Infinite Canons: Maximally Self-Similar Melodic Lines and Canons with Infinite Solutions

We propose a general approach to enharmonicism within syntactic music theory; that is, we formalize several abstract structures of enharmonicism without any acoustic considerations. The structures of concern to this paper are constructed from diatonics, chromatics, and enharmonics, and we seek to present a general enharmonic theory that builds upon Hook's enharmonic theory published in "Enharmonic Systems: A Theory of Key Signatures, Enharmonic Equivalence and Diatonicism" (2007). We also propose that the two criteria of reflection and maximal evenness can be used to determine whether an arbitrary enharmonic system is musically practical. Moreover, we argue that preferential treatment of the standard enharmonic system (SES) can be motivated from an abstract mathematical perspective divorced from pitch consideration and conventional acoustic constructions of SES.

Architecture and music have been linked through proportion and temporal structure, yet architectural geometry is rarely viewed as a source of generative music. Revisiting Xenakis' one-directional transformation from string glissandi in Metastaseis to the ruled surfaces of the Philips Pavilion, we invert this workflow and sonify the completed Pavilion as a temporal composition. We reconstruct the Pavilion as nine ruled surfaces, extract their governing ruling lines, and subdivide each surface into structural lines and spatial sampling points. Four evenly spaced ruling lines per surface generate continuous string glissandi, while 3357 sampled points develop five density-based energy blocks and a sparse brass and woodwind subsequence. Implemented in Python, the system produces MIDI rendered in Ableton Live, accompanied by a real-time 3D visualization that reveals architectural motion, stasis, and structural contrast through sound and image. In general, this work paves the way for the transfer of architectural geometry as a performable musical structure, extending Xenakis's architectural and musical thinking to sonification and interactive music practice.

We present vega-mir, an open-source Python library that bundles nine information-theoretic and statistical metrics for the analysis of symbolic music corpora behind a small, tested, citable API, and demonstrates two of them at corpus scale in case studies not addressed by the upstream Cygnus paper. Of the nine metrics, three (Shannon entropy, Kullback-Leibler divergence, Zipfian fits) were deployed in the companion Cygnus arXiv preprint; two (network analysis on chord-transition graphs and spectral analysis of rubato curves) are deployed in full case studies here; the four remaining (multi-dimensional Gini, chi-squared stationarity, Higuchi fractal dimension, interval distribution) are validated against analytic anchors and exercised as sanity checks on a bundled 8-composer dataset. The two case studies yield two main observations. First, on the fourteen MAESTRO composers with N >= 10 pieces, the PageRank value of the gravity-centre node correlates with the marginal Kullback-Leibler distance at rho = 0.61 (Spearman, composer-level jackknife N = 14); the categorical gravity-centre identity takes five distinct values across the corpus but is not itself correlated with marginal KL (rho = 0.13, p = 0.21). Second, on the 247-piece Bach multi-master corpus (Schiff, Gould, Richter), Gould holds the highest periodicity ratio of the three performers, not the lowest, inverting the cliché that low scalar rubato reads as "metronomic": Gould's rubato is small in amplitude but structured in time, with a median dominant period of 66 beats against Schiff's 102 and Richter's 104.