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[Quicunque]

How does one calculate the value of a musical instrument? I am guessing it would be

((material value x 10 (instrument value according to the wiki) x quality modifier) for each component, added together for the subtotal) x quality modifier for whole instrument

For example, a "birir" is composed of a drum, a stand, and mallets. Thus:

drum:   cave croc leather (4) x (10) x exceptional (5) = 200
stand:  fungiwood (1) x (10) x masterful (12) = 120
mallet: silver (10) x (10) x superior (4) = 400
Subtotal (720) x exceptional (5) = 3,600

Does this seem to be in accord with your experience, or am I missing something?

[Fleeting Frames]

You have two quality modifiers there. That only really occurs for building designer, I think? In traction benches parts are discarded. But who knows.

A few examples of values in ascending order in my save:

wild boar leather mid-size hand-held wind i. w. wild boar leather/giant hedgehog bone/ash/silver, decorated with rings of reindeer bone &-wombat bone- = 210
earthenware mid-size hand-held silk-stringed i. w. earthenware/earthenware/Enslaved Doom silk/sea serpent bone = 270
Well-crafted green glass huge stationary i. w. metal-stringed green glass/iron/blue peafowl bone = 330
Silver mid-size hand-held metal bowl i. w. silver, no quality: 500
Well-crafted crystal glass large stationary silk-stringed i. w. crystal glass/brown recluse spider silk = 1110
Well-crafted large stationary silk-stringed i. w. wood/wood/wood/clear blue cloth = 3130

Fourth the bowl is the easiest: total 500, silver is 10, therefore item value is 50.
First, without decorations would be 180. Everything but silver has modvalue 1, therefore the multipliers might be something like 10/10/10/15.
Fifth is also relatively easy with 2 parts. Crystal glass is 10, brown recluse silk 1, well-crafted is x2. 555 could be divided into 50*10 + 55*1. For comparision, a green glass no quality body part in same caravan is 20.

I can already conclude the instrument values are proc-genned, of course. This means that if one is to experiment with trading instruments, they must craft samples first.

E: Raw dump of names/raw item value claims all instruments have 50 value, which doesn't seem to work for multi-part instruments.

E2: Interesting. Disregard above calculations for well-crafted stuff at least - Setting the 2nd to well-crafted gave it 420 item value - when doubling would have been 540. Seems the instrument parts are kept as decorations.

This comes to main part value: 150.
earthenware part 1: 30
earthenware part 2: 30
Dom silk part: 10
Sea serpent part: 50

The total does check out to 270. Earthenware has 3 modvalue and sea serpent 5, so the parts are 10 each and main body is 50.

Thus instrument value for single part instruments is same as wheelbarrow/minecart, and for multi-part instruments each part is added on as a decoration, with the quality (but not the improvements, I guess?) of each part kept.

Using this, the fifth would be 2*10*50+10*10+10*1, which is indeed 1110.

[Saiko Kila]

How does one calculate the value of a musical instrument? I am guessing it would be

((material value x 10 (instrument value according to the wiki) x quality modifier) for each component, added together for the subtotal) x quality modifier for whole instrument

For example, a "birir" is composed of a drum, a stand, and mallets. Thus:

drum:   cave croc leather (4) x (10) x exceptional (5) = 200
stand:  fungiwood (1) x (10) x masterful (12) = 120
mallet: silver (10) x (10) x superior (4) = 400
Subtotal (720) x exceptional (5) = 3,600

Does this seem to be in accord with your experience, or am I missing something?

My experience is somewhat different. Instrument value is the instrument itself (50 x quality multiplier x material of main part), plus decorations (10 x quality multiplier x material multiplier). Each part is a decoration in multi-pieces instruments, including the one counted also as a main part. Single part instruments do not have decorations or main part, so they are less valuable (maximum 600*material value with masterwork quality). Additionally if instrument has flag "artifact_mood" its whole value is multiplied by 10 (like for every true artefact).

So for your example:
50 x 5 x ? = 250*? (exceptional instrument)
10 x 5 x 4 = 200 (drum)
10 x 12 x 1 = 120 (stand)
10 x 4 x 10 = 400 (mallet)

Total would be 250x?+200+120+400. You haven't said which one is the main part, substitute ? for its material value. However, with you materials, I cannot see possibility for total value of 3600.

