We investigate an optimised non-linear frequency warping scale for speech emotion recognition (SER). The proposed scale maps the speech spectrogram onto another time-frequency domain which is invariant to speaker-specific variations. Generally, the famous mel-scale designed on human audio perception is considered the de facto standard of frequency warping. However, designed mainly for speech recognition, the generalisability of mel on other speech processing tasks is debatable. Our experiments show that an emotion-specific scale designed on an SER database outperforms the standard mel-scale. Along with performance improvement, the proposed approach also provides insight into the emotion-relevant frequency regions for SER. Despite the database-dependent design of our approach, we find that the scale obtained from our experiments also shows SER performance improvement when tested on two other databases.