Is there an equivalent to cantillation or tajweed in Christianity? In both Islam and Hebrew, the respective holy books have rules for pronunciation and recitation so that they can be sung. 


  Cantillation is the ritual chanting of readings from the Hebrew Bible in synagogue services. The chants are written and notated in accordance with the special signs or marks printed in the Masoretic text of the Hebrew Bible (or Tanakh) to complement the letters and vowel points.
  
  These marks are known in English as accents, notes or trope symbols, and in Hebrew as טעמי המקרא taamei ha-mikra or just טעמים teamim. Some of these signs were also sometimes used in medieval manuscripts of the Mishnah. The musical motifs associated with the signs are known in Hebrew as niggun or neginot (not to be confused with Hasidic nigun) and in Yiddish as טראָפ trop: the word trope is sometimes used in English with the same meaning. Cantillation (Wikipedia) 
  
  Tajweed sometimes rendered as tajwid, refers to the rules governing pronunciation during recitation of the Quran. The term is derived from the triliteral root j-w-d meaning "to make well, make better, improve". Tajweed is a mustahab (preferred, but not an obligation) when reciting the Quran to the best of one's ability. Tajwid (Wikipedia)


Examples of cantillation: 


  Haftorah Audio - B'reisheet
  
  Torah Lessons (2015)


Examples of tawjeed (al-Fatihah):


  Al-Fatihah (TvQuran) 


Has there been any attempt to do so with any Christian Bible?
There are indeed methods for singing / chanting the scriptures. Here is some explanation &amp; teaching of the (Catholic) mechanics.

Some lovely Catholic examples:

Latin

Greek

Arabic

English

Some lovely Orthodox examples:

English

English

Russian (Gospel at about 51:00)

Ge'ez