Here is a fascinating quote from Fr. Joseph Fessio: http://www.catholiceducation.org/articles/religion/re0540.html
Now, just a little footnote on the Gregorian Chant. In reflecting on these things about Church music, I began to think about the Psalms a few years back. And a very obvious idea suddenly struck me. Why it didn’t come earlier I don’t know, but the fact is that the Psalms are songs. Every one of the 150 Psalms is meant to be sung; and was sung by the Jews. When this thought came to me, I immediately called a friend, a rabbi in San Francisco who runs the Hebrew School, and I asked“Do you sing the Psalms at your synagogue?” “Well, no, we recite them,” he said. “Do you know what they sounded like when they were sung in the Old Testament times and the time of Jesus and the Apostles?” I asked. He said, “No, but why don’t you call this company in Upstate New York. They publish Hebrew music, and they may know.”
So, I called the company and they said, “We don’t know; call 1-800-JUDAISM.” So I did. And I got an information center for Jewish traditions, and they didn’t know either. But they said, “You call this music teacher in Manhattan. He will know.” So, I called this wonderful rabbi in Manhattan and we had a long conversation. At the end, I said, “I want to bring some focus to this, can you give me any idea what it sounded like when Jesus and his Apostles sang the Psalms?” He said, “Of course, Father. It sounded like Gregorian Chant. You got it from us.”
I was amazed. I called Professor William Mahrt, a Professor of Music at Stanford University and a friend. I said, “Bill, is this true?” He said, “Yes. The Psalm tones have their roots in ancient Jewish hymnody and psalmody.” So, you know something? If you sing the Psalms at Mass with the Gregorian tones, you are as close as you can get to praying with Jesus and Mary. They sang the Psalms in tones that have come down to us today in Gregorian Chant.