A Re-Valuation of the Ancient Science of Harmonics

Abstract

Harmonics was the theoretical arithmetic underpinning the tuning of musical instruments in ancient times. It was a numerical science based on ratios of string-length. The ancients believed that the planets circled the heavens in similar mathematical proportions, and that, by analogy, these also corresponded to powers in the human psyche. Harmonics survived as such until the 17th century. Only recently, however, have musicologists made a breakthrough to a more comprehensive understanding of its coherence and cultural significance. This article offers a short re-valuation of harmonics. It seeks to stimulate debate about the relevance of the relationships between number and tone to contemporary thought, and whether an understanding of harmonics has anything to contribute to future interdisciplinary research into the evolution of music and the human mind.

Pitch chroma discrimination, generalization, and transfer tests of octave equivalence in humans

“…From the earliest times, human cultures have recognized that the octave is formed at a ratio of 2:1 between notes and have used that fact to tune their musical instruments (Crickmore, 2003). Later, after written languages developed, diverse cultures-including those of India, Babylon, and Egypt-provided lasting records of how they used the octave to tune instruments, write music, and conceptualize mathematics (McClain, 1978).…”

“…Thus, the ability to resolve out the octave in sound and in sequences of sounds might be a useful skill. Octave equivalence affects both speech (Peter et al, 2008) and music (Burns, 1999), and octaves are used in this way in all cultures (Crickmore, 2003). Consider, as an example, that sex recognition and sexual signals are basic skills common across species.…”

The Evolution of Musicality: What Can Be Learned from Language Evolution Research?

“…our last common ancestor with that species was endowed with a predisposition toward the behavior under scrutiny, or (2) convergent evolution, i.e., similar evolutionary pressures gave rise to similar genetic predisposition for proto-musical behaviors in humans and other species (Fuhrmann et al, 2014 ; Ravignani et al, 2014 , 2016b ; Wilson and Cook, 2016 ). For instance, recent studies found evidence for beat perception and production, relative pitch and tonal encoding (Hoeschele et al, 2015 ; Hoeschele and Bowling, 2016 ), octave generalization (Crickmore, 2003 ), and consonance (Cook and Fujisawa, 2006 ) in animals. Based on theoretically driven empirical research (Honing et al, 2015 ), we argue that, if musical tasks designed for humans are adapted - by modifying their form, not substance—to the specific species under inquiry, many “unthinkable tasks”—sensu Chomsky ( 2015 )—may become manageable.…”

Pitch chroma information is processed in addition to pitch height information with more than two pitch-range categories

“…The shared perceptual quality of frequencies separated by an octave is referred to as the “pitch chroma” of these notes. Pitch chroma, and thus the octave, is cross-culturally used as a common basis of pitch perception (Burns, 1999 ; Crickmore, 2003 ; but see Jacoby et al, 2019 ). The octave relationship is important not only to music but also to language learning: Young children as well as adults use the octave relationship in producing successful imitations of song or speech with a fundamental frequency outside of their own vocal range (Peter et al, 2008 , 2009 , 2015 ; see also Hoeschele, 2017 , for a review).…”