Targeted detuning aiming for sensory pleasantness – A case study of Pipe Organs and Accordions★

Two simultaneously sounding tones differing in frequency by a few Hertz generate a waveform, whose amplitude modulation is related to the psychoacoustic quantity “fluctuation strength”. In accordance with the widely accepted definitions of consonance, any deviation from a pure interval (a dyad, whose tone frequencies yield a frequency ratio of small integers) generates dissonance. Nevertheless, imperfect intonation is a common occurrence in musical performance. Recent publications have demonstrated that slightly detuned dyads are perceived as more pleasant than their corresponding pure intervals. Some instruments even contain a separate set of tone generators that are intentionally detuned to a slight degree. Examples of instruments that exhibit this feature include various flat and sharp Celeste ranks in the Pipe Organ or the Accordion. The resulting undulating sounds are pictured as pleasant, shimmering, or “celestial”. This work demonstrates that the tonal timbre of two harmonic complex tones, whose fundamental frequencies slightly deviate from ratios of small integers, can undergo notable periodic changes within a beat cycle while maintaining sensory pleasantness. The acceptable limit of detuning unison intervals is related to the frequency difference limen, as evidenced by data on CELESTE ranks in Pipe Organs and Accordions tuned by instrument builders. This allows for the derivation of general tuning progression rules for Celeste ranks in Pipe Organs and Accordions, which can be used to increase the auditory pleasantness of dyads despite their slight detuning.