Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula

Area of Science:

• Acoustics
• Musical Instrument Physics

Background:

• The production of musical tones on string instruments typically involves the fundamental frequency and its harmonics.
• Complex tones with unique spectral characteristics can be achieved through advanced playing techniques.

Purpose of the Study:

• To investigate the acoustic phenomenon behind the production of complex tones using specific bow and finger placements on a string.
• To explain the underlying physics of how these tones are generated and controlled.

Main Methods:

• Analysis of string vibration patterns using impulse responses.
• Application of the Poisson summation formula to model the system properties.
• Experimental manipulation of bow and finger positions on cello and double bass strings.

Main Results:

• Acoustic conditioning of the string spectrum yields narrow bands of pronounced energy.
• The phenomenon is attributed to two additional signal loops phase-locked to the fundamental.
• Slip pulse characteristics (shape, size, timing) within the nominal period are non-uniform and variable.

Conclusions:

• The described technique allows for the creation of multiple complex tones with the Helmholtz fundamental as the lowest pitch.
• The positioning of the bow and finger relative to the bridge influences the emphasis on the fundamental.
• This method is applicable to cello and double bass, offering novel timbral possibilities.