The North Germanic dialects can, in one very special sense, be divided into two groups: (1) "broad" dialects, and (2) "narrow" dialects. The broad dialects are in majority. So, in what sense are the dialects "broad" and "narrow"? With a dialect being "broad" we mean specifically that Old Norse short i [i]/[ɪ] and short y [y]/[ʏ] in front of a short (or none) consonant have become openened to something like [e] and [ø] (not bothering about length here), respectively.
One example of a "broad" dialect is (the by icelanders mocked into near-extinction) northern Icelandic where e.g. skip 'ship' is pronounced something like [sceːb̥] instead of standard Icelandic [scɪːp]. Standard Swedish is yet another "broad" dialect, in this case one has skepp [ɧɛpː]. (A quality [ɛ] instead of [e] since the vowel has become short.)
Jamtlandic is, just like the two examples above, a "broad" dialect. The sample word would be pronounced [ʂepː] in the most genuine form of the dialect.
The immediate question arises: How should we spell a broadened i? I think the key observation that the northern Icelandic dialect, though being "broad" like Jamtlandic, has the rule that the orthography's i is actually pronounced [e]. This could definitely be used in Jamtlandic too. The phoneme [i] in Jamtlandic can be spelled í, i.e., just like the ON etymology. The letter e should be used for the [ɛ] sound, etymologically from ON e. Needless to say, since y is just a rounded i, we employ the same rule for y, i.e., it's pronounced [ø].
To conclude, when in front of a single or
none consonant, the letters i and y denote
the phonemes [e] and [ø], respectively.
As an example for i, we already have skip [ʂepː] 'ship'. For y, take e.g. kyn [tʃøːn] 'gender'.