We don't have synonyms for major thirds yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are major third and minor thirds.
(n) :
(music) A musical interval in Western music that is equal to or approximates a frequency ratio of 5/4. In twelve-tone equal temperament, it consists of four standard semitones, spans three degrees of the diatonic scale, and is enharmonically equivalent to a diminished fourth. Major scales are so named because of the major third interval between the tonic and mediant of a major tonic triad.
(n) :
(music) A musical interval in Western music that is equal to or approximates a frequency ratio of 5/4. In twelve-tone equal temperament, it consists of four standard semitones, spans three degrees of the diatonic scale, and is enharmonically equivalent to a diminished fourth. Major scales are so named because of the major third interval between the tonic and mediant of a major tonic triad.