Perceptually Motivated Alignment and Interpolation of Pitch-Aligned Time-Frequency Representations

Audio-to-score alignment is a long-standing challenge in music information retrieval and arguably the most widely applicable alignment task for music research. Alignment algorithms match two versions of a piece of music, and for this to work these versions need to be in comparable formats. Audio-to-audio alignment matches audio features; when matching audio files to scores, they must either synthesize the score or derive audio-like features by means of piano rolls or similar feature sequences. Symbolic alignment, by contrast, matches symbolically encoded notes; in an audio-to-score scenario these would be obtained by a transcription of the audio file. In this article, we present an algorithm that bridges audio-like and symbol-level features directly. Sequential audio features encoding onset and spectral activation are matched to score positions by a bespoke dynamic programming-based matching algorithm derived from symbolic alignment methods. The resulting method is both precise - surpassing widely used audio-to-audio approaches based on synthesized scores -, and remains flexible in its digital signal processing components, i.e., the method is adaptable to diverse timbral characteristics without requiring a separate transcription model. Furthermore it inherits some of the symbolic alignment runtime advantages with an algorithmic complexity that is at worst linear in the length of the (typically short) symbolic score and (typically long) audio feature sequence. In the following sections, we provide a detailed algorithm description and evaluate its alignment quality on a large-scale dataset of solo piano recordings.

How can we understand what a music foundation model has learned internally? Most interpretability approaches, such as probing and Sparse Autoencoders (SAEs), focus on identifying individual features with minimal structural assumptions. We argue that many concepts are better understood as structured relations rather than isolated features. This is especially prominent in music, where tonal structures are organized in the space of pitch and time. For example, concepts such as chords or keys are naturally expressed as structured sets (e.g., the 12 transpositions of a chord or the diatonic system within a key), rather than isolated features. In this study, we shift from feature identification to structure-based analysis, asking whether the learned inner representations of music foundation model emerge as organized structures over features. To this end, we introduce a framework that uses pitch transposition as an inductive bias to induce ordered orbits via multi-view SAE alignment. Concretely, we generate pitch-shifted input pairs and align their SAE representations to discover structured groups of pitch-related features. Experimental results show that this approach recovers orbit structures corresponding to chords, keys, and melodic patterns across two state-of-the-art music foundation models, while requiring only minimal grounding (e.g., a few anchor examples) to interpret entire concept families.

Conventional music representations describe acoustic energy over time and frequency but do not explicitly expose relations among simultaneous frequency components. We introduce the Dissonance Spectrum (DS), a nonnegative time--frequency representation that applies a tolerance-based rational pitch-relation kernel with logarithmic harmonic distance to a constant-Q spectrum and attributes aggregate pairwise interactions back to individual frequency bins. Controlled music-theory tests show strong ordinal agreement for intervals, harmonic-function connections, and church modes, and weaker but significant agreement across diverse chord voicings. DS is then encoded by a lightweight parallel branch whose zero-initialized residual projection preserves the baseline function at initialization. Across six paired training seeds in open-ended music question answering and categorical and dimensional music emotion recognition, DS obtains the highest mean on every reported endpoint relative to the unchanged baseline, a parameter-matched Gaussian-input branch, and an architecture-matched magnitude-CQT branch. These results support DS as an interpretable, complementary representation, while listener-specific perception and broader task coverage remain open problems.