Numbered musical notation

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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.

Contents

[edit] Numbered notation described

[edit] Musical note

Numbers 1 to 7 represent 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   B
Solfege:  do  re  mi  fa  sol la  ti
Notation: 1   2   3   4   5   6   7

In printed Traditional Chinese music books, the numbers are usually printed in a very bold font.

[edit] Octaves

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
                      · ·

Where there is more than one dot above or below the number, the dots are placed vertically on top of each other.

Where there are note length lines (see below) underneath the numbers, any dots are placed below the lines. Thus the dots below numbers do not always vertically align with each other, since some of them may be moved slightly downward so as not to collide with the note length lines.

[edit] Chords

Chords can be transcribed by vertically stacking the notes, with the lowest note at the bottom as with Western notation. Each note has its own octave dots, but only the lowest note has the length lines (next section).

Arpeggiated chords are notated by writing the standard Western arpeggiation symbol to the left of the chord.

[edit] 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 are frequently 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
         =

[edit] 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 |".

[edit] 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 ||

[edit] Bar lines

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.

When several lines of music are notated together to be sung or played in harmony, the bar lines usually extend through all the parts, except they do not cut across the lyrics if these are printed between the upper and lower parts. However, when notating music for a two-handed instrument (such as the Guzheng), it is common for the bar lines of each hand to be drawn separately, but a score bracket to be drawn on the left of the page to "bind" the two hands together. This bracket is not the same as the bracket used on a Western piano staff; it's more like the bracket used to bind an orchestral section together in Western music. Sometimes the final double barline, and any barlines marked with repeat signs, also pass through both hands, but this is not consistent even in the same publication (see for example Xinbian Guzheng Jiaocheng ISBN 7-5359-2188-4 pages 108 and 138, where they do and do not pass through both hands respectively).

If a piece of music for a two-handed instrument has a passage where only one hand is notated, lines of numbered notation without score brackets at the left can be used for this passage. Hence a piece of music may shift between two-handed (with bracket) and one-handed (without bracket) layouts during the course of the piece.

Cadenza-like passages can have dotted barlines, or barlines can be omitted altogether.

Repeat signs also resemble the standard notation. First and second time bars can be used; these are printed above the music in a way that resembles standard notation, but the font is much smaller (it is usually a little less than half the size of the font used to print the numbers of the notation itself).

It is possible to print a small fermata above a bar line; this represents a brief pause between the measures either side of the barline, as in Western notation.

[edit] 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. Some pieces that start with cadenza passages are not marked with time signatures until the end of that passage, even if the passage uses dotted barlines (in which case 4/4 time is usually implied).

Sometimes a piece is written with multiple time signatures simultaneously. For example it might specify 4/4 2/4 3/4 5/4, meaning that the length of measures is irregular and can be 4, 2, 3 or 5 quarter-notes. The time signature of the first measure is always specified first, and the others are placed in increasing order of length.

Usually, the time signature is formatted as two numbers placed vertically on top of each other, with a horizontal line separating them. This is slightly different from the formatting illustrated in the text above, due to technical restrictions.

A metronome mark may be placed immediately after the time signature if the time signature is part-way through the music, or below it if the time signature is at the beginning. If present, this will be identical to the metronome marks used in Western music (this is the only place in numbered notation where Western symbols for note values such as quarter-notes and eighth-notes are used).

[edit] 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.

[edit] Ties, slurs and tuplets

Ties and slurs are curves resembling that in the standard notation, although they are always written above the music line in numbered notation. Ties are much flatter than slurs; usually only the ends of a tie are curved, whereas slurs are curved throughout. Chinese music books often draw ties and slurs with a single thin line, in contrast with the Western practice of making the line thicker in the middle.

In music for two hands, it is possible to write a slur that begins in one hand and ends in the other; this is usually done when the first hand has nothing more to play in that measure and hence there is room to draw the slur in the space which would normally have been used to draw further notes. This is similar to some Western keyboard music where slurs between the staves are possible.

A slur with a small arrowhead on its right-hand end indicates a pitch bend between the notes under the slur, which is possible on some instruments.

Tuplets (such as triplets, quintuplets, etc) are notated by writing a slur-like symbol over the notes and printing a small digit (3 or 5 or whatever is appropriate) in the center of this symbol, so that the line passes through the digit.

[edit] Expression marks and dynamics

Expression marks (including fermatas) are also written above the music line. 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.

