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MUSICAL NOTATION
http://en.wikipedia.org/wiki/Numbered_musical_notation

All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

# Numbered musical notation

The numbered musical notation, better known as jianpu (Traditional Chinese: 簡譜, Simplified Chinese: 简谱, pinyin: jiǎnpǔ; literally "simplified notation") in Chinese, is a musical notation system widely used among the Chinese people. Some people call it the numeric notation or numerical notation, but it is not to be confused with the integer notation. It is also known as Ziffersystem, meaning "number system" or "cipher system" in German. It should be noticed that some other unrelated musical notation systems are also called cipher notations.

The same system or very similar systems are used to some extent in some European countries, and are popular in some Asian countries. This article first describes the Chinese jianpu in some detail, then describes its possible variations.

## Numbered notation described

### Musical note

Numbers 1 to 7 represents the musical notes. They always correspond to the diatonic major scale. For example, in the key of C major, their relationship with the notes and the solfege is shown below:

`Note:     C   D   E   F   G   A   BSolfege:  do  re  mi  fa  sol la  tiNotation: 1   2   3   4   5   6   7`

### Octave change

Dots above or below a musical note raise or lower it to other octaves. The number of dots equals the number of octaves. For example, "6" with a dot below is at an octave lower than "6". Musical scales can thus be written like this:

`                                    .major scale:          1 2 3 4 5 6 7 1 natural minor scale:  6 7 1 2 3 4 5 6                      · ·`

### Note length

The plain number represents a quarter note. Underlines shorten it. One underline represents an eighth note, two underlines represent a sixteenth note, and so on. Notice how the underline imitates the number of flags in the standard notation. The underlines may even be joined together like beaming in the standard notation. Dashes after a note lengthen it, each dash by the length of a quarter note.

A dot after the plain or underlined note works increases its length by half, and two dots increases by three-quarter, similar to the standard notation. The rule is different for notes longer than the quarter note. An additional dot after the dashes actually means half the length of a quarter note.

`whole:   1 - - -  dotted whole:   1 - - - - -  double dotted: 1 - - - - - - half:    1 -      dotted half:    1 - -        double dotted: 1 - - · quarter: 1        dotted quarter: 1·           double dotted: 1·· eighth:  1        dotted eighth:  1·           double dotted: 1·· 16th:    1         =`

### Musical rest

The number "0" represents the musical rest. The rules for length is similar to that of the note, except that it is customary to repeat "0" instead of adding dashes for rests longer than a quarter rest. Unlike the standard notation, there is no single symbol for the bar rest. The bar rest of 3/4 time is "| 0 0 0 |" and the bar rest of 4/4 time is "| 0 0 0 0 |".

### Undetermined pitch

The rhythm of percussion instruments of undetermined pitch is usually represented by "X" or "x" using rules similar to that of the musical note. For example, a common clap pattern used in cheers can be written like this:

`4/4                              > >Clap: | X  X  X X X  | X X X X 0 X X ||`

### Bar line

The end of a measure is marked with a vertical line. Two vertical lines represents the double bar line, and usually also the end bar line, though the thin and thick line variation resembling the standard notation is also used. Repeat signs also resemble the standard notation.

### Time signature

The time signature is written as a fraction: 2/4, 3/4, 4/4, 6/8, etc. It is usually placed after the key signature. Change of time signature within the piece of music may be marked in-line or above the line of music.

### Accidentals and key signature

The notation uses a movable Do(1) system. The key signature defines the pitch of "1". So "1=C" means "C major". Minor keys are based on the natural minor or the Aeolian mode, and the key signature defines the pitch of "6". So "6=C" means "C minor". Naturally, the Dorian mode of D should be marked as "2=D". Some people prefer to write "Key: C" or "Key: Cm" instead.

The same accidentals in the standard notation are used, and as in common practice, an accidental is placed before the notes "1 2 3 4 5 6 7" to raise or lower the pitch and placed after the note names "C D E F G A B", which are used for key signature and chord markings in the numbered system.

There is one caution about the use of the accidentals. In the standard notation, the C minor has flats on B, E, and A in the key signature. So when we write the harmonic minor scale, we put a natural before the B♭ for the leading note. In the numbered notation, however, the leading note is always "♯5", because the system itself does not flat the "5" note.

### Tie, slur, and other marks

Ties and slurs are curves resembling that in the standard notation, although they are always written above the music line in numbered notation. Expression marks are written similarly. Special attention has to be paid on the staccato dot since it looks like the octave changer. It is either represented by a bolder dot further away from the music line or by the staccatissimo sign instead, which is an inverted triangle.

### Variations

In some versions of the numbered musical notation, underlines indicating note length are written above the note instead. Ties and slurs may be written below the music line.

In some versions, octave change is represented in a different way. Instead of dots above or below the numbers, a horizontal line is drawn and the number is written on, above, or below the line.

## History and Usage

The invention of the system is usually attributed to Jean-Jacques Rousseau in his work presented to the French Academy of Sciences in 1742. However, due to its straightforward correspondence to the standard notation, it is possible that many other claims of independent invention are also true.

Although the system is used to some extent in Germany, France, and Holland, and more by the Mennonites in Russia, it has never become popular in the Western world. See the external links for more information.

The system is very popular among some Asian people. Some Chinese people can sight read jianpu but not the standard notation. Some Chinese hymnals and Cantopop song books are published exclusively in jianpu. Many modern Chinese-English bilingual hymnals add jianpu of the melody above the standard notation, and make use of it in the index for the songs.

An index using the numbered notation allows us to find a song if we remember the tune but not the name. To appreciate that, we can look at an example. A children's song book may have an index like this:

`|1·  1·  |1  23·  |  Row, row, row your boat |1 1 5 5 |6 6 5 - |  Twinkle, twinkle little star |1 2 3 1 |1 2 3 1 |  Frere Jacques`

A reason of its popularity among Chinese is that jianpu fits in with the Chinese music tradition. It is a natural extension and unification of the gongche notation widely used in ancient China for recording music. Gongche uses a number of characters to indicate the musical notes, and jianpu can be seen as using numbers to replace those characters.

Compared to the standard notation, the numbered notation is very compact for just the melody line. It is even possible to transcribe music in between the lines of text. Transcribing harmony can be done by vertically stacking the notes, but the advantage of compactness decreases as the harmony becomes more complex.

## Examples

The two images below illustrate how the same piece of music is written using the standard notation and the numbered notation.

The hymn "Amazing Grace" written in standard notation.
The hymn "Amazing Grace" written in numbered musical notation.

• A page in The Life and Work of Jean-Jacques Rousseau shows his published work.
• Ziffersystem (Numerical Musical Notation) in the Global Anabaptist Mennonite Encyclopedia Online.
• Canaan Hymnal (Simplified Chinese) is an example of a Chinese hymn book written in jianpu.
• Can You Shake It? The Angklung of Southeast Asia has examples of cipher notation used in South Asian music.
• Magith is a shareware to create music using numbered musical notation.
• S-Music Alpha version is a freeware editor for simplified music notation.