In recent times, contrastive learning based loss functions have become increasingly popular for visual self-supervised representation learning owing to their state-of-the-art (SOTA) performance. Most of the modern contrastive learning loss functions like SimCLR are Info-NCE based and generalize only to one positive and multiple negatives per anchor. A recent state-of-the-art, supervised contrastive (SupCon) loss, extends self-supervised contrastive learning to supervised setting by generalizing to multiple positives and multiple negatives in a batch and improves upon the cross-entropy loss. In this paper, we propose a novel contrastive loss function - Tuned Contrastive Learning (TCL) loss, that generalizes to multiple positives and multiple negatives within a batch and offers parameters to tune and improve the gradient responses from hard positives and hard negatives. We provide theoretical analysis of our loss function's gradient response and show mathematically how it is better than that of SupCon loss. Empirically, we compare our loss function with SupCon loss and cross-entropy loss in a supervised setting on multiple classification-task datasets. We also show the stability of our loss function to various hyper-parameter settings. Finally, we compare TCL with various SOTA self-supervised learning methods and show that our loss function achieves performance on par with SOTA methods in both supervised and self-supervised settings.