Dynamics (p, f, mf, etc) and hairline crescendos and diminuendos are written below the line of music to which they apply, as in Western notation. The font of the dynamics is usually lighter than the font used in Western notation, so as not to be as heavy as the font for the numbers.

[edit] Fingering and other instrument-specific marks

Instrument-specific symbols can be written above notes as well. For example in music for stringed instruments it is common to see wavy lines representing rolls. Fingering can be marked using four different kinds of finger symbol, respectively appearing like a lightning strike, the top half of a semicircle, a backslash, and the bottom left corner of a square.

Other instrument-specific symbols that are sometimes used include one resembling three slashes progressing diagonally downward, placed to the lower right of the numeral. This represents a tremolo. Another symbol is formed of a line proceeding from slightly to the right of the top right corner of the numeral and curving upwards, ending with the left half of an arrowhead. The meaning of this symbol is unclear.

If there are slurs or ties and also fingering symbols, then the fingering symbols are written above the slurs or ties. Rolls (wavy lines) and tuplets are usually written below the slurs or ties. However, if a one-off chord results in many digits being stacked on top of each other and also has a roll symbol, it is possible to place that roll symbol above any slur or tie line in order to save space (to avoid moving the slur or tie any higher than the chord has already needed to move it).

[edit] Glissandi

Glissandi are represented by diagonal wavy lines with arrowheads at the end. The glissandi symbol proceeds from bottom left to top right for an upward glissando, or from top left to bottom right for a downward glissando. It is used in place of a numeral. For stringed instruments, it usually indicates playing all the notes of the scale in rapid succession, i.e. for a downward glissando,

.
1 6 5 3 2 1

and for an upward glissando,

          .
1 2 3 5 6 1

Note that a pentatonic scale is normally used in Traditional Chinese music, so "all the notes of the scale" in this case are 1, 2, 3, 5 and 6.

Extended glissandi (over several octaves) are also possible, usually written with a longer diagonal wavy line that is nearly touching the numbers on either side of it. In this case the numbers on either side determine the starting and ending pitches for the glissando.

[edit] Grace notes

Grace notes are notated like normal notes but are written in a small (about half-size) script on the line just above. They are written with octave dots and note-length lines, and they are connected to the main note by means of a slur that proceeds vertically downward from the center of the note-length line of the grace notes and points toward the main note. Grace notes may be placed either before or after the main note, to be played very rapidly either before the start of the main note or after the end.

[edit] Variations of the numbered musical notation

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.

Another variation is to put octave bar "|" on the side of the number. An octave bar on the left is equivalent to a dot at the bottom. An octave bar on the right is equivalent to a dot on top. This is used in Digital Common Notation. Digital Common Notation attempts to combine the benefits of the standard notation and numbered musical notation and is targeted for keyboard performing.

[edit] Performing numbered music on keyboard

It is possible to perform music in numbered musical notation in the tradition way. The player first locates the root note of the key on the keyboard and then mentally map the number to the keys on the keyboard. This should not be difficult for someone who can play the scales with traditional piano training.

A simple way is to transpose the root note to where the middle C is. The music can then be performed with the same fingering as in C Major. This approach actually reduces the 12 sets of fingering down to one. The method is described in MRN Method (Middle Root Note Method).

[edit] 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 the Netherlands, 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 for 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. The standard notation, with its graphical notation, is better in representing the duration and timing among multiple notes.

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

For a slightly more complex example, see Dao Chuilian (倒垂帘) - Falling Curtain - on sibeliusmusic.com (free to view, but requires you to download and install at least version 5 of the Sibelius Scorch plugin for Windows or Mac OS). The composer He Yiping produced numbered musical notation in Sibelius even though Sibelius does not support it by design; presumably he did this by extensive use of manual symbol-positioning overrides. Note that the notation of this piece diverges from the most common standard in some respects; for example it places time signatures on every line rather than at the top of the music, and it stacks chords by creating columns that descend below the music line rather than rise above it.

An excerpt from a score for Chinese hammered dulcimer (yangqin), written in jianpu. Some standard notation is still used in jianpu.
An excerpt from a score for Chinese hammered dulcimer (yangqin), written in jianpu. Some standard notation is still used in jianpu.
Another example of jianpu in a yangqin score. The Chinese characters in parentheses serve to tell the player how to perform certain techniques, in the event where there is no specific symbol to represent them.
Another example of jianpu in a yangqin score. The Chinese characters in parentheses serve to tell the player how to perform certain techniques, in the event where there is no specific symbol to represent them.

[edit] External links