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I think it is possible to sustain lasting interest with only a few chords and singing BUT most often it requires a more comprehensive approach.

Chalmers Doane1)

The authors contend that the seminal starting point is melody and, moreover, that an initial focus on melodic techniques greatly facilitates student development in all areas of musicianship. It should be noted that an emphasis on single-note picking may also serve to broaden students' experience of harmony. …
Instead of constantly learning new chords, students are taught to use familiar chords in many different ways.

James Hill, Chalmers Doane2)


1)
President's Message“. In: Ukulele Yes! 2:1 (1977), 1
2)
Ukukele in the Classroom. Teacher Edition, t. 1. Chrystal Lake Media 2009, vii, viii