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This paper proposes an algorithm for separating monaural audio signals by non-negative tensor factorisation of modulation spectrograms. The modulation spectrogram is able to represent redundant patterns across frequency with similar features, and the tensor factorisation is able to isolate these patterns in an unsupervised way. The method overcomes the limitation of conventional nonnegative matrix factorisation algorithms to utilise the redundancy of sounds in frequency. In the proposed method, separated sounds are synthesised by filtering the mixture signal with a Wiener-like filter generated from the estimated tensor factors. The proposed method was compared to conventional algorithms in unsupervised separation of mixtures of speech and music. Improved signal to distortion ratios were obtained compared to standard non-negative matrix factorisation and non-negative matrix deconvolution.