Piano theory about musical abbreviations

Abbreviations are a means of writing musical passages and notes in a curtailed form. There is a great variety of abbreviations, a few of which we will explain. The following
musical abbreviations
is played in this manner:
eight abbreviations
The stroke across the stem of the half note and the chord, means that both are to be played as eighth notes; inasmuch as 4-8 make a 1-2, each is to be repeated four times. Notes of smaller value, if abbreviated, are written thus :
piano abbreviations on staff
and are played in this wise :
Notes written like these
are played thus
Octaves and chords when written in this manner:
are played as follows:
musical abbreviations on staff

Tremolo abbreviations for pianists

Often the word tremolo is added. This term means that octaves or chords are to be played in a trembling or tremulous manner, as fast as possible. This explains the above abbreviation.
Notes with dots over or under them
are to be played thus
or if written in this manner
they should be played as triplets, namely thus:
Chords or notes with a 6 over or under them should be repeated six times. This
is to be played thus:

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Other piano music abbreviations

The following abbreviation sometimes occurs:
which is to be played in this wise
The following sign means that the passage or group of notes that preceded it should be repeated.
is to be played in this manner