Study of "half-integer" harmonics in recorder tones and some speculations about their origin

Area of Science:

• Acoustics
• Musical Instrument Physics
• Fluid Dynamics

Background:

• Musical notes from flue instruments primarily contain integer multiples of the fundamental frequency (f1).
• However, other spectral components have been observed, contributing to the instrument's real tone.

Purpose of the Study:

• To investigate spectral components at odd half-integer multiples of the fundamental frequency (n±1/2 f1) in recorder tones.
• To identify the physical mechanisms responsible for these half-harmonics.
• To explore methods for suppressing these components.

Main Methods:

• Experimental studies on soprano recorders.
• Computational simulations of airflow dynamics.
• Analysis of spectral components in recorded instrument tones.

Main Results:

• Observed spectral components at odd half-integer multiples of the fundamental frequency (n±1/2 f1).
• Associated these half-harmonics with airflow patterns near the window and labium.
• Demonstrated suppression of half-harmonics through instrument modifications altering airflow.

Conclusions:

• Half-harmonics in recorder tones are linked to specific airflow dynamics at the window and labium.
• Instrument design modifications can control the presence of these components.
• Further research is needed to understand the perceptual significance of these spectral components.