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My copy of Leonard Cohen's Hallelujah includes the following measures:

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I don't know how to play the left hand. My problem is that I cannot reach from F2 to A3 (in the first bar, others correspondingly). My right hand is busy and far away, so I can't use that either.

The answer to similar questions regarding large chords is usually to arpeggiate them, but I'm not sure whether this applies (and how) in my situation where the wide range is in the melody rather than in the harmony.

Currently I'm playing it as if the F2 was only a dotted quarter, with the fingering 5, 2, 1, 2, 1, 2.

10

This is a case where use of the pedal is needed. You use the pedal to hold the bass note and you change it when the bass is changing. In this excerpt at the beginning of every measure.

2

As Tim H says, the pedal will come to your aid. Here, it works well, as the harmony stays the same for each bar, which is why the one bass note can last the bar too. If there were chord changes within the bar, but the bass note stayed long, it would be problematic.

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