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In Hanon's The Virtuoso Pianist - exercise 33, there are dotted lines with the numeral 8 above and below joining three measures together - what do they mean?

Hanon exercise 33, m. 12

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Ιt means it's supposed to be played an octave higher than indicated. You may also see this as 8va or 8a and 15ma for two octaves. Respectively, 8vb and 15mb is for 1 and 2 octaves lower than indicated.

People use this when they try to avoid adding many lines above the existing ones.

You can also see it on Wikipedia.

8va means all' ottava = at the octave.

Moreover, on some sheets you might see that after the 8va they write loco which means you are supposed to play it at the octave written.

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    It is "unconventional" to have two 8va lines on the same staff, but if the notes for both hands are written on the same staff, sometimes it is not obvious exactly what the 8va applies to. But it would be rather perverse to think there was anything ambiguous about the passage the OP is asking about. A simpler unambiguous way to write it would have been to use both staves for the whole exercise, with clef changes as necessary.
    – user19146
    Commented Sep 6, 2015 at 19:07

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