This is my proposal for a writing system for Sajem Tan using the Greek script. The sound values are based on various pronunciations of Greek used throughout the ages. In the headings, the phoneme will be first, and then the Greek grapheme.

/d/ <δ>

I chose the letter <δ> based on the reconstructed and Erasmian pronunciations as /d/.

/g/ <γ>

Chosen based on the reconstructed and Erasmian pronunciations.

/x/ <χ>

Chosen based on Erasmian and Modern pronunciation.

/j/ <γι>

Chosen based on Modern pronunciation. The letter <ι> is not used alone, so this digraph isn't going to cause any confusion. <Ι> is an element in digraphs much like <l> is in the Old Orthography of the Latin orthography. It marks palatalization in consonants, and fronting and/or raising in vowels.

/f/ <φ>

Chosen based on Erasmian and Modern pronunciation.

/v/ <β>

Chosen based on Modern pronunciation.

/θ/ <θ>

Chosen based on Erasmian and Modern pronunciation.

/s/ <σ>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

/z/ <ζ>

Chosen based on Modern pronunciation.

/ʃ/ <σι>

Chosen based on <γι> above.

/ʒ/ <ζι>

Chosen based on <γι> above.

/ɬ/ <λ>

Chosen based on Reformed Latin Orthography's <l>.

/ɮ/ <ρ>

Chosen based on Reformed Latin Orthography's <r>.

/m/ <μ>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

/n/ <ν>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

/æ/ <αι>

Somewhere between /ai/ and /ɛ/, the Greek digraph <αι> may have been pronounced as /æ/.

/œ/ <ευ>

Chosen based on Erasmian pronunciation.

/e/ <η>

Chosen based on reconstructed and Erasmian pronunciation.

/ø/ <οι>

Chosen based on reconstructed pronunciation.

/i/ <ει>

Chosen based on reconstructed and Modern pronunciation. <Ι> could not be used because it is used for digraphs.

/y/ <υι>

Matches reconstructed pronunciation. This digraph represents a fronted and raised /ʊ/. <Υ>, in digraphs, represents rounding and sometimes heightening, but since /y/ never comes after a vowel in Sajem Tan, there should be no confusion.

/ʌ/ <ο>

Based on the Bactrian pronunciation as /ə/. It is also an unrounded /ɔ/, and /ɔ/ is the Erasmian pronunciation of the letter <ο>.

/ʊ/ <υ>

I've seen /ʊ/ suggested as a pronunciation of <υ> in my New Testament Greek book, likely because English speakers often have trouble pronouncing /y/.

/t͡s/ <ξ>

I repurposed <ξ> (pronounced /ks/ in reconstructed, Erasmian, and Modern pronunciation of Greek), because it was the closest thing to /t͡s/ available in the Greek alphabet that isn't a rare letter that is hard to type. I'm also thinking of doing this with my Hellenic conlang.

/t/ <τ>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

/k/ <κ>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

/ɑ/ <α>

Chosen based on reconstructed, Erasmian, and Modern pronunciation, which is /a/.

/ɛ/ <ε>

Chosen based on reconstructed and Erasmian pronunciation.

/o/ <ω>

Chosen based on reconstructed, Erasmian, and Modern pronunciation. The use of <η> for /e/, <ε> for /ɛ/, <ω> for /o/, and <ο> for /ʌ/ strikes me as nice and symmetrical. I couldn't use <ο>, since it was better for /ʌ/.

/u/ <ου>

Chosen based on reconstructed, Erasmian, and Modern pronunciation.

Examples