Pitch-DFT encoding best aligns a Bach VAE with circle of fifths

Carvalho & Bernardes train an LSTM-VAE on 371 Bach chorales, comparing six input encodings (piano roll, MIDI-like, ABC, Tonnetz, and two DFT-based) for circle-of-fifths alignment of the PCA-reduced latent space [carvalho-bernardes-2023-tonal-vae-latent-spaces] Alignment is quantified via Davis-Bouldin, Dunn Index, and a circular Kendall's Tau against the true circle-of-fifths sequence [carvalho-bernardes-2023-tonal-vae-latent-spaces] Pitch DFT wins on all three metrics (Kendall's Tau .44+/-.32 vs next-best .15+/-.14), with ~16% of chorales reaching |Tau|>.9, disproportionately major-key and longer pieces [carvalho-bernardes-2023-tonal-vae-latent-spaces] Tonal alignment dissociates from reconstruction quality: ABC reconstructs best (82.6%) but aligns weakly (Tau .11+/-.09), while worse-reconstructing Pitch DFT (75.6%) aligns best [carvalho-bernardes-2023-tonal-vae-latent-spaces] The choice of input encoding materially determines whether circle-of-fifths geometry emerges at all; the study is entirely correlational with no intervention [carvalho-bernardes-2023-tonal-vae-latent-spaces]