English

Optimal Tuning of Two-Dimensional Keyboards

Sound 2017-11-16 v1 Audio and Speech Processing

Abstract

We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and provide exact solutions for many new keyboard dimensions. We also show that an optimal tuning for harmonic approximation can be obtained for any keyboard of given width, provided sufficiently many rows of octaves.

Keywords

Cite

@article{arxiv.1711.05260,
  title  = {Optimal Tuning of Two-Dimensional Keyboards},
  author = {Aricca Bannerman and James Emington and Anil Venkatesh},
  journal= {arXiv preprint arXiv:1711.05260},
  year   = {2017}
}

Comments

14 page, 3 figures

R2 v1 2026-06-22T22:45:57.385Z