I recall seeing an italicized 'i' to indicate that the second vowel in Joseph should be pronounced like the weak sound of the second vowel in "tendon," instead of a regular "i" sound. Can you tell me about any incidents of similar phonetic alphabet usage on the weak "i" sound elsewhere?"
IPA [ə], [ɪ], [ɪ̈], [ɨ], or [ᵻ]
If you’re looking for a short answer:
- In American transcriptions, Joseph can be represented as [ˈdʒosəf], or perhaps [ˈdʒozəf] for those who voice the middle consonant.
- It British transcriptions, Joseph might be represented as [ˈdʒəʊsɨf], or perhaps [ˈdʒəʊzɨf] for those who voice the middle consonant.
Whether those two actually represent two distinct pronunciations is debatable, but phonemically they are identical for virtually all native speakers.
It’s very unclear what you mean by your term “weak e”. All unstressed vowels in English are reduced, meaning that they are centralized and shortened, losing the distinctive characteristics that would otherwise let you tell one from the other if they occurred in a stressed syllable.
The IPA symbol most commonly used to represent this vowel is a turned e: [ə], which is a schwa. For example, the unstressed vowel in each of these words is a schwa, no matter their spellings: about, token, habit, lemon, focus.
On occasion other symbols are used for partially reduced vowels, but these vary. For some of these, including in words like system or habit, sometimes the API symbols [ɪ], [ɪ̈], [ɨ], and even the non-standard [ᵻ] are variously used to represent an intermediary state of partial reduction in words like roses as compared with Rosa’s.
Whether that is actually phonemic is a matter of some debate. See Fleming and Johnson in Rosa’s roses: reduced vowels in American English. You might also familiarize yourself with the IPA vowel charge with audio on Wikipedia. The UK sound comparisons site is even more interesting.