A Circular Plot for Rhythm Visualization and Analysis
A Circular Plot for Rhythm Visualization and Analysis
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用于节奏可视化和分析的圆形图
DOI：
10.30535/mto.13.3.1
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Fernando Benadon
中科院分区：
文献类型：
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作者：
Fernando Benadon
这篇报告提出了一种绘图方法，旨在帮助研究节奏和节拍音乐的表达时间。(1)我展示了如何使用极坐标系统来描述和分析表达时间的不同特征。大量研究表明，表达时机是节奏产生的核心。Clarke（1999）回顾的证据证实，音乐家经常沿着节拍细分值的连续体放置攻击点，而不是在由格栅间距提供的预定槽上，从而使表演具有表达深度。这种对明确的时间格的背离，如果用标准的音乐符号来表示的话，是不充分的。就像MIDI音序器使用的“钢琴卷”表示法一样，标准乐谱是一种可视化工具，它的两个“轴”捕捉音乐的两个最重要的特征：水平的时间和垂直的音高。需要以详细的方式表现音乐的特定方面，这导致了各种可视化方法的设计，我将在下面讨论。可视化和圆圈[2]音乐结构的某些属性可以用节奏图（Todd, 1994）、自相似方形（Foote & Cooper, 2001）或层次树（Lerdahl & Jackendoff, 1983）来描述。音色可以用各种形式的谱图来观察，用ski-hill图来观察半谱图（Cohn, 2001），用商拓扑来观察和声（Tymoczko, 2006），用螺旋来观察音高色度循环（Shepard, 1983）。几何思维也在构图过程中发挥了作用，雷诺兹（2004）和Wishart（1996）的手绘示意图证明了这一点，这只是最近的两个例子视觉化也在节奏和表达时间方面发挥作用。尽管微计时信息有时用数字表格显示，但可视化策略通常用于在更直观的感知层面上传达信息。Desain & Honing（2003）设计了一个三角形的时间图，绘制了三音符节奏的时间细微差别和分类边界。他们的绘图方法的一个重要和吸引人的特点是，地图上的每个点都代表一个独特的节奏模式。图表中彼此靠近的点表示相似的声音节奏，形成“团块”，代表不同的感知类别。然而，该地图仅限于仅由三个持续时间组成的节奏，因此在大多数现实世界的音乐环境中用途有限。对于较长的节奏，音符对音符的表达性计时数据通常用XY图形可视化，其中均匀划分的时间单位（如音符或小节）沿着横坐标划定乐谱位置；纵坐标通常表示节奏、间歇或与节拍细分的偏差。这种类型的设计在不同的音乐环境中被证明是有用的，包括爵士乐（例如，Benadon, 2006; Collier & Collier, 2002）和西方“古典”音乐（例如，Friberg & Sundberg, 1999; Palmer, 1996; Repp, 2002），但其线性的从左到右的方向往往掩盖了基于节拍模式的递归性质圆圈在音乐时间的形象化中享有特权地位。它们被音乐理论家、民族音乐学家和计算机科学家用来代表节奏的周期性方面。London（2004年，第64页）通过沿圆周放置“注意力能量的峰值”（节拍和细分）来可视化节拍。在Becker （1980, p. 107）对爪哇甘美兰锣（以锣为标志的时间结构单位）的表现中，时间也绕着一个圆圈流动，这是“循环而不是线性的”，在Anku（2000）对非洲节奏的表现中也是如此。Locke（1996，第90页）和Collins（2004，第59页）也使用圆形来描述非洲节奏，通过使用同心圆来描述多节奏的分层，使圆形概念更进一步。在Toussaint（2005）和McLachlan（2000）的工作中，圆圈有助于对节奏的数学解释，如最大均匀性和相似性测量。…
[1] This report presents a graphing method designed to aid the study of rhythm and expressive timing in beat-based music.(1) I show how the polar coordinate system can be used to describe and analyze different features of expressive timing. Numerous studies have shown that expressive timing lies at the core of rhythm production. The evidence-reviewed by Clarke (1999)-confirms that musicians often place attack points along a continuum of beat subdivision values rather than on the predetermined slots afforded by metrical grid spacing, thus imbuing the performance with expressive depth. This departure from a clear-cut temporal lattice is inadequately, if at all, represented by standard music notation. Like the "piano roll" representation used by MIDI sequencers, standard music notation is a kind of visualization tool whose two "axes" capture two paramount features of music: time horizontally and pitch vertically. The need to represent specific aspects of music in a detailed way has led to the design of various visualization methods, as I discuss next.Visualization and Circles[2] Certain properties of musical structure can be depicted using rhythmograms (Todd, 1994), self-similarity squares (Foote & Cooper, 2001), or hierarchic trees (Lerdahl & Jackendoff, 1983). Timbre can be viewed with various forms of spectrograms, hemiolas with ski-hill graphs (Cohn, 2001), harmony with quotient topologies (Tymoczko, 2006), and the pitch chroma cycle with helices (Shepard, 1983). Geometrical thinking has also served the composition process, as evidenced by the hand-drawn schematics of Reynolds (2004) and Wishart (1996), to name just two recent examples.[3] Visualizations also play a role in the realm of rhythm and expressive timing. Even though microtiming information is sometimes displayed with numerical tables, visualization strategies are often used to communicate information on a more perceptually intuitive level. Desain & Honing (2003) devised a triangular chronotopic map that plots the temporal nuances and categorical boundaries of three-note rhythms. An important and appealing feature of their graphing method is that every point in the map represents a unique rhythmic pattern. Dots that are near each other in the graph denote similar sounding rhythms, forming "clumps" that represent distinct perceptual categories. However, the map is restricted to rhythms that consist of three durations only and is therefore of limited use in most real-world musical contexts. For longer rhythms, note-for-note expressive timing data are often visualized with an XY graph where evenly partitioned time units (such as notes or measures) demarcate score position along the abscissa; the ordinate usually plots tempo, interonset interval, or deviation from a metronomic subdivision. This type of design has proved helpful in different musical contexts including jazz (e.g., Benadon, 2006; Collier & Collier, 2002) and Western "classical" music (e.g., Friberg & Sundberg, 1999; Palmer, 1996; Repp, 2002), but its linear left-to-right orientation tends to conceal the recursive nature of beat-based patterns.[4] Circles enjoy a privileged status in the visualization of musical time. They have been tapped by music theorists, ethnomusicologists, and computer scientists to represent cyclical aspects of rhythm. London (2004, p. 64) visualizes meter by placing "peaks of attentional energy" (beats and subdivisions) along a circle's circumference. Time also flows around a circle in Becker's (1980, p. 107) representation of Javanese gamelan gongan (structural units of time marked by a gong), which are "cyclical rather than linear," and in Anku's (2000) representation of African rhythms. Locke (1996, p. 90) and Collins (2004, p. 59) also use circles to characterize African rhythms, taking the circular concept one step further by employing concentric circles that describe the stratification of polyrhythm. In the work of Toussaint (2005) and McLachlan (2000), the circle facilitates mathematical explanations of rhythm such as maximal evenness and similarity measures. …