Timing by Skilled Musicians

Sternberg, Saul; Knoll, Ronald L.; ZukoJsky, Paul

doi:10.1016/b978-0-12-213562-0.50011-5

Cited by 59 publications

(50 citation statements)

References 40 publications

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“…The methods studied here are appropriate when the 2AFC task is used to generate a psychometric function to assess discrimination or detection performance. Although such psychometric functions are usually generated by the method of constant stimuli (e.g., Yeshurun, 1999), they can also be generated by adaptive procedures (e.g., Rinkenauer, Mattes, & Ulrich, 1999;Sternberg et al, 1982). It remains to be seen, however, how well the method will do when used with data obtained from adaptive psychophysical procedures (Klein, 2001).…”

Section: Discussion and Possible Extensionsmentioning

confidence: 99%

“…, k), associated with each stimulus value. 5 Then it can be shown (Church & Cobb, 1973;Sternberg et al, 1982, The values x 0 and x kϩ1 are chosen such that one can assume p 0 ϭ 0 and p kϩ1 ϭ 1.…”

Section: Extending the Spearman-kärber Methods To 2afc Tasksmentioning

confidence: 99%

“…The mean generally has better statistical properties than the median (e.g., Sen, 1985;Stuart & Ord, 1987), and the mean is known to be a more stable estimator than the median for psychometric functions in yes-no tasks (e.g., Church & Cobb, 1973;Miller & Ulrich, 2001). In addition, the mean may be more appropriate than the median for testing theoretical models that make predictions about the moments, rather than the percentiles, of psychometric functions (e.g., Mortensen, 2002;Sternberg & Knoll, 1973;Sternberg, Knoll, & Zukofsky, 1982;Ulrich, 1987). Of course, it does not matter whether the median or the mean is used if the assumed distribution F(x) is symmetric, because in that case, these two values are identical.…”

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confidence: 99%

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Threshold estimation in two-alternative forced-choice (2AFC) tasks: The Spearman-Kärber method

Ulrich

Miller

2004

Perception & Psychophysics

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The Spearman-Kärber method can be used to estimate the threshold value or difference limen in two-alternative forced-choice tasks. This method yields a simple estimator for the difference limen and its standard error, so that both can be calculated with a pocket calculator. In contrast to previous estimators, the present approach does not require any assumptions about the shape of the true underlying psychometric function. The performance of this new nonparametric estimator is compared with the standard technique of probit analysis. The Spearman-Kärber method appears to be a valuable addition to the toolbox of psychophysical methods, because it is most accurate for estimating the mean (i.e., absolute and difference thresholds) and dispersion of the psychometric function, although it is not optimal for estimating percentile-based parameters of this function.

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Section: Discussion and Possible Extensionsmentioning

confidence: 99%

Section: Extending the Spearman-kärber Methods To 2afc Tasksmentioning

confidence: 99%

mentioning

confidence: 99%

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Threshold estimation in two-alternative forced-choice (2AFC) tasks: The Spearman-Kärber method

Ulrich

Miller

2004

Perception & Psychophysics

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“…Furthermore, not only is there dependence on context in rhythm perception: without context, categorisation is hardly possible. Sternberg et al (1982) showed that even experienced musicians have difficulty in recognising and reproducing relatively simple ratios like 1 X 5 or 3 X 4 if they are presented in isolation. While in music practice these ratios (and even much more complex ones) are quite common, one always needs some context to be able to recognise and perform them well.…”

Section: Introductionmentioning

confidence: 99%

The Formation of Rhythmic Categories and Metric Priming

2003

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Abstract. Two experiments on categorical rhythm perception are reported, the object of which was to investigate how listeners perceive discrete rhythmic categories while listening to rhythms performed on a continuous time scale. This is studied by considering the space of all temporal patterns (all possible rhythms made up of three intervals) and how they, in perception, are partitioned into categories, ie where the boundaries of these categories are located. This process of categorisation is formalised as the mapping from the continuous space of a series of time intervals to a discrete, symbolic domain of integer-ratio sequences. The methodological framework uses concepts from mathematics and psychology (eg convexity and entropy) that allow precise characterisations of the empirical results.In the first experiment, twenty-nine participants performed an identification task with 66 rhythmic stimuli (a systematic sampling of the performance space). The results show that listeners do not just perceive the time intervals between onsets of sounds as placed in a homogeneous continuum. Instead, they can reliably identify rhythmic categories, as a chronotopic time clumping map reveals. In a second experiment, the effect of metric priming was studied by presenting the same stimuli but preceded with a duple or triple metre subdivision. It is shown that presenting patterns in the context of a metre has a large effect on rhythmic categorisation: the presence of a specific musical metre primes the perception of specific rhythmic patterns.

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“…But to repeat, these patterns do not represent actual perception, although expert professional musicians who can image a performance in terms of score notation and who learned as conservatory students to transcribe dictation according to notational prescriptions may categorically believe that these are exactly the durations that they are hearing. But only mechanically produced stimuli replicate notation absolutely, and even artists have trouble playing beat divisions in a proportionately accurate way (Sternberg, Knoll, & Zukofsky, 1982) …”

Section: Durational Elements As Length Rate Speed and Pacementioning

confidence: 99%

Toward a Unified Theory of the I-R Model (Part 1)

Narmour

2015

Music Perception

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By extensively revising the I-R model of melody (Meyer, 1973; Narmour, 1984, 1989, 1990, 1991a, 1991b, 1992, 1996, 2000) we can explain the structural functions of many musical parameters. Here I will deal with melodic interval, registral direction, pitch height, scale-step (major and minor), duration (interval, length, rate, speed, and pace), tempo, dynamics (loudness), and texture (saving the other parameters for a later essay). By reconceptualizing the model’s core concept of functional directionality within parametric scales, only three isomorphic structural analogues become cognitively necessary, namely, process (and its variant duplication), reversal, and return. Attached signs (0, ∼, −, and +) augment the main symbols (P, D, and R) so as to track strength of implication, realization, and denial. A new theory of rhythmic structure is put forth. And with an aim toward theoretical unification, the reconfigured model confronts the combinatorial complexities of parametric interactions and offers convincing interpretations of congruence and noncongruence—the primary sources of musical affects. Works of Brahms, Debussy, Mussorgsky-Ravel, and Schoenberg are analyzed.

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Timing by Skilled Musicians

Cited by 59 publications

References 40 publications

Threshold estimation in two-alternative forced-choice (2AFC) tasks: The Spearman-Kärber method

Threshold estimation in two-alternative forced-choice (2AFC) tasks: The Spearman-Kärber method

The Formation of Rhythmic Categories and Metric Priming

Toward a Unified Theory of the I-R Model (Part 1)

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