"9 string Guqin", requested by Juni Yeung, and the raison d'être - long story short

Juni explains what she wishes for her paper in Aug, to demonstrate her idea with a real working model.

Juni adds a simpler explanation to readers.... the longer version will be in the paper to come

"I'm not really changing anything but the way how we tune our 7 strings heptatonically. To do that I need 2 more strings"

Image of a 9 string qin here,

stay tuned for update of suitable image

further reading and references on page of John Thompson,

http://www.silkqin.com/09hist/qinshi/taizong.htm?fbclid=IwAR3dbERYpk7_Ye1V2foIcvddJJiEo-jQFiwf7dTWNv4Bplo-jHOLlzgkQSM#9string

Failure of the nine-string qin
The Qin Shi entry mentions the attempt to develop a nine-string qin but does not give details. For example, it does not mention tuning. The common assumption is that, as with 1618, the tuning remained pentatonic, adding notes on top or bottom, rather than using these extra strings to create a diatonic tuning (perhaps the 7 note scale plus two octave notes). A related observation: with a nine-string qin it should still be possible to play open string octaves (on the 1st and 8th or 2nd and 9th strings, assuming one can make slightly smaller instruments for smaller hands).

Thus it seems likely that the nine-string qin failed largely because the aim was to make the new instrument play the old music better rather than to develop new music: new idioms. But had they been trying to create a new idiom, what might that have sounded like?

Qin music has always been largely pentatonic; non-pentatonic notes, while more frequent in the surviving early repertoire (see especially modal details for Jieshi Diao You Lan), seem to be there largely for extra color rather than being structurally important: thus even there the melodies all remain primarily pentatonic.⁶ Furthermore, preliminary attempts to play melodies from the pentatonically tuned nine-string qin tablature from 1618 suggest that they can fairly easily be adapted for seven-string qin. This can perhaps be partially explained by showing the notes available in the most common harmonic positions (7th plus 5th and 9th hui) if a seven-string qin tuned pentatonically is expanded to be a nine-string qin:

Seven string qin tuned pentatonically:

7th:               5 6 1 2 3 5 6
5th and 9th:           2 3 5 6 7 2 3

Nine string qin tuned pentatonically:

7th:               5 6 1 2 3 5 6 1 2
5th and 9th:           2 3 5 6 7 2 3 5 6

As can be seen, the relative note 4 (fa) cannot be played here. To play 4 in harmonics requires a string tuned to 4 played in the 7th position and/or one tuned to 7 played in the 5th or 9th position. This seems to demonstrate the difficulties of playing an interesting diatonic melody on a qin using pentatonic tuning, whether it has seven-strings or nine.

Does this mean that for playing truly diatonic (heptatonic) melodies one should try either a 7 string or a 9 string qin using a relative diatonic tuning. Since qin idiom strongly suggests that it sounds good to play octaves, for diatonic music one should perhaps first try a nine-string qin tuned diatonically. For example,

1 2 3 4 5 6 7 1 2   (harmonics at 9th hui: 5 6 7 1# 2 3 4 5# 6)
  this now is the same relative tuning as
5 6 7 1 2 3 4# 5 6 (harmonics at 9th hui: 2 3 4# 5 6 7 1 2 3)

Harmonics are used in this analysis because they are such a strong part of the qin idiom. As a result, this preliminary outline shows not only why the seven-string qin has difficulty playing melodies based on a diatonic scale (common Western melodies, for example), but also why extending the qin to having 9 strings, even if tuned diatonically, might still not make it easy to play diatonic melodies and still take advantage of all the opportunities provided by a qin, particularly in terms of playing the extended harmonic passages.

Thus the main use of a nine string qin might be for trying to create a radically new idiom.

 
Footnotes (Shorthand references are explained on a separate page)

1. Song Taizong 宋太宗
趙匡儀 Zhao Kuangyi (939 - 997; 38015.209) reigned 976-998; his younger brother 趙匡胤 Zhao Kuangyin (927 - 976) had reigned as 太祖 Taizu 960-976.
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2. Song Taizong entry: 13 lines
Original text:

太宗
太宗皇帝神武聖文紹天承統，既平晉陽，混一六合，於 是戢雕戈，橐大弓，悠遊岩廊之上，講修盛德之事。而天 縱多能，博總群藝，書冠神品，棋登逸格，至於今古音律， 罔不研精。謂夫五弦之琴，文武加之以成七，乃留睿思 而究遺音，作為九弦之琴，五弦之阮，非達與禮樂之情 者，孰能與於此？ 又制九弦琴、五弦阮歌詩各一篇，琴譜 二卷，九弦琴譜二十卷，五經阮譜十七卷，藏於禁閣，副 在名山，又嘗作《萬國朝天》《平晉》二樂曲，聖制樂章各五 首，曲名三百九十首，臣竊謂三代而下，漢孝元善琴，孝 章議樂，俱不能有所製作，梁武帝論鍾律而徒聞其言， 唐明皇解音曲而未嘗及雅，惟吾太宗勛德巍巍，敷被 天淵而留神於正聲，抒懷於妙曲，自三代而下，未之有 也。

Not yet translated.
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4. Zhu Wenji 朱文濟
Qin Shi #142 tells of Zhu Wenji and the 9-string qin (see also the next footnote).
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5. Extant melodies for 9-string qin
The only ones I have found so far are the 5 examples in the 1618 handbook Lixing Yuanya (QQJC, VIII/318-332). These were presumably made up during the Ming dynasty, quite likely by the compiler of that handbook himself. All melodies in that handbook have lyrics.
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6. Persistence of pentatonic qin melodies
This runs counter to claims often made today that old qin melodies were often non-pentatonic. For example, Jieshi Diao You Lan (mentioned above) is sometimes said to be nine-tone whereas actually it is basically pentatonic with much added color from non-pentatonic tones..
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"Carbon Fiber guqin - Half HunDun"  Shuen-git 2016

7 string wood qin, "Large Handscroll", in fir, Shuen-git 2006