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import IPython.display as ipd


# Sheet Music RepresentationsÂ¶

Music can be represented in many different ways. The printed, visual form of a musical work is called a score or sheet music. For example, here is a sheet music excerpt from Mozart Piano Sonata No. 11 K. 331:

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ipd.SVG("https://upload.wikimedia.org/wikipedia/commons/2/27/MozartExcerptK331.svg")

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ipd.YouTubeVideo('dP9KWQ8hAYk')

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Sheet music consists of notes. A note has several properties including pitch, timbre, loudness, and duration.

Pitch (Wikipedia) is a perceptual property that indicates how "high" or "low" a note sounds. Pitch is closely related to the fundamental frequency sounded by the note, although fundamental frequency is a physical property of the sound wave.

An octave (Wikipedia) is an interval between two notes where the higher note is twice the fundamental frequency of the lower note. For example, an A at 440 Hz and an A at 880 Hz are separated by one octave. Here are two Cs separated by one octave:

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A pitch class (Wikipedia) is the set of all notes that are an integer number of octaves apart. For example, the set of all Cs, {..., C1, C2, ...} is one pitch class, and the set of all Ds, {..., D1, D2, ...} is another pitch class. Here is the pitch class for C:

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ipd.Image("https://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pitch_class_on_C.png/187px-Pitch_class_on_C.png")

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Equal temperament (Wikipedia) refers to the standard practice of dividing the octave into 12 uniform scale steps.

The difference between two subsequent scale steps is called a semitone (Wikipedia), the smallest possible interval in the 12-tone equal tempered scale. Musicians may know this as a "half step."

The key signature (Wikipedia) follows the clef on a staff and indicates the key of the piece by the sharps or flats which are present throughout the piece. In the Mozart sonata excerpt above, the key signature is A major.

The time signature (Wikipedia) follows the key signature on the staff and indicates the rhythmic structure, or meter, of the piece. In the Mozart sonata excerpt above, the time signature is 6/8, i.e. six eighth notes in one measure.

Tempo (Wikipedia) denotes how slow or fast a piece is played as measured by beats per minute (BPM). In the Mozart sonata excerpt above, the tempo marking is "Andante grazioso".