As for the earlier origin of this melody, another factor suggesting this is its topic. During the 2nd century BCE the Han dynasty military leader Li Ling⁷ and the political ambassador Su Wu (see Han Credentials) were both captured and held in long captivity in north central Asia by the Xiongnu. Their stories became very popular again during the 13th and 14th centuries as the Southern Song dynasty was collapsing under northern pressure, then came under Mongol control during the Yuan dynasty. This made the main issue brought up by their stories particularly relevant: should one serve non-Han rulers? This issue is behind a number of Yuan and late Song dynasty artistic creations, including three 12th/13th century poems in Qinshu Daquan that mention this title,⁸ and several surviving contemporary paintings with this theme.⁹

Li Ling was a skillful archer and cavalry officer from a family in Chang An with a long history of military leadership.¹⁰ When the Han Wudi emperor first sent Li Ling on an expedition against the Xiongnu he met with success. This led the emperor in 99 BCE to send a major force against the Xiongnu, then located in the western Gobi desert and eastern Tianshan (Qilian) mountains.¹¹ The main body had 30,000 troops while Li Ling, with 5,000 cavalry, went off separately in an attempt to divide the Xiongnu army. However, Li Ling ventured too far and near Juyan found himself surrounded by about 30,000 (or 80,000) Xiongnu. The Han soldiers tried to escape, but after 8 days half the men were dead and they had no more weapons. Finally, cornered in a valley and out of food, Li Ling surrendered to the Xiongnu. Only 400 soldiers managed to escape. Because of Li Ling's family and personal bravery the Xiongnu leader honored Li Ling by giving him a daughter in marriage. However, when Wudi heard this back in Chang'An, and that Li Ling was serving the Xiongnu, he had Li Ling's mother, wife and children executed.¹²

Several years earlier, a court official named Su Wu had been sent by Han Wudi as an envoy to the Xiongnu (see Han Jie Cao). The Xiongnu detained Su Wu and tried to get him to work for them. They tried various methods, including having Li Ling talk with him (see image with Han Jie Cao), but Su Wu refused. In 86 there was peace and in 81, after 18 years in captivity, Su Wu was able to return to Han. His farewell to Li Ling is another famous theme in Chinese are. Li Ling himself could never go home. He spent the rest of his life amongst the Xiongnu, dying amongst them 74 BCE.

Early writers often praised Su Wu and criticized Li Ling. Some later writers were more sympathetic to Li Ling, but he has always remained controversial, not so much for his surrender as for his willingness to work for the enemy.¹³

Wen Xuan has three poems attributed to Li Ling,¹⁴ plus a letter¹⁵ he is said to have written to Su Wu.

Modally the scale is predominantly do re mi sol la with the main tonal center being la and secondarily mi. However, the last phrase in Section 9 ends with the note sequence mi flat - re - do. Then the closing harmonics, which are written out but are identical to those in the modal prelude, also end on and use do as the tonal center.

 
Original Preface¹⁶

Li Shaoqing lost his ambition amongst the fur (-wearing Xiongnu), and had no way to give expression to his loneliness and resentment. When Su Wu returned home (Li Ling) had a melancholy yearning for the homeland; this brought out his moral loftiness. 100 generations later, just hearing these sounds still causes people's hat and hair to stand on end (in alarm).

 
Music
Nine sections, titled;¹⁷ no lyrics

 
Footnotes (Shorthand references are explained on a separate page)

1. Li Ling Si Han references
14819.1082 李陵 has only Li Ling himself, no mention of music. For poetic references see below. There is a Peking opera called Li Ling Stele (李陵碑 Li Ling Bei) about a Song dynasty general who commits suicide by hitting his head against a stele commemorating Li Ling rather than surrendering to the northern invaders (compare Su Wu Miao).
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2. Huangzhong Mode
From standard tuning lower the third string. The 1539 version uses the same tuning but calls the mode Manjiao (lowered third). For more information on this tuning see Shenpin Biyu Yi and Modality in Early Ming Qin Tablature.
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3. Li Ling and Su Wu
The image above was extracted from the online version of a famous painting called Parting of Su Wu and Li Ling (National Palace Museum, Taiwan). For more on images with this theme see below.
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4. Tracing Li Ling Si Han
Zha's Guide 16/167/363 has only two entries for Li Ling Si Han, the one in 1539 with lyrics, and the present one, which has none. However, both the 1539 lyrics and the 1549 melody seem to have some connection to some versions of 蘇武思君 Su Wu Si Jun (see footnote below. For the poetic references see below.
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5. Li Ling Si Han in Fengxuan Xuanpin
The tablature for Li Ling Si Han in Fengxuan Xianpin has lyrics. I have written out a transcription and studied this version, but the one I have actually learned is the related melody in here in Xilutang Qintong (1549).
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6. Li Ling Si Han and Su Wu Si Jun
Zha's Guide 22/194/380 includes melodies with the title 蘇武思君 Su Wu Si Jun under the title Han Jie Cao. This is presumably based on the statement to that effect under the title of the only surviving version of Han Jie Cao (q.v.). However, the actual melody and lyrics of the later pieces entitled Su Wu Si Jun suggest that they have more connection to both the 1539 lyrics and the 1549 melody called Li Ling Si Han.
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7. Li Ling (d, 76 BCE)
14819.1082 李陵 Li Ling 字少卿 style name Shaoqing. Biography in Loewe, A Biographical Dictionary of the Qin, Former Han and Xin Periods. See also in Wikipedia.
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8. Poetic references to Li Ling Si Han
Qinshu Daquan (1591) includes at least three relevant poems,

