The expansion and contraction of the material are as follows:

(1) Bow hair:

-Relationship with humidity: positively correlated with humidity. Stretching when humidity increases; When the humidity decreases, it shortens.

-The relationship with temperature: irregular. Some experimental results show that human hair is longest at 1.5 ℃. When<1.5 ℃, the length increases rapidly with the increase of temperature. At 1.5-15 ℃, it shortens with increasing temperature; The segmented temperature and data of bow hair (ponytail) should differ from human hair. However, it can be roughly assumed that the relationship between the length of the ponytail and temperature is also irregular.

(2) Bow rod:

       

-Relationship with humidity: Wood usually expands and elongates with increasing humidity.

-Relationship with temperature: thermal expansion and contraction.

[Analysis]:

(1) The changes in bow hair and bow rod length are positively correlated with humidity. When the humidity decreases, the bow hair shortens and the bow rod also shortens. Therefore, their contributions to "tension" are mutually offsetting. However, the impact of humidity on bow hair and the sensitivity of bow hair to humidity response should be significant for the bow rod. The expansion and contraction rate of the bow rod material is also very small compared to the bow hair. Therefore, in terms of humidity, the main contradiction is the bow hair. The influence of changes in bow length can be ignored.

        

Conclusion: When the humidity decreases, the arch hair shortens and produces a "tightening" phenomenon. Vice versa.

(2) The effect of temperature on bow hair is somewhat complex.

In the high temperature range (assumed to be 1.5-15 degrees), the overlapping of the "tension" phenomenon between the bow hair and the bow rod. As the temperature increases, the bow hair shrinks and the bow rod elongates, resulting in a "tightening" phenomenon.

However, the expansion coefficients of these two materials have not yet been found. I estimate that the expansion rate of these two materials will not be too high. More importantly, when playing indoors, when taking out the bow from the case, the temperature difference should not be significant and can be ignored. Therefore, the influence of environmental temperature on "tension" can be disregarded.

In the temperature range of 1.5~15 ℃, although the contributions of the two materials to "tightening" are superimposed, I believe that the expansion and contraction systems of these two materials in this temperature range will not be significant. Therefore, the impact can be ignored. More importantly, if temperature changes are the main cause of the "tightening" phenomenon, then every time the piano is played (especially during rapid playing), the "tightening" phenomenon should occur. However, the actual situation is not like this. Therefore, I believe that temperature is not the main influencing factor.

Conclusion: Temperature changes (referring to the heat generated by playing the qin) do not directly cause the phenomenon of "tension".

(3) The relationship between temperature and humidity is quite complex. To simplify the discussion, we assume that temperature and humidity are negatively correlated. When the temperature rises, the humidity decreases. As discussed earlier, humidity has a significant impact on "tension". However, in low humidity environments, even small changes in humidity do not cause the phenomenon of "tension".