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Furthermore, the state transfer matrix of HMM often makes the fingering of notes in compact scales unplayable without moving the hands. The direct adoption of notes interferes with mapping between specific pitches and the corresponding fingering. Inspired by human annotation and the note span constraints used in rule-based methods (in which fingering knowledge is acquired from span), we developed a model by which to match pitch difference and finger sequences (PdF). Playable fingering is achieved by combining learned finger-transfer knowledge with priori finger-transfer knowledge. The playability of the model was evaluated using a novel index, referred to as the irrational fingering rate (IFR). Experiment results demonstrate that the proposed model outperforms the third-order hidden Markov finger annotation model in terms of average match rate (by 4.06%) and highest match rate (by 2.87%). The proposed scheme also resolves the unplayable-without-hand-movement problem in compact scales.<\/jats:p>","DOI":"10.1186\/s13636-022-00237-8","type":"journal-article","created":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T11:06:33Z","timestamp":1649675193000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Estimation of playable piano fingering by pitch-difference fingering match model"],"prefix":"10.1186","volume":"2022","author":[{"given":"Xin","family":"Guan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyue","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"237_CR1","doi-asserted-by":"crossref","unstructured":"C. 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Automatic decision of piano fingering based on hidden Markov models (Hyderabad, 2007), pp. 6\u201312."},{"key":"237_CR11","unstructured":"E. Nakamura, N. Ono, S. Sagayama, in Paper presented at the 15th International Society for Music Information Retrieval Conference, ISMIR 2014. Merged-output HMM for piano fingering of both hands (Taipei, 2014), pp. 27\u201331."},{"key":"237_CR12","unstructured":"L. Qiang, L. Chenxi, G. Xin, Automatic fingering annotation for piano score via judgement-HMM and improved viterbi. J Tianjin Univ. (Sci. Technol.)53(08), 2020."},{"issue":"8","key":"237_CR13","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S. Hochreiter","year":"1997","unstructured":"S. Hochreiter, J. Schmidhuber, Long short-term memory. Neural Comput.9(8), 1735\u20131780 (1997).","journal-title":"Neural Comput."},{"key":"237_CR14","unstructured":"D. Kingma, J. 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