Chinese scholarship dating back to the middle of the third century BCE details society’s conceptualizations and manipulations of sound. Numerical values were ascribed to sound, leading to its use as a system of measurement. Utilizing pitch as the system’s unit, sound became a means of gauging cosmic qi—the energy responsible for the formation of all entities—and of discerning humanity’s alignment with the cosmos. By precisely matching pitch with fluctuations of qi over time, humans could synchronize their world with cosmic processes.
Initially, the tuning system relied upon a musical model consisting of twelve pitches, with each assigned a numerical value. These pitches, or tuning standards, were then correlated with the months of the year. This model, however, possessed an inherent mathematical problem. While the first and thirteenth tuning standards were meant to match, the numbers associated with each pitch varied. This created a gap, referred to as the Pythagorean comma in Western contexts. This gap would also be apparent when the two pitches were played.
In the article “Mind the Gap: Acoustical Answers to Cosmological Concerns in First-Century BCE China,” published in Isis: A Journal of the History of Science Society, Noa Hegesh examines how Han court official and prognosticator Jing Fang discovered and addressed this comma. Commas present acoustical issues, and while Jing Fang’s expansion of the musical temperament model offers an acoustical solution that reduces the comma, Hegesh argues the cosmological context behind this reduction is overlooked.
Given Jing Fang’s experience with prognostication, tuning computation, and hexagram studies, Hegesh asserts that, in Jing Fang’s view, “sound was a natural phenomenon, and tuning standards were the technology for assessing the state of cosmic qi throughout the year.”
Previous research discusses the deliberate methodology behind Jing Fang’s calculations but fails to acknowledge his perception of sound. Analyses of texts and treatises reveal that Jing Fang viewed sound as a means of predicting weather events and natural disasters.
In line with cosmic models of the period, Jing Fang sought to construct a closed cycle where the initial tuning standard, Yellow Bell, would possess the same numerical value and pitch as the cycle’s thirteenth standard, which would commence the next cycle. The comma, from Jing Fang’s perspective, was indicative of a flaw in the cycle. The “Addition and Subtraction by a Third” algorithm behind tuning standard production was likewise to blame for the comma.
Jing Fang added forty-eight tuning standards and crafted a model encompassing sixty pitches, which could be allocated among days in a year. While the tuning standard he desired to reach did not match the initial Yellow Bell pitch exactly, it reduced the comma noticeably, and was similar enough numerically and audibly to satisfy his goal. Following this, a seven-note scale pattern replaced the traditional five-note pattern, and Jing Fang used it to separate the year into seven segments, with the Yellow Bell pitch occurring on the winter solstice—a time signifying the beginning of the astronomical year, when yin is at its apex and yang begins to rise. Through this connection to the winter solstice, Jing Fang’s model creates a yearly cycle, allowing for his predictions of seasonal changes.
In fact, Hegesh suggests references to qi and the yin-yang principle in Jing Fang’s theorization are indicative of his cosmological perspective. The cosmos operated according to principles of yin, yang, and qi. Sound, as part of the cosmos, operated in accordance with them. Moreover, the cyclical nature used in the constructing of tuning standards is yet another indicator of how acoustics reflected contemporary cosmological principles and concerns. Hegesh likewise contends that Jing Fang’s selective calculations provide insights into his contextualization of sound.
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Mind the Gap: Acoustical Answers to Cosmological Concerns in First-Century BCE China
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