I highly recommend the three part series on how to read Dominican chant notation, by Fr. Augustine Thompson at NLM. You can find it here.
He spells out the basic rules on reading. There are a few changes from Solesmes that surprised me -- e.g., the quarter bar is used as the equivalent of the Solesmes dot, and the notes of the clivis are lengthened.
I think most chant historians would agree that the melodic readings in the Dominican books are inferior to those in the Vaticana. I think that if you are going to look beyond the Vaticana, you would do better to look into more recent editions, such as the Graduale novum than to turn to Domincan books.
Dominican books (like the Sarum) don't differntiate quilismas (quilismata?) from other notes.
Choirs that have uses the Vatican edition without the Solesmes rhythmic signs (as well as those that have sung from the Domincan books) have usually lengthened both notes of a clivis before a quarter bar.
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