowel sound in which the speech organs (hereafter articulators) remain more or less in the same position throughout the articulation of the vowel. That is, the vowel quality remains constant.
A 'diphthong', however, involves a change in the position of the tongue, thereby changing the vowel quality. The articulators glide from one vowel position to another.
Paper, major, mate have the diphthong /eɪ/ whereas pepper, measure, met have the monopthong /ɛ/ (sometimes transcribed /e/ for convenience). The [e] in some of the words you mentioned is a part of the diphthong /eɪ/.
Also note that /phonemes/ can be [realised in more than one way].
So when pronouncing measure, bed, pepper etc., make sure your tongue remains in the same position throughout the vowel sound. In some American accents, major, mate, paper have the long monopthong [e]. The main difference between [ɛ] and [e] is vowel openness; [ɛ] is more open than [e].
If you understand IPA, here are the transcriptions of 'day' (/eɪ/) in different American accents:
[All these transcriptions are from Sound Comparisons]
I think this is a good audio example:
Paper: http://www.howjsay.com/index.php?word=paper
vs.
Pepper: http://www.howjsay.com/index.php?word=pepper&submit=Submit
A tip would probably be easier to provide if we knew what your mother tongue is.
Like Damkerng T. says, the American English [e] is actually more-or-less a [ei] or [ɛi] diphthong. So, for practice sake, try wedging in an explicit [i] (as in the word "bee") after the [e] and smooshing it into it. That is, try pronouncing "paper" as [pɛi-pɛr] and major as [mɛi-jɛr]. You might start by making it three syllables [pɛ-i-pɛr], and then try running them together.
My mother language is Chinese.
According to the Chinese vowel diagram on Wikipedia, Mandarin Chinese includes the vowels:
(Disclaimer: I don't speak Chinese, and can't vouch for the accuracy of the above.)
