This article uses phenomenological analysis to examine pitch-related elements in commercial popular music, focussing on Primaal, a successful electronic music brand whose works have been licensed by major international companies. Working in collaboration with the producers, we identify musical parameters related to pitch and document how their treatment differs radically from Western classical music conventions. Central to Primaal's aesthetic is the deliberate cultivation of pitch uncertainty, achieved through multiple techniques: tone inharmonicity, quasi-harmonic tones designed to evoke multiple simultaneous pitches, strategic boosting of upper partials, and continuous frequency trajectories inspired by the Roland TR-808 bass drum. Rather than discrete notes, pitches are distributed around scale degrees ('poles'), with the distribution width serving as an expressive parameter. The music is organised modally rather than tonally, typically focussing on a few degrees with one functioning as a 'final'. We show how these pitch-related parameters articulate both large-scale and small-scale musical structure. Signal analysis, supported by psychoacoustic weighting, serves as our transcription method, avoiding the biases inherent in score-based notation. The findings contribute to music analysis, music information retrieval, computational creativity, and psychoacoustics, suggesting that pitch in contemporary popular music often operates as a continuous, multidimensional phenomenon that resists reduction to discrete note representations.
This paper presents a web-based application for navigating and composing microtonal harmony, built on the Harmonic Eigenspace, a four-dimensional psychoacoustically grounded space in which tetrad chord types are located by their spectral dissonance profiles, computed with Sethares's roughness/dissonance model. The coordinate system is transposition-invariant: a coordinate triple (α, e̱ṯa̱, γ) locates the three upper notes in relation to the root, so a chord quality corresponds to a direction in the space, the invariant ray along which transposition acts, while the root frequency sets the scale. The dissonance field over these coordinates can be computed at any register; the locations of its local minima are register-invariant, as they arise from partial-coincidence ratio conditions. The dissonance volume contains 100 local minima that align with just-intonation intervals and act as landmarks, organising the space into basins around the most consonant tetrads. We embed tetrads from three tonal equal temperaments as discrete lattices within this continuous volume. The application presents this space through two components: the Harmonic Eigenspace as a navigable 3D visualisation of the dissonance volume in which all nodes are playable, and a Modal Studio that extends modal interchange logic to the ten-gradation interval vocabulary of 53-TET. The application also functions as a MIDI controller with MIDI Polyphonic Expression support, usable in any digital audio workstation that supports this format. A listening study with 31 participants used both scenes of the application: listeners first rated isolated 53-TET chords alongside chords familiar from Western practice, such as the maj7 and the m7; they then rated chord progressions composed in the Modal Studio, measuring their acceptance or rejection of microtonal progressions heard for the first time.
Automatic music generation has a long history. One significant example from the 1600s is Athanasius Kircher's concept of a music-generating machine. Today, automatic music generation has advanced significantly thanks to the rapid growth of machine learning and AI techniques. While Kircher's machine was quite primitive, relying on direct combinatorial methods, the core idea shares similarities with modern AI algorithms for music composition. In this study, we focus on Kircher's music theory for automatic generation, specifically his set of musical arrays, Syntagma, and the creation of Kircher-style music not found in his original tables. The number of Pinax he provided is limited and insufficient for further training to generate more phrase blocks. To enhance training, we first transform the Pinax data into image form and apply a diffusion model. For this transformation, we use nearest-neighbour interpolation, paying special attention to boundary values in the images. By employing the diffusion model, we demonstrate that it is possible to generate new phrase blocks beyond Kircher's original set. This approach not only enables the creation of a wider variety of Kircher-style music but also potentially provides new insights through the generated compositions.
Not all perceived (experienced) pitches in a chord correspond to notes. A simple masking model predicts that a typical C major triad has audible partials at pitch classes B and D (third harmonics of E and G), regardless of voicing; an A minor triad, at G, B, and D. In a listening experiment, two successive chords were heard in each trial. The chords were identical except that one partial was removed from one of them. Participants rated how much the chords differed. We tested major and minor triads in root position and inversion, augmented and diminished triads, other common trichords ([025]/CDF, [035]/DFG), and one tetrachord (major-minor 7th). All chords were in close position on C4. To simplify the stimuli and allow for testing of a simple model, chord partials had equal physical amplitude, were tuned to 12-tone equal temperament, and were included only if predicted by a simple psychoacoustic model to be audible (perceptually relevant). We predicted and demonstrated empirically that common musical trichords have 10 to 15 audible partials, some of whose pitch classes deviate from chord tones. Results imply that notes commonly added to trichords to form tetrachords (e.g. 7ths and 9ths) often correspond to spectral or virtual pitches in the original trichord. Commonly added tones also minimally increase dissonance. Results did not correlate with predicted spectral or virtual pitch salience according to Ernst Terhardt's pitch algorithm, perhaps because it neglects complex temporal effects.
