Course:Phys341 2020/Qin

The guqin (literally the ancient qin, also known as the Chinese qin or simply the qin) is a plucked seven-string instrument that originated in China. The prefix gu, though indicates the guqin's aintiquity, is a modern invention to differentiate the guqin from other western instruments such as the gangqin(piano), the xiaotiqin (violin) and the shuqin (harp), etc.. The qin belongs to the zither family. It has a playing ranging from C2 to D6.

History

The qin was first recorded in the Classic of Poetry (11th to 7th BCE) as a ceremonial instrument used in religious rites and royal feasts in the Zhou Dynasty. It was therefore associated with the upper class. Historical records show that Confucius learned the qin and was a fervent player. Since Confucianism became the national philosophy in Han Dynasty, the qin was seen as the instrument of the scholarly gentlemen (often landed gentry, later included the elitist bureaucrats)。

From left to right: Top plate, inside and bottom plate of the qin.

Measurement

The physical structure is said to have great philosophical, religious and cosmological importance. According to Huan Tan, a first-century Chinese philosopher, the length of the qin is 1.22m (3 chi 6 cun 6 fen, representing 366 days of the year). The width is 60cm (1 chi 8 cunrepresenting number 3 and 6 which each have their own significance in the Yi Ching.). The distance between two sound boards is 20cm (6 cun which represents the 6 Lü, an abbreviation of the 12 equal temperaments which denotes music in general). The top board that imitates the shape of heaven has a curved shape. The bottom board that imitates the shape of earth has a flat shape.

Structure

The qin, as shown in Fig. 1, is consisted of 2 different boards, one on the top and the other bottom. Strings are attached horizontally between the tuning peg and the bridge.There are 2 sound holes called Dragon's pool and phoenix's pond.

Materials

Historically, only certain specific woods can be made into a qin. The Classic of Poetry (11th to 7th BCE) specifies that the making of a qin requires four trees, the Zi, the Yi (an ancient synonym of the Zi), the Tong and the Qi trees. The bottom part requires the Zi wood (catalpa ovata). Whereas the top part is made out of either the Paotong (Paulownia tomentosa) or the Wutong (Firmiana simplex). Dried and coloured sap of the Qi (Chinese lacquer) tree is used to varnish the surface. Deer antlers extracts, a form of glue, are dried and powdered to be mixed with the lacquer. A few layers of lacquers are applied and each layer has to dry before adding another layer.

Aside from the very traditional woods, Chinese fir (Cunninghamia lanceolata) had also been used to construct the top board of the qin since 7th century by the qin maker family, the Lei family. From the sound quality analysis of 5 qins by Waltham and colleagues (2012), we see that the instrument will sound fair or good if the bottom board is made out of catalpa. From the same analysis, it is clear that a qin with a Chinese fir top board produces better sound than the Paulownia top board.

The strings traditionally were made out of silk. Today, however, manufacturers use steel or nylon in silk's stead. It should be noted that there is a recent resurgence of production of silk strings. The strings are usually tuned to F scale (zhengdiao, or the proper scale), from the lowest 1st to the highest 7th strings are C₂ D₂ F₂ G₂ A₂ C₃ D_3,and their lowest fundamentals from 65 to 147 Hz.

The first five wood modes of the first qin examined by Waltham and colleagues.

Acoustics

Wood and cavity modes

At low frequencies, the qin has two modes, the bending mode and the torsional mode. Waltham and colleagues (2012) test a typical qin, of which the first bending mode (0,2) is at 105 Hz, the first torsional mode (1,1) at 238 Hz; the second bending mode (0,3) at 255 Hz, mode (1,2) at 384 Hz and mode (0,4) at 429 Hz.

Another qin they tested have the lowest bending mode (0,2) lies at 156 Hz; the (1,1) torsional mode is split into 296 and 310 Hz by a cavity mode, the second bending mode (0,3) may be mixed with the predominantly cavity modes at 389 and 426 Hz. and lastly the third bending mode (0,4) is split into modes at 533 and 593 Hz.

The hike on the very left of the graph represents infrasound in the lab. The first fundamental is represented by the second hike in the graph around 83 Hz. (Own work, recording from Prof. Chris Waltham)

At high frequencies, a mix of cavity and wood modes dominate. Since qin has a long length compared to its height and width, the cavity mode of which can be seen as that of a tube with two side holes and analyzed with a one-dimensional transmission matrix model. At above 500Hz, the modes are largely 150Hz apart as would be expected in a 1100mm-long simple pipe.

Radiativity

The qin's radiativity does not become appreciable until about 400 Hz, so the radiation is dominated by the higher harmonics of the strings. However, the low tones are an essential part of the qin's character and can be sensed, although possibly through the missing fundamental effect.

The sound analysis of the recording of plucking a qin string on the right illustrates qin's radiativity as described by Waltham and colleagues. The x-axis represents frequencies and the y-axis sound intensity. The graph shows that the most appreciable (i.e. the loudest) harmonic frequency is the fifth fundamental at 413 Hz.