{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:36:06Z","timestamp":1762079766714,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T00:00:00Z","timestamp":1605225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["POCI-01-0145-FEDER-031380"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031380"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010790","name":"Erasmus+","doi-asserted-by":"publisher","award":["ES01-KA201-064933"],"award-info":[{"award-number":["ES01-KA201-064933"]}],"id":[{"id":"10.13039\/501100010790","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In tonal music, musical tension is strongly associated with musical expression, particularly with expectations and emotions. Most listeners are able to perceive musical tension subjectively, yet musical tension is difficult to be measured objectively, as it is connected with musical parameters such as rhythm, dynamics, melody, harmony, and timbre. Musical tension specifically associated with melodic and harmonic motion is called tonal tension. In this article, we are interested in perceived changes of tonal tension over time for chord progressions, dubbed tonal tension profiles. We propose an objective measure capable of capturing tension profile according to different tonal music parameters, namely, tonal distance, dissonance, voice leading, and hierarchical tension. We performed two experiments to validate the proposed model of tonal tension profile and compared against Lerdahl\u2019s model and MorpheuS across 12 chord progressions. Our results show that the considered four tonal parameters contribute differently to the perception of tonal tension. In our model, their relative importance adopts the following weights, summing to unity: dissonance (0.402), hierarchical tension (0.246), tonal distance (0.202), and voice leading (0.193). The assumption that listeners perceive global changes in tonal tension as prototypical profiles is strongly suggested in our results, which outperform the state-of-the-art models.<\/jats:p>","DOI":"10.3390\/e22111291","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T10:32:47Z","timestamp":1605263567000},"page":"1291","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Computational Model of Tonal Tension Profile of Chord Progressions in the Tonal Interval Space"],"prefix":"10.3390","volume":"22","author":[{"given":"Mar\u00eda","family":"Navarro-C\u00e1ceres","sequence":"first","affiliation":[{"name":"Department of Computer Sciences, University of Salamanca, Pza de los Ca\u00eddos, s\/n, 37007 Salamanca, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5119-8964","authenticated-orcid":false,"given":"Marcelo","family":"Caetano","sequence":"additional","affiliation":[{"name":"Schulich School of Music &amp; CIRMMT, McGill University, 555 Sherbrooke Street West, Montr\u00e9al, QC H3A 1E3, Canada"},{"name":"Aix Marseille Univ, CNRS, PRISM (Perception, Representations, Image, Sound, Music), Marseille, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3884-2687","authenticated-orcid":false,"given":"Gilberto","family":"Bernardes","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and INESC TEC, University of Porto, 4200-465 Porto, Portugal"}]},{"given":"Mercedes","family":"S\u00e1nchez-Barba","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Salamanca, Pza de la Merced, s\/n, 37007 Salamanca, Spain"}]},{"given":"Javier","family":"Merch\u00e1n S\u00e1nchez-Jara","sequence":"additional","affiliation":[{"name":"Department of Didactics of Musical, Plastic and Corporal Expression, University of Salamanca, Calle Madrigal de las Altas Torres, 3, 05003 Avila, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1525\/mp.2007.24.4.329","article-title":"Modeling tonal tension","volume":"24","author":"Lerdahl","year":"2007","journal-title":"Music Percept. 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