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, indicating that they are to be played very rapidly either before the start of the main note or after the end. 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. History and usage A similar invention was presented by Jean-Jacques Rousseau in his work presented to the French Academy of Sciences in 1742. Due to its straightforward correspondence to the standard notation, it is possible that many other claims of independent invention are also true. Grove's credits Emile J. M. Chevé. 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. Number notation was used extensively in the 1920s and 30s by Columbia University, Teachers College music educator Satis Coleman, who felt it "proved to be very effective for speed with adults, and also as a means simple enough for young children to use in writing and reading tunes which they sing, and which they play on simple instruments." See the external links for more information. The system is very popular among some Asian people, making conventions to encode and decode music more accessible than in the West, as more Chinese can sight read jianpu than standard notation. Most Chinese traditional music scores and popular song books are published in jianpu, and jianpu notation is often included in vocal music with staff notation. Indexing with numbered notation makes