Zhu Xi's commentary on the Da Xue is included with the qin melodies Mingde Yin and Kongsheng Jing.⁹

Tong Kin-woon's Qin Fu, pp.1690-1, has selections from something called Mr. Hui'an Zhu Wen'gong's Literary Collection.¹⁰ It mentions Zhu Xi's Qin Book, generally called Qin Lü Shuo (Speaking of Qin Music Standards), suggesting it was originally part of that work. More details are with Qinshu Cunmu #108.¹¹

One of Zhu Xi's nicknames was Ziyang, and there is a Ziyang Qinshu perhaps by him.¹²

Zhu Xi apparently transcribed into gongche notation Zhao Yansu's Fengya Shiershi Pu (ca 1180). This was later set to qin tablature.¹³

Shuangqin Shuwu Qinqu Jicheng (1884), in its preface to Shishang Liu Quan, connects Zhu Xi to the melody Bijian Liu Quan (see also the Zha Guide).

Zhu Xi wrote some poems that mention qin; see Qinshu Daquan:

Zhu Xi's father Zhu Song,¹⁴ 1097 - 1143, was a scholar and high official who opposed peace with the Jin, and so retired.

The biography in Qinshi Xu begins,¹⁵

Not yet translated.

 
Footnotes (Shorthand references are explained on a separate page)

1. Zhu Xi references
14779.803 朱熹. Giles; ICTCL has many references but no separate entry
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2. Image
Copied from 14778.803, which took it from 三才圖會 Sancai Tuhui (cleaned up).
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3. 朱子 Zhuzi
In addition to Zhuzi one can also find 朱夫子 Zhu Fuzi, as with Confucius. In fact Zhu Xi used many style names: 元晦 Yuanhui, 仲晦 Zhonghui; and nicknames: 晦庵 Hui'an, 沈郎 Shenlang, 季延 Jiyan, 晦翁 Huiweng, 遯翁 Dunweng, and 雲谷老人 Yun'gu Laoren. He was made a 公 duke and canonized 文 Wen, making another name Wen'gong
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4. 尤溪 Youxi, in central Fujian province.
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5. 婺源、徽州 Wu Yuan
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6. Wuyi Shan 武夷山 has a number of buildings commemorating Zhu Xi, including his grave and a memorial hall.
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7. 岳麓書院, named after Yuelu Shan, a range of hills across the Xiang River from central Changsha. The current building marking the old academy is of much more recent construction
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8. 白鹿洞 There is apparently a plaque on 五老山 Wulao Shan (Five Elders Peak) commemorating the spot.
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9. There is no suggestion that he had any connection with the music.
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10. Mr. Hui'an Zhu Wen'gong's Literary Collection (晦庵先生朱文公文集 Huian Xiansheng Zhu Wengong Wenji)
The selections in Tong Kin-woon's Qin Fu, pp.1690-1, are:

1. Folio   1. Melodies: 招隱操 and 反招隱 plus a poem: 聞琴
2. Folio   4. Poem: 趙君澤携琴載酒見訪分韻得琴字
3. Folio 16. Miscellaneous writings: 琴律說：定律、調絃
4. Folio 85. Inscriptions: 劉屏山復齋蒙齋二琴銘、黃子厚琴銘、紫陽琴銘
     The last inscription is "養君中和之正性，禁爾忿欲之邪心。乾坤無言物有則，我獨與子鈎其深。"

I do not yet know of any available translations.
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11. Discussing Qin Tones (琴律說 Qin Lü Shuo)
21570.xxx. Qinshu Cunmu #108 has 28 lines discussing this work. An article published in 1971 suggests that at the time it was one of the few writings on the qin with which people were then familiar. Perhaps it was part of 晦庵先生朱文公文集 Mr. Hui'an Zhu Wen'gong's Literary Collection (see above).
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12. Ziyang Qinshu 紫陽琴書
See further information.
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13. 風雅十二詩譜 Fengya Shiershi Pu by 趙彥肅 Zhao Yansu
This book, published ca. 1180, set 12 Shi Jing poems to music. Zhu Xi himself apparently transcribed these melodies into gongche notation. These were later set for qin in at least two handbooks:

1. Lüyin Huikao (1835)
   A setting for qin from Zhu Xi's gongche notation
2. Qinzhi Shen Qiu (1889)
   Developed from/copying the Lüyin Huikao setting

I have not yet seen any of these.
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14. 朱松 Zhu Song
Zhu Song (Giles, Bio/542), style name 喬年 Qiaonian, nickname 韋齋先生 Mr. Weizhai, wrote several poems connected to the qin. See

15 The entry, 34 lines long, gives 宋史 the official Song history as its reference.
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