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This question already has an answer here:

What is the meaning of those lines: enter image description here

marked as duplicate by Dave, Richard, Doktor Mayhem Apr 1 '17 at 11:25

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It's actually very simple: it means that the right hand (which was originally playing in the top-most clef) is to play the half note pointed to in the lower clef.

So basically, you are supposed to play the chords in both your hands, then your left hand jumps down to play the octave on the D, and the right hand goes down to play the D below middle C.

The line that goes back up shows that the right hand moves back up into the higher clef to play the chord in the next measure.

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    How is an indication of a glissando different? – Neil Meyer Mar 31 '17 at 12:04
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    @NeilMeyer, a glissando is a wavy line. – anonymous2 Mar 31 '17 at 12:05
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    A glissando line isn't necessarily wavy, but it doesn't make much sense to write a gliss starting on a 4-note chord and ending on a single note. (Is the single note supposed to be the top note or the bottom one?) Actually, writing a gliss on a 4-note chord doesn't make much sense for piano, period, though it might make more sense on an "unweighted" organ keyboard. – user19146 Mar 31 '17 at 13:10
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    What's the point of using the line to denote the hand movement when it is already implied by the left hand notes having upsidedown stems? – EvSunWoodard Mar 31 '17 at 14:26
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    @EvSunWoodard Because there are big jumps here, the lines might be there to emphasize this (useful when sight-reading). In other cases, these lines might also be used to emphasize a melody line that goes from one hand (/staff) to another. – Karlo Mar 31 '17 at 14:43
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Perhaps this is a comment and not an answer.

In music scored for the Barbershop style, such a diagonal line indicates that the melody is passing from one part to another. Reasoning by similarity, the diagonal line may indicate that the melodic line moves in an unexpected way, which could alter the interpretation.

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