In this paper we present a 12-dimensional tonal space in the context of the Tonnetz, Chew’s Spiral Array, and Harte’s 6-dimensional Tonal Centroid Space. The proposed Tonal Interval Space is calculated as the weighted Discrete Fourier Transform of normalized 12-element chroma vectors, which we represent as six circles covering the set of all possible pitch intervals in the chroma space. By weighting the contribution of each circle (and hence pitch interval) independently, we can create a space in which angular and Euclidean distances among pitches, chords, and regions concur with music theory principles. Furthermore, the Euclidean distance of pitch configurations from the centre of the space acts as an indicator of consonance.

The amplitude modulations of musical instrument sounds and speech are important perceptual cues. Accurate estimation of the amplitude, or equivalently energy, envelope of a time-domain signal (waveform) is not a trivial task, though. Ideally, the amplitude envelope should outline the waveform connecting the main peaks and avoiding over fitting. In this work we propose a method to obtain a smooth function that approximately matches the main peaks of the waveform using true envelope estimation, dubbed true amplitude envelope. True envelope is a cepstral smoothing technique that has been shown to outperform traditional envelope estimation techniques both in accuracy of estimation and ease of order selection. True amplitude envelope gives a reliable estimation that follows closely sudden variations in amplitude and avoids ripples in more stable regions with near optimal order selection depending on the fundamental frequency of the signal.

In tonal music, musical tension is strongly associated with musical expression, particularly with expectations and emotions. Most listeners are able to perceive musical tension subjectively, yet musical tension is difficult to be measured objectively, as it is connected with musical parameters such as rhythm, dynamics, melody, harmony, and timbre. Musical tension specifically associated with melodic and harmonic motion is called tonal tension. In this article, we are interested in perceived changes of tonal tension over time for chord progressions, dubbed tonal tension profiles. We propose an objective measure capable of capturing tension profile according to different tonal music parameters, namely, tonal distance, dissonance, voice leading, and hierarchical tension. We performed two experiments to validate the proposed model of tonal tension profile and compared against Lerdahl’s model and MorpheuS across 12 chord progressions. Our results show that the considered four tonal parameters contribute differently to the perception of tonal tension. In our model, their relative importance adopts the following weights, summing to unity: dissonance (0.402), hierarchical tension (0.246), tonal distance (0.202), and voice leading (0.193). The assumption that listeners perceive global changes in tonal tension as prototypical profiles is strongly suggested in our results, which outperform the state-of-the-art models.

Sound morphing is a transformation that gradually blurs the distinction between the source and target sounds. For musical instrument sounds, the morph must operate across timbre dimensions to create the auditory illusion of hybrid musical instruments. The ultimate goal of sound morphing is to perform perceptually linear transitions, which requires an appropriate model to represent the sounds being morphed and an interpolation function to obtain intermediate sounds. Typically, morphing techniques directly interpolate the parameters of the sound model without considering the perceptual impact or evaluating the results. Perceptual evaluations are cumbersome and not always conclusive. In this work, we seek parameters of a sound model that favor linear variation of perceptually motivated temporal and spectral features used to guide the morph towards more perceptually linear results. The requirement of linear variation of feature values gives rise to objective evaluation criteria for sound morphing. We investigate several spectral envelope morphing techniques to determine which spectral representation renders the most linear transformation in the spectral shape feature domain. We found that interpolation of line spectral frequencies gives the most linear spectral envelope morphs. Analogously, we study temporal envelope morphing techniques and we concluded that interpolation of cepstral coefficients results in the most linear temporal envelope morph.