Convergent evolution in a large cross-cultural database of musical scales John M. McBride1,* and Tsvi Tlusty1,2,* 1Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, South Korea 2Departments of Physics and Chemistry, Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea *
[email protected],
[email protected] August 3, 2021 Abstract We begin by clarifying some key terms and ideas. We first define a scale as a sequence of notes (Figure 1A). Scales, sets of discrete pitches used to generate Notes are pitch categories described by a single pitch, melodies, are thought to be one of the most uni- although in practice pitch is variable so a better descrip- versal features of music. Despite this, we know tion is that notes are regions of semi-stable pitch centered relatively little about how cross-cultural diversity, around a representative (e.g., mean, meadian) frequency or how scales have evolved. We remedy this, in [10]. Thus, a scale can also be thought of as a sequence of part, we assemble a cross-cultural database of em- mean frequencies of pitch categories. However, humans pirical scale data, collected over the past century process relative frequency much better than absolute fre- by various ethnomusicologists. We provide sta- quency, such that a scale is better described by the fre- tistical analyses to highlight that certain intervals quency of notes relative to some standard; this is typically (e.g., the octave) are used frequently across cul- taken to be the first note of the scale, which is called the tures.