Does music performance allude to locomotion?: A model of final ritardandi derived from measurements of stopping runners
Does music performance allude to locomotion?: A model of final ritardandi derived from measurements of stopping runners
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DOI：
10.1121/1.426687
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发表时间：
1999-03-01
影响因子：
2.4
通讯作者：
Sundberg, J
中科院分区：
文献类型：
--
作者：
Friberg, A;Sundberg, J
本研究通过比较跑步的停止和一段音乐的终止，探讨了音乐和运动密切相关的普遍假设。录制专业舞者在不同减速条件下停止奔跑的视频，估算体速、步频和步长的瞬时值。在编舞小组高度评价美学质量的减速中，平均身体速度可以通过时间的平方根函数来近似，这相当于位置的立方根函数。这意味着动能和时间之间存在线性关系，即恒定的制动功率。平均身体速度与音乐表演中最后的 ritardandi 的平均节奏模式有着惊人的相似性。恒定的制动功率被用作描述最终 ritardandi 中节奏变化和跑步者减速中速度变化的模型的基础。通过假设速度和音乐节奏相等，实现了物理运动到音乐节奏的转换。模型中添加了两个参数，以解释在个体 ritardandi 和个体减速度中观察到的变化：(1) 控制曲率的参数 q，q = 3 对应于跑步者的减速度，(2) 参数 upsilon(end) 分别表示最终速度和节奏值。进行了听力实验，根据具有不同 q 值的模型或替代函数呈现具有最终 ritardandi 的音乐示例。 q = 2 和 q = 3 的模型获得最高评级。在三个函数中，该模型最适合单独测量的 ritardandi 以及单独的减速度。以前用于对与短语相关的节奏变化进行建模的函数（节间持续时间是乐谱位置的二次函数）产生了最低的评分，并且对个体 ritardandi 的拟合最差。因此，结果似乎证实了人们普遍认为的运动和音乐之间的类比。 (C) 1999 年美国声学学会。 [S0001-4966(99)01402-2]。
This investigation explores the common assumption that music and motion are closely related by comparing the stopping of running and the termination of a piece of music. Video recordings were made of professional dancers' stopping from running under different deceleration conditions, and instant values of body velocity, step frequency, and step length were estimated. In decelerations that were highly rated for aesthetic quality by a panel of choreographers, the mean body velocity could be approximated by a square-root function of time, which is equivalent to a cubic-root function of position. This implies a linear relationship between kinetic energy and time, i.e., a constant braking power. The mean body velocity showed a striking similarity with the mean tempo pattern of final ritardandi in music performances. The constant braking power was used as the basis for a model describing both the changes of tempo in final ritardandi and the changes of velocity in runners' decelerations. The translation of physical motion to musical tempo was realized by assuming that velocity and musical tempo are equivalent. Two parameters were added to the model to account for the variation observed in individual ritardandi and in individual decelerations: (1) the parameter q controlling the curvature, q = 3 corresponding to the runners' deceleration, and (2) the parameter upsilon(end) for the final velocity and tempo value, respectively. A listening experiment was carried out presenting music examples with final ritardandi according to the model with different q values or to an alternative function. Highest ratings were obtained for the model with q = 2 and q = 3. Out of three functions, the model produced the best fit to individual measured ritardandi as well as to individual decelerations. A function previously used for modeling phrase-related tempo variations (interonset duration as a quadratic function of score position) produced the lowest ratings and the poorest fits to individual ritardandi. The results thus seem to substantiate the commonly assumed analogies between motion and music. (C) 1999 Acoustical Society of America. [S0001-4966(99)01402-2].