# Why F-1 is a better score than the harmonic mean between true negative rate and recall?

Beside of the easy interpretation, F1 measure is very sensible to the relative frequency between positives and negatives. ROC AUC metric don't, but it is difficult to optimize. Are there any special reason why nobody (or very few people) use any kind of mean between true negative rate and recall? For example the harmonic mean as the following structure $$H(T_{nr},R_c)=\frac{2 Tn Tp}{F_n T_n + (F_p + 2 T_n) T_p}$$ It is independent from relative frequencies of the classes and has the same structure of the F1 score.