Using unusual modes from scales can help produce some interesting melodies. This major #9 #11 melody comes from the 3rd mode of harmonic minor. This mode is a wonderful substitution for Lydian or Ionian. Lydian gives you a Major 7 with #11 where as the 3rd mode of harmonic minor gives you a Major 7 with #9, #11, and natural 9; it’s a very beautiful sound. Here’s a simple melody from this harmonic minor mode that starts with an ascending Major triad in 2nd inversion fallowed by a descending triad a half step below and ending with a diatonic enclosure of the 5th. You’ll see that although the melody is constructed of triads, all the notes are diatonic to the 3rd mode of harmonic minor.
The melody is played 3 times in triplets. Once starting on the first triplet of beat 1, next starting on the 2nd triplet of beat 1 and lastly starting on the 3rd triplet of beat 1. Remember, you can start the melody on any beat.