"Guanghan" is the name given to a palace said to be on the moon,⁵ hence it can also refer to the moon itself. On a basic level, then, the title here might also be translated simply as "Autumn Moon". Zhu Quan's preface elaborates on this somewhat by alluding to legends connected to the moon while rhapsodizing on feelings evoked when encountering the moon on a cool evening in autumn.

In Chinese tradition the moon is at its clearest in autumn and at its largest on the 15th day of the 8th lunar month; this has long been celebrated through the Mid-Autumn Festival, also known as the Moon Festival.⁶ Legends associated with the festival include those regarding the goddess of the moon, Chang E, also known as Heng E or, here, Su E.⁷

According to legend Chang E/Heng E lives in her moon palace with a three-legged toad,⁸ a rabbit,⁹ and the woodcutter Wu Gang.¹⁰ One legend says that Chang E was once married to the archer Hou Yi.¹¹ Hou Yi was given the elixer of immortality in return for using his arrows to shoot down extra suns which had appeared in the sky, but Chang E tricked him out of the elixir and drank it herself. In anger Hou Yi began shooting arrows at her, so she fled to the moon, where she was turned into a three-legged toad. Meanwhile Wu Gang, who as an alchemist had also offended the gods, was condemned to live on the moon until he could chop down (zhe) a certain cassia tree (gui), known for its red color. However, each time Wu Gang makes a cut, the trunk grows right back. Hence, "chopping down a cassia tree" (zhe gui) came to mean accomplishing a very difficult task (like passing the imperial examinations).

It is a zhe gui story that apparently connects Guanghan Qiu to the poetic rhythm¹² of that name, as well as to the story of a Yuan opera.¹³ The titles of these can be Guanghan Qiu, but the latter in particular was perhaps better known by the title Zhe Gui Ling (Cutting down the Cassia Tree Melody).¹⁴ These concern a scholar passing the imperial examinations.

However, although Zhu Quan was also a writer of and expert on opera, there is nothing specific to connect this melody with any of the opera stories.

In addition to my own, there have also also been reconstructions of this melody by Wang Mengshu (listen) and Tony Wheeler.

 
Original Preface¹⁵

The Emaciated Immortal says,

as for this piece it is as though, during the clear autumn season, nights are cool and people are tranquil; the heavens are vast and bright, the moon [toad] ascends gloriously, and the moon [goddess] is beautiful. A pure fragrance spreads throughout the universe, and red cassias seem to float around in the [Nine] Heavens. This piece has the joy of wandering to and fro while doing what one wants. How could a commonplace person achieve or understand this? So these interests are best expressed on the qin. Only people who eat the wind and drink the dew can attain this.

 
Music (timings follow the recording on my CD; 聽錄音 listen with my transcription)
Three sections, untitled¹⁶

(00.00) 1.
(00.46) 2.
(01.19) 3.
(02.17) -- play harmonics of the modal prelude
(02.28) -- Melody ends

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Footnotes (Shorthand references are explained on a separate page)

1. 廣寒秋 Guanghan Qiu
9693.205 "廣寒秋﹕詞牌名，即折桂令。 Guanghan Qiu: cipai name, same as Zhe Gui Ling." The entry then quotes a story called Guanghan Qiu from 輟耕錄 Chuo Geng Lu concerning 虞邵菴 Yu Shao'an (i.e., Yu Ji) while he was in the 翰苑 Hanlin Academy.
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2. Shang mode (商調 shang diao)
For further information on shang mode see Shenpin Shang Yi and Modality in Early Ming Qin Tablature.
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4. Tracing Guanghan Qiu
See chart below

For more on the SQMP melodies that tend also to be found in only these later handbooks see a footnote related to text in the Shen Qi Mi Pu general introduction.
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5. 9693.200 廣寒 guanghan; for a discussion of the lunar palace, see also the melody Guanghan You.
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6. (Wiki) Mid Autumn Festival (中秋節 Zhongqiu Jie)
There is a later qin melody called 中秋月 Mid-Autumn Moon. Neither melody makes any mention of the popular customs associated with this festival, such as moon cakes, lanterns or matchaking.
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7. Goddess of the Moon (月神 Yue Shen)
月神 14658.xxx; 神女 25211.11 女神也; 女神 6170.xxx. Her various names, Chang E (6818.1 嫦娥), Heng E (姮娥), and Su E (素娥), apparently came about when emperors had one of these as a given name, so for a time it was forbidden to use that name for the goddess. She and her companions mentioned below are also depicted in an opera discussed under Guanghan You
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8. Toad (蟾 chan)
This toad is often depicted dancing; toad hall (蟾宮 chan gong, as on my logo) is another name for the moon.
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9. Rabbit (兔 tu)
The rabbit (a.k.a. the 白兔 white rabbit or the 玉兔 jade rabbit) has also been associated with the moon since antiquity; it is said to use a mortar to pound cinnamon sticks on a pestle in its attempt to make the elixir of immortality.
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10. Wu Gang 吳剛
Wu Gang spends all his time trying to chop down a tree which keeps growing new leaves; however, he was able to stop long enough to defend Heng O. This punishment of Wu Gang - to 折桂 zhe gui - is apparently used as an allegory in the story called Zhe Gui Ling. (See also section title 5 of Guanghan You.
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11. 后羿 Hou Yi (Wiki)
Hou Yi is the title of 有窮 You Qiong, a famous archer of antiquity. "Strongman Jiao" and others later claimed descendancy from him. After Chang E stole his elixer of immortality he is said to have changed from hero into tyrant.
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12. 詞牌 cipai; Ci for Qin discusses their use as qin lyrics.
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13. 曲牌 qupai
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14. 折桂令 Zhe Gui Ling
12168.84 Zhe Gui Ling says 曲牌名 name of a qupai, i.e., Yuan opera; it then mentions seven other names for Zhe Gui Ling, including Guanghan Qiu. However, it does not seem to mention a specific story. Zhe Gui is also part of title of an apparently lost qin melody called The Scholar Chops the Cassia Tree (Youren Zhe Gui).
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15. For the original Chinese text see 廣寒秋.
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16. For the original Chinese section titles see 廣寒秋.
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Appendix: Chart Tracing 廣寒秋 Guanghan Qiu
Further comment above; based mainly on Zha Fuxi's Guide, 4/45/--.

琴譜     (year; QQJC Vol/page)	Further information (QQJC = 琴曲集成 Qinqu Jicheng; QF = 琴府 Qin Fu)
1.  神奇秘譜       (1425; I/138 [here])	Shang mode; 3 sections
2. 風宣玄品       (1539; II/184)	Same as 1425
3. 陽春堂琴譜       (1611; VII/387)	Same as 1425
4. 琴苑新傳全編       (1670; XI/488)	Very similar to above but some mistakes (e.g. first note) Also seems to change some of the flatted thirds

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