Acoustic Decaphonic Piano: Calculating Safe Retunings from 12-TET to 10-TET and Beyond

This paper presents a method for safe retuning of fixed-pitch string instruments to alternative musical scales with fewer degrees than their original design. Our approach uses a systematic monotonic surjective mapping to assign the existing set of strings to a new, smaller set of pitch classes. The primary goal is to preserve the instrument’s timbre and structural integrity by keeping string tension changes within safe limits. We demonstrate the method on a grand piano and an upright piano retuned from 12-tone equal temperament (12-TET, 12EDO) to 10-tone equal temperament (10-TET, 10EDO). Presented approach may be generalized for retuning from N- to M-step scales (N > M) and to other fixed-pitch string instruments. A grand piano was safely retuned using the proposed method and successfully used in a professional concert.