Those symbols are ledger lines and octave signs.
Ledger Lines
A ledger (or leger) line is a short horizontal line above or below the staff and represents a temporary vertical extension of the staff. Multiple ledger lines are spaced at the same vertical distance apart as the lines on the staff itself.
Ledger lines originated in 16th-century Italian organ music. However, at that time, the extra lines were drawn clear across the page as entirely new staff lines. This practice resulted in bloated, hard-to-read staves of up to 15 lines.
Today a ledger line is just a little longer than the width of a notehead.
Octave Signs
If ledger lines extend too far from the staff or continue too long, they weary the reader. In such cases, the notator should either change clefs or use an octave sign.
An octave sign is any one of many symbols and variant forms indicating an octave displacement. They fit into four basic categories.
(1) 8va. This is an abbreviation of Italian ottava ("octave"). Placed above a staff, it indicates that the notes should be played an octave higher than written.
The sign is placed over the first note in the affected passage and is followed by a broken or dotted line ending with a downstroke after the final note.
Instead of 8va, a simple 8 may be used. Instead of either symbol, any of the following Italian terms may substitute (though they are uncommon nowadays): all' ottava ("at the octave"), ottava alta ("high octave," i.e., "octave higher"), and ottava sopra ("octave above").
This sign should be used only above the treble staff. Problems with excessive ledger lines on bass, tenor, or alto staves should be solved by using a higher clef.
(2) 8va bassa. This is an abbreviation of Italian ottava bassa ("octave below"). It indicates that the notes should be played an octave lower than written.
The sign is placed under the first note in the affected passage and is followed by a broken or dotted line ending with an upstroke after the final note.
Instead of 8va bassa, any of the signs 8va, 8vb, or 8 may be used. Available, though seldom used, is the Italian term ottava sotto ("octave under").
This sign should be used only under the bass staff. Problems with excessive ledger lines on treble, alto, or tenor staves should be solved by using a lower clef.
(3) 15va. This is an abbreviation of Italian quindicesima ("at the 15th"). Placed above a staff, it indicates that the notes should be played two octaves higher than written.
This sign is treated exactly like 8va.
Technically available, though rarely used, is 15va bassa, an indication to play two octaves lower.
(4) Coll' 8va. This is an abbreviation of Italian coll' ottava ("with the octave"). It indicates that the written notes should be duplicated at the octave, either higher or lower depending on its placement.
To indicate duplication at the higher octave, the sign, normally found in the treble staff, is placed over the first note in the affected passage and is followed, to distinguish it from the other octave signs, by a solid line to the end of the passage, marked by a downward jog.
To indicate duplication at the lower octave, the sign, normally found in the bass staff, is placed under the first note in the affected passage and is followed by a solid line to the end of the passage, marked by an upward jog.
Both the over and under versions may use the shortened form coll' 8.
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The New Grove Dictionary of Music and Musicians. 2nd ed. London: Macmillan, 2001.
Published by Darryl Lyman
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