Journal of Vibration and Sound

Journal of Vibration and Sound

Acoustic Performance Improvement in Stringed Musical Instruments through Golden Ratio-Derived Sound-Hole Design

Document Type : research article

Author
Alumnus of the Department of Mechanical Engineering, Qazvin Islamic Azad University, Iran
Abstract
This study presents a systematic geometric methodology, termed the "Golden Method," for optimizing sound-hole positioning and sizing in lute-family musical instruments using mathematical principles of the golden ratio. Traditional sound-hole design has primarily relied on empirical approaches and accumulated craft knowledge, lacking systematic optimization frameworks that bridge mathematical theory with practical lutherie applications. The proposed method employs geometric constructions based on golden rectangles and logarithmic spirals to determine optimal sound-hole parameters through proportional relationships derived from soundboard dimensions. Validation was conducted through comprehensive acoustic analysis of three Persian setar instruments using advanced digital signal processing techniques and standardized measurement protocols. Professional acoustic analysis encompassed temporal characteristics, spectral properties, harmonic content, and signal quality metrics to provide a complete acoustic characterization of each instrument. Statistical analysis revealed significant improvements in decay time, ranging from thirteen to twenty percent, amplitude enhancement reaching thirty-two percent in sustained energy measures, and improved harmonic characteristics with a sixty-eight percent reduction in distortion compared to traditional designs. Effect size analysis using Cohen's d demonstrated values ranging from 1.45 to 2.2, indicating large practical significance beyond statistical thresholds. Frequency response analysis confirmed that acoustic improvements occurred without altering fundamental frequency characteristics, thereby preserving essential tonal properties while enhancing projection capabilities. The methodology provides instrument makers with systematic guidance for sound-hole optimization while accommodating natural variations in traditional construction materials and techniques and establishing a reproducible framework for musical instrument optimization.
Keywords
Subjects

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