{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T07:40:12Z","timestamp":1785829212525,"version":"3.56.0"},"reference-count":40,"publisher":"The Royal Society","issue":"1835","license":[{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/-\/media\/journals\/author\/Licence-to-Publish-20062019-final.pdf"},{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"},{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,10,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Rhythms are important for understanding coordinated behaviours in ecological systems. The repetitive nature of rhythms affords prediction, planning of movements and coordination of processes within and between individuals. A major challenge is to understand complex forms of coordination when they differ from complete synchronization. By expressing phase as ratio of a cycle, we adapted levels of the Farey tree as a metric of complexity mapped to the range between in-phase and anti-phase synchronization. In a bimanual tapping task, this revealed an increase of variability with ratio complexity, a range of hidden and unstable yet measurable modes, and a rank-frequency scaling law across these modes. We use the phase-attractive circle map to propose an interpretation of these findings in terms of hierarchical cross-frequency coupling (CFC). We also consider the tendency for small-integer attractors in the single-hand repeated tapping of three-interval rhythms reported in the literature. The phase-attractive circle map has wider basins of attractions for such ratios. This work motivates the question whether CFC intrinsic to neural dynamics implements low-level priors for timing and coordination and thus becomes involved in phenomena as diverse as attractor states in bimanual coordination and the cross-cultural tendency for musical rhythms to have simple interval ratios.<\/jats:p>\n                  <jats:p>This article is part of the theme issue \u2018Synchrony and rhythm interaction: from the brain to behavioural ecology\u2019.<\/jats:p>","DOI":"10.1098\/rstb.2020.0333","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T03:10:50Z","timestamp":1629688250000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Cross-frequency coupling explains the preference for simple ratios in rhythmic behaviour and the relative stability across non-synchronous patterns"],"prefix":"10.1098","volume":"376","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5543-360X","authenticated-orcid":true,"given":"Dobromir","family":"Dotov","sequence":"first","affiliation":[{"name":"LIVELab 1 , ,"},{"name":"McMaster University 1 , ,"},{"name":"1280 Main Street West, Hamilton, Ontario, Canada L8S4K1 1 , ,"},{"name":"Psychology, Neuroscience and Behaviour 2 , ,"},{"name":"McMaster University 2 , ,"},{"name":"Ontario, Canada 2 , ,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3397-2079","authenticated-orcid":true,"given":"Laurel J.","family":"Trainor","sequence":"additional","affiliation":[{"name":"LIVELab 1 , ,"},{"name":"McMaster University 1 , ,"},{"name":"1280 Main Street West, Hamilton, Ontario, Canada L8S4K1 1 , ,"},{"name":"Psychology, Neuroscience and Behaviour 2 , ,"},{"name":"McMaster University 2 , ,"},{"name":"Ontario, Canada 2 , ,"},{"name":"Rotman Research Institute 3 ,"},{"name":"Toronto, Canada 3 ,"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2021,8,23]]},"reference":[{"key":"2026010105342039000_RSTB20200333C1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1093\/biolinnean\/blx096","article-title":"Evolution of synchronies in insect choruses","volume":"122","author":"Greenfield","year":"2017","journal-title":"Biol. 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