In order to improve the performance of hand-crafted features to detect playback speech, two discriminative features, constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients, are proposed for playback speech detection in this work. They rely on our findings that variance-based modified log magnitude spectrum and mean-based modified log magnitude spectrum can enhance the discriminative power between genuine speech and playback speech. Then constant-Q variance-based octave coefficients (constant-Q mean-based octave coefficients) can be obtained by combining variance-based modified log magnitude spectrum (mean-based modified log magnitude spectrum), octave segmentation, and discrete cosine transform. Finally, constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients are evaluated on ASVspoof 2017 corpus version 2.0 and ASVspoof 2019 physical access, respectively. Experimental results show that variance-based modified log magnitude spectrum and mean-based modified log magnitude spectrum can produce discriminative features toward playback speech. Further results on the two databases show that constant-Q variance-based octave coefficients and constant-Q mean-based octave coefficients can perform better than some common features, such as mel frequency cepstral coefficients and constant-Q cepstral coefficients.