The minor harmonic scale is a minor scale with a seventh major, and an interval of one and a half tones between the minor sixth and the major seventh. Instead of the Bb as the seventh, here we raise it to a B. This gives it the very recognizable sound of “middle eastern” music. In fact, this scale was once known as the Mohammedan scale.
You'll find below the 5 different positions/shapes of the C Harmonic minor Uke scale in Slack-key Tuning (gCEG), along with their ascending tab patterns.
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