Diagram of the Eight Sounds from the Scroll of the River Luo

original: "Luoshu Ba Yin Tu" (洛書八音圖). The Luoshu is an ancient Chinese mathematical grid where the numbers 1 through 9 are arranged so that every row, column, and diagonal adds up to 15.

The central figure consists of 5 circles connected in a cross shape, representing the number 5, which acts as the unmoving axis of the diagram.

original: "Guan" (官); literally "Official" or "Bureau," referring here to the "Central Palace" of the magic square which governs the surrounding eight directions.

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Xun (Southeast)

Represented by 4 circles in the Luoshu grid.
Clear and Bright Wind Associated with the time of the Qingming festival in late spring.
Generation Number of Metal In this system, "Generation" (Sheng 生) refers to the primary creative numbers 1–5.
Wood Sound Refers to instruments made of wood, such as the zhu (a struck box used to start music) or the yu (a tiger-shaped scraper used to end it).

Li (South)

Represented by 9 circles.
Luminous Wind
Completion Number of Metal "Completion" (Cheng 成) refers to the secondary numbers 6–10 produced by adding the central 5 to the generation numbers.
Silk Sound Refers to stringed instruments like the qin (zither), which traditionally used silk strings.

Kun (Southwest)

Represented by 2 circles.
Cool Wind
Generation Number of Fire
Earth Sound Refers to instruments made of clay, specifically the xun, a globular vessel flute.

Zhen (East)

Represented by 3 circles.
Wind of the Common People original: "Ming-shu Feng" (明庶風); a wind signaling the growth of crops.
Generation Number of Wood
Bamboo Sound Refers to vertical and transverse flutes made of bamboo stalks.

Dui (West)

Represented by 7 circles.
Gate of Heaven Wind original: "Chang-he Feng" (閶闔風); named after the mythical gate to the celestial realm.
Completion Number of Fire
Metal Sound Refers to bronze bells (zhong) or gongs.

Gen (Northeast)

Represented by 8 circles.
Gentle Wind original: "Tiao Feng" (條風); a wind associated with the budding of branches.
Completion Number of Water
Gourd Sound Refers to mouth organs like the sheng, which used a dried gourd as a wind chest for its bamboo pipes.

Kan (North)

Represented by 1 circle.
Vast and Boundless Wind
Generation Number of Water
Skin Sound Refers to drums made with animal hide or leather.

Qian (Northwest)

Represented by 6 circles.
Imperfect Wind original: "Bu-zhou Feng" (不周風); literally "the wind that does not go all the way around," associated with the onset of winter.
Completion Number of Wood
Stone Sound Refers to lithophones, or chime stones (qing), carved from resonant jade or limestone.