1. one by Chen Qiuyan (13th/14th c.) that mentions the title Li Ling Si Han,
2. one by Xie Ao (1249 - 1295) that mentions a melody simply called Li Ling, and
3. one by Yun Ruo (1280 - 1359) entitled Li Ling Si Han.

The poems by Yun Ruo (which mentions 5-character verse) and Xie Ao are 7x4; that by Chen Qiuyan is quite lengthy. None of these poems sheds any light on the actual music.
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9. Paintings on the theme of Su Wu and Li Ling
A net search for "Li Ling" "Su Wu" yields other online examples, including:

1. Parting of Su Wu and Li Ling (see excerpt above)
2. Su Wu and Li Ling, with Attendants (Farewell of Su Wu and Li Ling) (Berkeley Art Museum)
3. Images from folk art such as the one under Han Jie Cao.

See also Michael Sullivan, The Three Perfections; NY, George Braziller, 1999, pp.42-44, for a discussion of the meaning of "Sheep and Goat" by Zhao Mengfu (Freer); Zhao was forced to work for the Mongols.
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10. Ancestor of Li Ling: Li Guang 李廣
Shi Ji #109 has Li Guang's biography and that of several descendents, including Li Ling; the account in this paragraph comes from this source. (中文, p. 2877.) Watson (RGH II, p.128, fn.4) says the end of Chapter 110, including comments attributed to Sima Qian praising Li Ling, was a later edition.
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11. Qilian 祁連
Qilian is said to have been the Xiongnu name for 天山 Tianshan (Heavenly Mountains), a vast mountain range running east west in Xinjiang province. About 500km east of its eastern end was the Xiongnu capital 居延 Juyan (mentioned later), near the modern city of 額濟納旗 Ejin Qi, near 42°N, 101°E in what is today far western Inner Mongolia
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12. After Li Ling surrendered, the only person who defended him at Han Wudi's court was Sima Qian, who as a result was given the choice of honorable suicide or shame and castration; he chose the latter so that he could complete the Shi Ji.
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13. A net search for "Li Ling" "Su Wu" gives more detail.
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14. Li Ling poems in 文選 Wen Xuan
The three poems, all in Chapter 29 (中文, p. 1295), are written in 5-character (pentasyllabic) lines. Giles credits 嚴羽 Yan Yu (ca. 1200) with saying Li Ling invented pentasyllabic verse, perhaps based on these poems. However, most critics now doubt the attribution of these three poems to Li Ling himself. The third one begins:

15. A letter by Li Ling in 文選 Wen Xuan
The letter to Su Wu attributed to Li Ling, included in Chapter 42 (中文, p. 1881), has been translated by Giles. See, e.g., Herbert Giles, A History of Chinese Literature; NY, Grove Press (originally 1923; Evergreen Reprint, 1958?), pp.84-9.
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16. Original commentary
QQJC III/191 ; I haven't found its source; the text is as follows: 李少卿失志氈裘，莫攄孤憤。其於典屬國之歸，淒然懷土；此其清也。百世之下一聞其音，猶將使人冠髮上指。
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17. Chinese titles
The original titles are:

1. 材騎 (cai qi; 14800.xxx; 漢書 Han Shu entry on Li Ling says 善騎射 shan qi she, skilled rider and archer)
2. 扼虎 (e hu; 12132.5 quotes from 漢書 Han Shu entry on Li Ling)
3. 河梁 (17634.130; see above)
4. 入塞
5. 窮追
6. 矢盡 (漢書)
7. 懷鄉
8. 逢友
9. 泣別
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