A question about Baroque G strings

the effect you heared with that g-string technically is called "amplitude dependence of resonance frequency". Your guess that the effect depends on the thickness of the string is partly right.
For understanding that effect you have to take in account that the string needs to stretch for reaching the maximas of it's transversal deflection. That stretching of the string results in an increase of the tension of the string. That means that the vibration of the string causes a periodical change of the string tension. As a result of this the temporal average of the tension of a vibrating string T_vs is higher than the tension T_nvs of the same non vibrating string. An increase of the maximas of transversal deflection causes an increase of the temporal average of the tension T_vs. Since the frequency of a vibrating string depends among other parameters on the tension of the string, the pitch of the string will be slightly increased when the string is played louder.
It depends on the size of the relation
(T_vs - T_nvs)/T_nvs
how big the deviation of the pitch of a loudly played string will be. The bigger the value of the above relation is, the bigger is the deviation of the pitch of a loudly played string. When the value of the above relation exceeds a certain threshold you can hear that deviation of the pitch. And obviously that was the case for the g-string you played.
Since T_nvs is the denominator of the above relation, the value of that relation decreases when T_nvs (that is the tension of the non vibrating string) increases. That means that you have to increase T_nvs to diminish the value of the relation above and push it's value below that threshold for that the deviation of pitch can be heard.

Using the average density of string gut of 1330 kg/m³ at a relative humidity of 50% together with Taylors formula for the string tension, a 1.2 mm plain gut g-string with a vibrating length of 0.325 m delivers T_nvs = 24.4 N = 2.5 kp.
That's pretty low tension, even for a barock g-string. On the other hand, 1.2 mm is a pretty thick gut string for a violin bow. Increasing the diameter of the plain gut string increases it's stiffness and because of that will result in awkward sound effects. As written by the contributors above, you should use a wound g-string.

Just a last recommendation: on wound gut strings you can combine different diameters of gut with wires of different diameters made of differnt materials so that you get wound gut strings with different diameters >>BUT<< same tension for a certain vibrating length and pitch! So it's rather meaningless to sell or buy wound gut strings by diameter. Instead look for the value of the mass per unit length. That will give you a reliable and commensurable measure for the tension the string will have on an instrument with a certain vibrating length at a certain pitch.
According to my experience for a barock violin the mass per unit length of a g-string should be in the region between 180 g/100m (gramm per 100 meter) to 200 g/100m depending on what the violin likes. For playing classical or romantic repertoire on a modern violin you can choose a wound gut g-string in the range of 200 g/100m to 240 g/100m. By the way that is about the range Pirastro offers for their standard Eudoxa and Wondertone Gold g-strings.

Have a nice day!

I had a chance to visit a bit with him afterwards, and while the A and E strings were gut, the D and G strings were metal wound gut strings. (Pirastro Olive Strings to be precise.)

I had a chance to visit a bit with him afterwards, and while the A and E strings were gut, the D and G strings were metal wound gut strings. (Pirastro Olive Strings to be precise.)

A pure gut G string will give you an opportunity to explore the unique tonality that players and composers were used to in the early baroque--at a cost in terms of playability depending on the exact construction (and the violin, its setup, and the bow).

Even reproductions of the best historical baroque violin G strings exact a price for the exploration they allow--which is why you find violinists who proudly aver their historicity using non-historical Oliv D and G strings. The implied principle being "Well there are limits you know!" :-)

It's not a G string.

Now, I know that I should not take my history from fictional movies, but this info from Claire Givens website would tend to bear that out.

https://www.givensviolins.com/violin-strings-history/

Leaving the movie aside, since the period we frame as 'baroque' goes from 1600 to 1750, there wasn't a single type of baroque G string.

Thank you very much for the link to that detailed discussion of the subject.