Bo, I have read a lot of music history, and I have never seen anything definite on tunings as far back as Old Testament times. You are never going to get a good answer on ancient tunings. The best thing for you to do is to find out what tuning(s) the harp maker had in mind. The instrument will sound its best when tuned to resonate within itself. I learned this as a beginning guitarist. In my amateur efforts, I gradually made the strings way too high. When I bought an electronic tuner and brought it down to where it belonged, it was suddenly much louder and warmer in tone. The tuning given above (Eb,D,C,Bb,G#,G,F,Eb,D,C) is merely the E-flat major scale going down. The is a common tuning for lever harps today. Even if you could find some strange tuning from the time of King David (1000 BC) what songs could you play on it? It's disappointing to think of new song you'd like to play, then find that you can't because a note is missing. I think the best thing you could do is to tune it to a major scale which resonates with the instrument. Or it could be a minor scale, depending on what the maker had in mind.
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