The only way to generate Great Musician's is building the musician's guild and setting specialists to work on it. There are however, several ways to speed up that process.
NOTE: You must have the specialists working the musician's guild for the +% Great Person bonuses to actually affect the generation of Great Musicians from the guild. If you don't have the specialists working the guild, you will always have 0 generation no matter how many of the following bonuses you have. Though the instant ways to get Great People will still, of course, work.
As for a leader Suggestion I went with Pedro II of Brazil for the 50% Great Musician/Writer/Artist boost during golden ages.
Faster Great Person generation
Aesthetics (Social Policy Tree)
- Adopting this policy tree increases Great Musician/Writer/Artist generation by +25%
Arts Funding (World Congress Resolution)
- +33% generation of Great Artists/Musicians/Writers, at the cost of -33% generation of the other Great People.
Avant Garde (Freedom Level 1 Ideological Tenet)
- +25% Great Person Generation in All Cities.
Garden (Building)
- Requires Theology, City next to River or Lake
- +25% Great People Generation in this City.
- The Hanging Gardens Wonder (requires Tradition, Mathematics) provides a free Garden.
Hero of the People (Order Level 1 Ideological Tenet)
- +25% Great Person Generation in All Cities.
Leaning Tower of Pisa (World Wonder)
- Requires Printing Press
- +25% Great People Generation in all Cities
Liberty (Social Policy Tree)
- Getting all 5 Policies in Liberty will let you choose a Free Great Person.
National Epic (National Wonder)
- Requires Drama & Poetry, Monument in All Cities.
- +25% Great people Generation in this City.
Instant Great Persons/Musicians
Aesthetics (Social Policy Tree)
- Adopting all policies in this tree allows you to buy Great Musician/Writer/Artists with faith beginning in the Industrial Era.
Broadway (World Wonder)
- Requires Radio
- Grants 1 free Great Musician in the city this wonder is built in.
Leaning Tower of Pisa (World Wonder)
- Requires Printing Press.
- 1 Free Great Person of your Choice.
Patronage (Social Policy Tree)
- Finishing the Patronage Social Tree will result in City-States occasionally gifting you Great People. Not as reliable, but is an option.
To the Glory of God (Reformation Belief)
- Taking this reformation belief allows you to purchase any Great Person with Faith beginning in the Industrial Era.