General Terms:
* Learned by ear: This is the most straightforward and accurate description.
* Memorized arrangement: This emphasizes the act of memorizing the arrangement, but doesn't specify the learning process.
* Improvised arrangement: This term is used when the musician creates the arrangement on the spot, which often involves learning by ear.
* Intuitive arrangement: This implies a more organic and natural approach to arranging, often based on listening and understanding rather than strict notation.
More Specific Terms:
* Aural arrangement: This emphasizes the use of hearing in the learning process.
* Transcription: This term is typically used when someone writes down a piece of music that they have learned by ear.
* Ear training: This is a general term for developing the ability to learn music by ear.
The best term to use will depend on the specific situation and the level of detail you want to convey.