How do numerical notation systems represent pitches in Javanese, Balinese, Japanese, and Chinese music?

In the context of musical notation, numerical systems represent pitches by assigning specific numbers to the degrees of a scale. While such systems are relatively rare, they are utilized in several Asian musical traditions:

• Javanese and Balinese Music: A modern Javanese system assigns the numbers 1–7 to the pitches of the seven-note pelog scale. A similar five-note numerical system is also used in Bali.1
• Japanese Music: Modern notation for the samisen (a type of lute) employs the numbers 1–7 to represent the diatonic scale, with 7 denoting the lowest note.1
• Chinese Music: While traditional systems like gongche use characters to indicate pitch, modern China frequently uses a numerical system for popular songs and ensemble scores. This system is based on the 19th-century French chevé method, using numerals 1–7 for scale degrees and incorporating Western-style dots and beams to indicate rhythm.12

These numerical notations are distinct from syllabic systems, such as the ancient Chinese kung, shang, chiao, chih, yü or the Balinese ding, dong, deng, dung, dang, which use specific names to identify scale degrees.3