Perceiving and Distinguishing Simple Timespan Ratios without Metric Reinforcement

Tapping to Carter: Mensural Determinacy in Complex Rhythmic Sequences

“…The lower degree of mensural determinacy suggested by the ambiguous phase profile of the right-hand layer, which is characterized by frequent changes in the rate of surface (first-order) events, is consistent with previous findings that pulse finding appears to depend mostly on first-order relationships (e.g., Demany & Semal, 2002). The higher level of mensural determinacy of the left-hand layer and the observed differential effect of accents also provides further evidence of the influence of accent on the perception of second-order periodicity (Jones & Pfordresher, 1997); this is consistent with the finding that an unmetered series of acoustic events can be perceived as more regular if streaming (via loudness or pitch distance) gives rise to second-order periodicity (Carson, 2007).…”

“…One notable example is Carson (2007), who investigated SOP in non-metric contexts. Using newly composed materials with nonisochronous sequences that exhibited "dissonant" (large-sum) first-order ratios (e.g., 11:2:10:16), but "consonant" (small-sum) second-order ratios (e.g., 1:2) in a range of tempi, Carson found that participants were able to detect underlying periodicities (referred to as "pulsedness") under certain loudness and pitch streaming conditions, with loudness and pitch distance resulting in higher "pulse confidence" ratings.…”

“…[5] Rhythmic complexity is commonly operationalized following structural criteria that rest on some form of isochronicity. [6] One widespread approach to measure complexity is based on the specific IOI ratios exhibited by a given rhythmic sequence, with the identity ratio (1:1) judged to be the simplest, followed by simple integer ratios (2:1, 3:1, and 4:1), and non-integer ratios such as 3:2 or 4:3; an alternative formulation of this principle involves a contrast between small-sum and large-sum ratios (e.g., Carson, 2007). The preference for smaller integer ratios has been linked to cognitive limits involving working memory (Drake & Bertrand, 2003), and it would seem that the total duration of a rhythmic pattern also plays a role.…”