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and
Midi File by:
Maria Dumitru
 
Carnival, by Robert Schumann

From Math to Music

By Maria Dumitru
"Duiliu Zamfirescu" School
Focsani, Romania
 

Musical notation is a form of communication of musical events. The three basic attributes of a typical note are pitch, duration and location in time.

The pitch of a note is represented by its vertical position on the five-line staff. All pitches in music correspond to letter names A through G, with optional flat or sharp assignments. Two notes can have the same letter name, but be different pitches. For instance, if one note is an A -with a frequency vibration of 440 Hz- and a second note is also an A -with a frequency of 880 Hz, the pitches are an octave apart. A grouping of successive pitches that span an octave is called a scale.

The World of Music
There are several clefs in use today. The most common are the treble clef and bass clef. The reason several clefs are necessary is because there is such a wide range of pitches produced by musical instruments. A standard piano keyboard has 88 keys, but a staff can only comfortably contain about 15 different pitches. Music for keyboards is commonly divided into two staves, treble and bass clefs, divided at Middle C.

Standard music has twelve notes, from which we derive twelve keys. Each key gets its name from its starting or tonic note. For keys with sharps or flats, a key signature showing these sharps or flats in their proper order and position on the staff appears after the clef. Any affected pitches are played either sharp or flat for the duration of the song, unless indicated by a natural sign. Sharps and flats never appear in the same key signature.

Each key signature relates to two keys, one major and one minor. For example, the key signature is the same for C major and A minor.

Its particular shape in notation represents the duration of a note. A whole note is a hollow circle, a half note is a hollow circle with a stem, a quarter note is a filled circle with a stem, an eighth note is a filled circle that has a flag on its stem, and so on.
A whole note = 2 half notes = 4 quarter notes = 8 eighth notes etc.

A dot placed after a note increases its duration by one-half. For instance, placing a dot after a half note, equal to two beats increases its duration to three beats.

A tie placed between two notes of identical pitch adds the value of the second note to the first note. The bar line conveniently divides a piece of music into manageable areas, called measures. It is simply a vertical bar that intersects the staff at regular intervals, specified by the time signature. Measures do not affect the way the music sounds, but act as markers to help you keep track of your location in the music.

The time signature seen most frequently is 4/4, also known as Common time. Also seen frequently is 3/4, or waltz time. More unusual meters such as 5/4 and 12/8 are found in jazz and progressive music. Common meters are found in popular styles because they are more accessible, due to their greater predictability.

Time signatures consist of two numbers, written like a fraction. The top number indicates the number of beats in a measure. The bottom number indicates the duration of one beat. For instance, in 3/4 time there are three beats to a measure, and each beat is equal to a quarter note. In 5/8 time there are 5 beats to a measure, and each beat is equal to an eighth note.

Fractals Challenge
Statistics as Mathematical Attribute of Our Lives