The patron saints of musicians are:
Genesius of Rome
Gregory the Great
Paul the Apostle
The patron saints of teachers are:
Cassian of Imola
Catherine of Alexandria
Francis de Sales
Gregory the Great
John Baptist de La Salle
The patron saints of artists are:
Catherine of Bologna
Luke the Apostle
Michael the Archangel
While the Church has saints for certain causes, one is permitted to pray to any saint for whatever cause, as one feels so inclined. In light of the vocations above, there is one modern saint who would be efficacious in helping for all three - St. Mutien-Marie Wiaux of Malonne (1841-1917, Belgium). To my knowledge he didn't compose any great piece of music, had no natural inclination for teaching at all, and didn't paint any masterpiece frescoes, not having a natural talent for art either. But he nonetheless came to excel in teaching the disciplines of music and art to students - and to become, by persevering, quite competent in both.
He "excelled", in that whatever he did, he made sure to do it well. For Mutien, to do it well was also to do it with unwavering exactitude and discipline. This is how unwavering: late in Mutien's life, a brother once approached one of the senior brothers, Brother Maixentis (these would be the Christian Brothers, or the Lasallian Brothers, formerly known as The Institute of the Brothers of the Christian Schools, the largest Catholic order of religious brothers devoted to educating the young, founded by Saint Jean-Baptiste de la Salle, patron saint of teachers), and asked him about something he observed Brother Mutien doing. He noticed every morning at 9:00 Brother Mutien went to the music room and practiced on the harmonium. After some thought, trying to remember something long in the past, Brother Maixentis suddenly realized that it was fifty years ago, when Mutien began as his assistant, that he had told Mutien to practice his music each morning, and that he had forgotten to rescind this order. Not once over those fifty years did Mutien bring this up to Brother Maixentis; never forgetting to perform his morning practices, never asking to have it rescinded, not even a casual, 'should I continue with the morning practices?'
And this is how Brother Mutien came to win over students, by being the example of what they themselves should be: submitting humbly and steadfastly to a discipline; to give oneself over to it as a means of one's sanctification.
(Forget the clever cold hand of some Picasso; I would love to see the drawings from this brother's earnest and diligent hand.)
He was almost sent away after one year of teaching a classroom of nine-year-olds (his first year of teacher training college) because he was too gentle and not disciplinarian enough; his class was, it seems, a disaster - hence the chapter meeting to decide whether to send him away. He was only able to make his first vows because Brother Maixentis, who taught music and art, asked to have him appointed as his assistant.
It looks as if Brother Mutien did not become any more of a disciplinarian than he was before, but as implied above, won students over by his patience and piety and through applying himself to the disciplines which he taught. He was always praying, was always seen with rosary in hand, often saying Ave Marias. He once said he had asked Our Lady to be always at his side, and that he was in fact aware of her presence.
In a letter he wrote these words, as though straight from the mouth of St. Louis de Montfort:
"If you wish to find a short and easy path to intimate union with Our Lord, go through Mary. The more you love the Most Blessed Virgin, the more you will love her divine Son."
Yes, and do not neglect your small tasks and duties, I seem to hear the humble brother say; because they are claimed for eternity and are of infinite worth.
Biographical information and anecdotes taken from Modern Saints: Their Lives and Faces, Book Two, By Ann Ball