Men should, indeed everyone should, sing Hildegard’s music! You know the old story about St. Gregory receiving the chant propers by divine inspiration? I do believe the propers are a sacramental and are in many ways a miraculous gift, but in Hildegard’s case it was actually true! Here is a quote from her last secretary on how she composed her chants:

For on those rare occasions when she enters the mystery of the Living Light, as she herself tes­tifies, she seems to herself to be completely transformed, as it is written “thy youth shall be renewed like the eagle’s.” [Ps 102:5] And just as she feels herself to be a young girl again, she completely forgets all troubles that have befallen her—infirmity, sadness, pain, and the feebleness of her advanced years—and carried away by the sweetness of the symphonic harmony, a delight inexpressible to her and inconceivable to us (since, although well-known to her, it surpasses our senses), she, mentally, grows quiet and sleeps in peace in that Light, while, physically, she is fully awake. Moreover, returning to ordinary life from the melody of that internal concert, she frequently takes delight in causing those sweet melodies which she learns and remembers in that spiritual harmony to reverberate with the sound of voices, and, remembering God, she makes a feast day from what she remembers of that spiritual music. Furthermore, she composes hymns in praise of God and in honor of the saints, and has those melodies, far more pleasing than ordinary human music, publicly sung in church.

As for the Leonine connection, I can’t think of an exact parallel in Hildegard’s theology, since her emphasis is more on getting away from the affairs of the world, with a heavy focus on the goods of virginity and the religious life. One connection that does occur to me is the central idea of viriditas, a sort of green fruitfulness that characterized humanity before the fall and that is restored in Christ’s incarnation and fulfilled at the end of time. In the religious life, this kind of “productivity” is associated with the Opus Dei of the divine office. Check out the amazing antiphone “o nobilissima viriditas,” which is for virgin saints, and which is also based on the melody of “Ave Regina caelorum.” It speaks of the virgin saints being embraced by the “divinorum ministeriorum,” or something like that. That is at least tangentially connected to the idea of work.

She also frequently refers in various places to Christ’s weariness and sweat; the labor of redemption and that sort of thing.

Attached is my edition (on four lines!) of the ending of Ordo virtutum. It's a spectacular piece and sums up much of H's Christology.

Here it is without that hyphen. It comes from making Gregorio files in a hurry!

The columns are just a regular table made with the tabular environment.

Thank you Charles Weaver. From what source is that quote from Hildegard's secretary?