It's called a "rising tone" chant, and it does NOT require a start in basso-profundo and an end in soprano territory. The chanter needs to have a reasonable vocal range, and, most importantly, must make himself familiar with the epistle he is to read, annotate (literally or mentally) where each rise will occur, and how many rises, and ensure that he does not run out of vocal range. The rises must be in no greater than quarter tone intervals.
It is also essential that the reader remains dispassionate in his delivery, allowing the words to speak for themselves. He must not turn it into a grand performance, and must never use an operatic style.
Baritones who can drop into bass range and rise towards second tenor range are generally best for the rising tone technique. Most true tenors sound ghastly if they start too low, and most true bases struggle with the higher notes. Falsetto must be avoided at all costs!
The local Russian church in the city where I live is blessed with an epistle reader of more than 30 years' experience, who has a rich and mellow voice, and who uses the rising tone routinely and beautifully. It is a joy to listen to him.