In this article, we read a brief biography of her, whom many faithful Catholics look to, in anticipation of that blessed renewal of traditional music.
As the father of Gregorian chant, Pope St. Gregory the Great was the obvious candidate for patron of singers and musicians. His position went unchallenged for 700 years until the proliferation of pipe organs in churches and a misreading of a line in the Divine Office pushed Gregory into the background and advanced St. Cecilia (3rd century; feast day November 22) as the patron of all things musical.St. Cecilia, pray for us.
[via Catholic Exchange]

Although I was quite sure that the antiphon did not refer to pipe organs, I was surprised by this translation; I had thought that "cantantibus organis" referred to her internal harmony, sort of a microcosmic harmony of the spheres but still accompanying the melody of her heart. Unfortunately, I cannot find the context to this antiphon to the first reading of the first vigil of matins, and that is what the whole interpretation of the first two words depends on.
R. Cantantibus organis, Caecilia virgo in corde suo soli Domino decantabat dicens: Fiat, Domine, cor meum et corpus meum immaculatum, ut non confundar.
V. Biduanis et triduanis jejuniis orans, commendabat Domino quod timebat.
Fiat.
Here are a couple interesting excerpts from the reading for the modern Office of Readings (matins)-- which no longer has the above antiphon; Saint Augustine on Psalm 32:
"Cantate ei canticum novum." ... Cantet canticum novum, non lingua, sed vita.
"Cantate ei canticum novum, bene cantate ei." ... Canta illi, sed noli male. Non vult offendi aures suas. Bene cantate, fratres.
The latter would make a nice inscription for the choir loft!
Erm, "patroness" or "patron saint," I believe.
Sancta Caecilia, o.p.n.