This tip deals with the word-initial sequence <peri>.
For the word period and its derivatives, such as periodic, periodicity and the like the vowel in the first syllable is ɪə.
The list below contains examples of words where the main stress falls on the first syllable of the prefix, so the pronunciation is ˈperi
pericarp peridot perigee periscope periwig periwinkle
The next list shows examples of words where the first syllable bears a secondary stress — ˌperi
pericardium perihelion peripatetic periphrastic peristalsis peritonitis
Finally, here are some words where it is the second syllable of the word which bears the main stress and the pronunciation is pəˈrɪ
perimeter peripheral periphery periphrasis
Thanks to Petr Rösel and Hyacinth Bucket for an addition.