(I'm not summarizing the book here, I'll just give background for the choices I made.)
Tigana is set on an unnamed earth-like planet. Technology is at about 17th-century level. The action takes place on a peninsula on which there are nine provinces. These provinces have a common culture and would like to think of themselves as one country, but in practice they are more inclined to vie with each other than to collaborate. This lack of unity has enabled foreign powers to invade and conquer the peninsula; in the main storyline, the main characters are on a quest to encourage a sense of unity in people, in order to ultimately oust the tyrants and maybe even become a real country.
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Music in the peninsula in some ways resembles our jazz: it seems to consist mostly of "standards" that every musician knows, and that can be performed by any combination of singers and/or instrumentalists. One band is described in some detail, a group of nine people that travels the whole peninsula and performs for a living.
Here's the lineup of that band. I cannot resist giving all the member's names. Per the author's request all names are to be pronounced the Italian way.
- Two dancers, Aldine and Nieri. Both are young women. The dance is designed to evoke a certain atmosphere and is an integral part of the performance.
- Three singers: Catriana (soprano), Devin (tenor), and Menico (bass). They each sing both lead and backing vocals. Menico is the bandleader.
- Four instrumentalists. Drenio and Pieve (syrenya), Alessan (Tregean Pipes), and Eghano (Senzian Drums and Certandan Deep Strings).
As for these instruments:
A syrenya is a stringed instrument. The number of strings is not mentioned, but at one point in the book a child is given "a scaled-down syrenya with three strings", so I assume a normal syrenya must have at least four. I imagine this instrument as resembling the five string Mexican Vihuela.
The Tregean Pipes (from the province of Tregea) are a kind of bagpipe. It is not clear to me whether this has any drone pipes, but it is described as playing melodies and counter-melodies and pitched rather high. So probably no drones.
The Senzian Drums (from Senzio) are a set of two drums built as a unity. I imagine them to be like our timpani, tuned to two definite pitches, but I have no evidence for that.
Since the Senzian Drums and the Certandan Deep Strings are played by the same player, presumably not at the same time, I feel they must sound sufficiently different to warrant having both of them. Especially since they would probably take quite some space during long horse-and-cart travels. This has given me the idea that the Deep Strings must be bowed, as that gives them a clearly different character from the Drums.
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Although the nine provinces have a shared culture, every province has its own character, dialects, products, and so on. A province can be known for a musical instrument, but also for a specific kind of wine, cheese, sculpture, or architectural style. They all have their own things. One strongly unifying element is the official religion, practiced by everyone.
For those who are curious about such things, here are the names of the provinces. They too have to be pronounced the Italian way. Roughly from the northeast to the southwest:
Senzio, Astibar, Chiara, Asoli, Ferraut, Tregea, Certando, Corte, Tigana. All nine have a capital of the same name.
As for the province of Certando, I find it rather mysterious. To me it has an "ancient" feel about it. As if old things that are outdated elsewhere are still present here. It even has a religion that's older than the official one, which is practiced in utter secrecy.
To me, then, it is no surprise that the "Deep" instrument is from here. I imagine it, not like a double bass which is basically a melodic instrument, but more of an evocative thing that with its long-drawn sounds summons ancient spirits. Therefore it willl not be capable of playing melody, and it will make extensive use of overtones.
The absence of drones in the Tregean Pipes would give space for use of these overtones in the band.
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To sum up: I have based my plan on far too little information, and filled all the gaps with my own imagination. If anyone else ever decides to build the Certandan Deep Strings, or has already done so, it will be a completely different instrument. And I think that's fine.
Six degrees of separation and all that. 