[Quicunque]

This morning I kept careful records as my dwarves crafted a birir. First, they made the components as follows:

drum: superior (4) x porcupine bone (1) x component (10) = 40
stand: masterful (12) x pear wood (1) x component (10) = 120
head: fine (3) yak leather (1) x component (10) = 30
mallet: exceptional (5) x quartzite (1) x component (10) = 50

These values were both predicted by the OP formula and verified in the Stocks menu, View. Next, I sent these components to the jeweler be gem encrusted. It turns out that instrument components are NOT improvable, so no encrusting at this stage is possible. Thus, the dwarves proceeded to assemble a fine (3) birir, but the total value was then 390 (so the OP formula is wrong). Applying Fleeting's formula above, where the main body is (50), times the fine quality (3) = 150, I arrive at the 390 figure only by adding the 240 value of the total components to the 150 of the instrument itself. This suggests:

((instrument quality) x (instrument base 50)) + (total component value) = instrument value

More !!SCIENCE!! is needed, I think.

[Quicunque]

Just finished 3 more birirs (which I use because they have 4 components; the drum is the base component):

Birir #1
Drum: exceptional (5) x skunk bone (1) x (10) = 50
Stand: normal (1) x cherry wood (1) x (10) = 10
Head: normal (1) x goat leather (1) x (10) = 10
Mallet: exceptional (5) x gabbro (1) x (10) = 50
Assembled as a superior (4) birir TOTAL = 320, which is (instrument quality 4 x instrument base value 50) + component subtotal (120)

Birir #2
Drum: superior (4) x skunk bone (1) x (10) = 40
Stand: well (2) x pecan wood (1) x (10) = 20
Head: normal (1) x wombat leather (1) x (10) = 10
Mallet: fine (3) x quartzite (1) x (10) = 30
Assembled as an exceptional (5) birir TOTAL = 350, which is (instrument quality 5 x instrument base value 50) + component subtotal (100)

Birir #3
Drum: exceptional (5) x skunk bone (1) x (10) = 50
Stand: fine (3) x pear wood (1) x (10) = 30
Head: normal (1) x skunk leather (1) x (10) = 10
Mallet: exceptional (5) x quartzite (1) x (10) = 50
Assembled as an exceptional (5) birir TOTAL = 390, which is (instrument quality 5 x instrument base value 50) + component subtotal (140)

Just out of curiosity, I tried a one-component instrument: a kulin
Kulin: exceptional (5) x mussel shell (1) x instrument base (50) = TOTAL 250 [Having no components, there is nothing to add]

So, for multi-component instruments, the VALUE = (instrument quality x instrument base value 50) + component subtotal [including the base component]

[Saiko Kila]

More !!SCIENCE!! is needed, I think.

I gave the formula, and it gives the value correct value. You are using bones, with value 1 as the main part, so you don't see that you also have to multiply by the value of material of this part for. So again:

total value = (50 x quality multiplier of instrument x material of main part), plus decorations (10 x quality multiplier x material multiplier)

You cannot decorate the parts, because they are not finished goods. You decorate whole instruments as finished goods.

[Fleeting Frames]

As a side note, this means platinum/aluminium single-piece instruments beat lesser value steel trap components (and all steel trap components if caravan demands instruments).

Though in terms of renewability, using fire clay to produce ceramic instruments might be best, followed by high-value breeding for bone and GCS silk farm.

[Quicunque]

Thanks for the correction, Saiko. I see my misunderstanding.

Also, Fleeting, the relative value of instruments against other exports was exactly why I wanted to know how to calculate their value. As you pointed out, they can be even better than trap components. Using just a piece of bone & a piece of wood, one could craft a 2 component instrument, and, assuming master craftsmanship, yield an instrument worth 840 [(12x50)+240]. That is a 420 time multiplier of value! 420x is better than prepared meals for multiplying value.
(By comparison, a 4 component instrument would be (12x50)+480=1080 from 4 value, which is only 270x)

[Fleeting Frames]

Average of 2 components per component is 23*quality (70 total/3 jobs), though, which is both not terribly high (below bigger cloth items or statues/mechanisms) and means 1 component instruments are better unless you're trying to stretch or avoid using nearly non-renewable metal.

Master craftdwarfship is little unreasonable consistently assume, Blue_Dwarf's research indicates between 6,79 and 7,26 average value multiplier for Legendary+5 depending on whether they have perfect attributes, item preference match and material preference match. I.e. your bone/wood would be, on average, 6,79*(50*1+10*1+10*1)=475,3.

It's good enough, still, but you'd need 25k of them to match 12 mil supersalads.