Nonlinear dynamic processes are fundamental to the behavior of acoustic musical instruments, as is well explored in the case of sound production. Such processes may have profound and under-explored implications for how musicians interact with instruments, however. Although nonlinear dynamic processes are ubiquitous in acoustic instruments, they are present in digital musical tools only if explicitly implemented. Thus, an important resource with potentially major effects on how musicians interact with acoustic instruments is typically absent in the way musicians interact with digital instruments. Twenty-four interviews with free-improvising musicians were conducted to explore the role that nonlinear dynamics play in the participants' musical practices and to understand how such processes can afford distinctive methods of creative exploration. Thematic analysis of the interview data is used to demonstrate the potential for nonlinear dynamic processes to provide repeatable, learnable, controllable, and explorable interactions, and to establish a vocabulary for exploring nonlinear dynamic interactions. Two related approaches to engaging with nonlinear dynamic behaviors are elaborated: edge-like interaction, which involves the creative use of critical thresholds; and deep exploration, which involves exploring the virtually unlimited subtleties of a small control region. The elaboration of these approaches provides an important bridge that connects the concrete descriptions of interaction in musical practices, on the one hand, to the more-abstract mathematical formulation of nonlinear dynamic systems, on the other.

中文翻译：

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非线性动力学在音乐家与数字和声学乐器交互中的作用

非线性动态过程是原声乐器行为的基础，这在声音制作中得到了很好的探索。然而，这些过程可能对音乐家如何与乐器互动产生深远的影响。尽管非线性动态过程在声学乐器中无处不在，但只有在明确实施的情况下，它们才会出现在数字音乐工具中。因此，在音乐家与数字乐器的互动方式中，通常不存在对音乐家如何与原声乐器互动产生重大影响的重要资源。对自由即兴音乐家进行了 24 次采访，以探索非线性动力学在参与者音乐实践中的作用，并了解这些过程如何能够提供独特的创造性探索方法。访谈数据的主题分析用于展示非线性动态过程提供可重复、可学习、可控和可探索的交互的潜力，并建立用于探索非线性动态交互的词汇表。详细阐述了处理非线性动态行为的两种相关方法：边缘式交互，包括创造性地使用临界阈值；和深入探索，包括探索一个小控制区域几乎无限的微妙之处。这些方法的阐述提供了一个重要的桥梁，一方面将音乐实践中相互作用的具体描述与非线性动态系统的更抽象的数学公式联系起来，另一方面。