Acoustic Decaphonic Piano: Calculating Safe Retuningsfrom 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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Fundamental Technological Research Polish Academy of Sciences
2025-08-01
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| Series: | Archives of Acoustics |
| Subjects: | |
| Online Access: | https://acoustics.ippt.pan.pl/index.php/aa/article/view/4214 |
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| Summary: | 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.
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| ISSN: | 0137-5075 2300-262X |