PhD students are trained to research. To find interesting solvable problems in existing knowledge, explore and make some advances. The whole process is very amorphous and self-directed. First, a large amount of time is spent finding a good problem. This is very fortuitous and often happens at a "Eureka" moment. Over time, the PhD student develops the ability to seek out interesting problems that are solvable. This is similar to a musician picking a piece that interests him/her and is within the reach of his/her technical ability.
After finding a problem, you are required to analyze it into smaller projects that can be tackled. It also involves a certain about "diagnostics" in the implementation phase, to figure out what stage of your solution has broken down. A violinist must also analyze his/her target piece. Usually there would be two phases, a technical analysis and a musical analysis. In the technical analysis, one must discover trouble spots and usually design efficient and clever "mini-etudes(studies)" to overcome such difficulty. These difficulties can include
- Left-hand: lack of finger pressure, side of fingers touching nearby strings, lack of finger dexterity (especially on the fourth finger), dreaded intonation (especially on double stops), getting a nice wide vibrato (difficult on double stops)
- Right-hand: awkward string crossing, spiccato, upbow staccato, fast whole bow strokes. Overly noticeable bow changes.
After technical analysis, the musician has to think about phrasing, composition background, balance, dynamics etc.
On the whole, my playing is more rigorous and I have gotten better at figuring out how to practice for a difficult piece. (Waxmen Carmen fantasy and Devil's Trill right now)