For an excellent introduction to this question, go here. For my own research, I have done the studies below with various other instruments (see link below).
Here are some important observations:
The instruments that get worse with age are:
The violins (or cellos and flutes) tend to get much lighter with age. A viola (which is a long-lived instrument) generally will have less sustain under more extreme conditions. It may get lighter at the same performance time, or lighter at different times; depending on a lot of things in the setup of the instrument (as well as it getting different types of strings, such as a hard wood, lighter and harder maple or something very similar, for instance).
The violas get lighter, but they don’t get as light as a large classical instrument.
The violas tend to have more body wear. Violin necks tend to get thinner with age. This may be partly a result of having had the instrument for very long, since the natural aging of the tissues is slower. Also, when the violin was made, the violin was relatively new. Since it is heavier now compared to when it was new, its vibration is less powerful and it is more susceptible to cracks.
The horns do not get lighter. They are a special case of the first two groups. The old horns get lighter. They also have a very slow reaction to change of a lot of things like material used, new construction, new colors, etc. It also takes a little longer to get lighter with age.
The horns of violins, cellos and flutes are very similar, in that they generally tend to get less light with age, and the violins (the most extreme violas, the ones you see in concert) usually get their lightest by the end of the 20th Century.
In other words, violins are much a lot like the first 3 classes of a musical instrument: they take on a different character with age, and they get less light with age.
The violas tend to get lighter and lighter as a class as they get older.
The flutes (and other instruments with high and low voices) tend to get much, much lighter over time. The violins (and all the instruments with a high voice, including cellos and violas) tend to get less light at the same time.
So, a viola gets lighter,
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