Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 20 min ago
PreprintarXiv licencearXiv

A General Approach to Enharmonicism

  • Caleb Scott Alons
Open at sourcePDFDOICite

Abstract

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.

Related

  1. Control analysis and synthesis for general control-affine systems
    Cyprien Tamekue, Shinung Ching
    SIAM Journal on Control and OptimizationPeer-reviewedLicence not statedAnalysis & PDEsDynamical systemsHAL
  2. A general theorem in spectral extremal graph theory
    John Byrne, Dheer Noal Desai, Michael Tait
    Transactions of the American Mathematical SocietyPeer-reviewedLicence not statedFull text24 citedCombinatorics & discrete mathematicsGeometry & topologyOpenAlex
  3. Bernstein’s inequalities for general Markov chains
    Bai Jiang, Qiang Sun, Jianqing Fan A B
    Annales de l Institut Henri Poincaré Probabilités et StatistiquesPeer-reviewedLicence not statedFull text40 citedStatisticsOpenAlex
  4. Design-Based Confidence Sequences: A General Approach to Risk Mitigation in Panel Experiments
    Dae Woong Ham, Michael Lindon, Martin P. Tingley +1
    Management SciencePeer-reviewedLicence not stated19 citedStatisticsOpenAlex
  5. Local minima of the empirical risk in high dimension: General theorems and convex examples
    kiana Asgari, Andrea Montanari A, Basil Saeed
    The Annals of StatisticsPeer-reviewedLicence not statedFull text14 citedStatisticsOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{alons2026general,
  title = {{A General Approach to Enharmonicism}},
  author = {Caleb Scott Alons},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10603},
  eprint = {2609.10603},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10603},
}
RIS
TY  - UNPB
TI  - A General Approach to Enharmonicism
AU  - Caleb Scott Alons
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.10603
UR  - https://arxiv.org/abs/2609.10603
AB  - 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.
ER  -