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

The musical notes produced by recorders and other flue instruments consist primarily of spectral components with frequencies given approximately by nf1, where n is an integer and f1 is the fundamental frequency. However, the real tones of these instruments contain other spectral components that have been observed and discussed by a number of authors. We report a study of spectral components in the tones produced by recorders that are odd half-integer multiples of f1, i.e., spectral components with frequencies n±12f1. Our results, obtained through a combination of experimental and simulation studies of soprano recorders, suggest that these components are associated with the air flow in the vicinity of the window region and the labium edge. We also show that these half-harmonics can be suppressed by modifications of the instrument that alter the pattern of air flow in those regions. Speculations concerning the importance of the half-harmonics and the degree to which they are perceptible by a listener are briefly discussed.

The chimney tube in musical acoustics: A textbook-level formulation for students and musicians.

The chimney tube, comprising connected body and chimney segments with respective diameters d1 and d2, is ubiquitous in musical acoustics and can be a useful analog for flute embouchure holes, woodwind toneholes, and organ pipes. Most treatments are complex and not readily accessible to lay audiences. Simple expressions for the input impedance of ideal chimney tubes are derived by two methods. Chimneys short compared to the overall length of the resonator are shown to have effective lengths larger than their physical length by the factor (d1/d2)2 when the chimney is open and smaller by the same factor when closed. Examples presented range from a simple cylindrical tube open at both ends to the classic Helmholtz resonator. Insights are provided about tonehole placement and the tradeoffs between a tonehole's position and diameter; how the resonance frequencies of an open-open chimney tube with a short chimney do not depend on which end is used as the input; and the interesting way in which a long chimney can change the spacing of the resonances from the 1:2:3 pattern of a cylinder open at both ends to the characteristic 1:3:5 pattern of a cylinder open at one end and closed at the other.

An examination of the resonances in modern flutes with ergonomically angled headjoints.

This paper investigates the passive resonance spectra of a modern Boehm flute body outfitted with a variety of transverse and end-blown ergonomic headjoints in an attempt to determine if there is anything intrinsic to the acoustics of these instruments that keeps them from being as good as the same flute with a standard headjoint. With the exception of a commercial U-shaped, recurved headjoint, the ergonomic headjoints examined were all home-built from plastic pipe Tees connected to the flute body by means of a modular jointed neck. Spectra were collected with a pressure-based method that uses a localized sound source placed just outside the flute's embouchure hole to generate forward-going and backward-going pressure waves (with amplitudes P+ and P-) inside the flute. Power spectra ( P++P- 2 vs frequency) are obtained by Fourier analysis of the acoustic pressure recorded by a microphone positioned inside the headjoint. The spectra are modeled with a transfer matrix method that extracts the input impedance from the computed values of P+ and P- at the measurement position. Detailed results on tuning and harmonicity provide clues to the differences between these instruments but suggest no fundamental deficiencies in the flutes designed to be ergonomic.

A pressure-based transfer matrix method and measurement technique for studying resonances in flutes and other open-input resonators.

This paper provides an alternative formulation of a transfer matrix method (TMM) long used for modeling the passive resonances of wind instruments. In the conventional, impedance-based TMMs, the quantities being evaluated are the acoustic pressure P and the acoustic flow U; in the present pressure-based TMM (a variation of the Heavens matrix method developed for thin film optics), the quantities being evaluated are the amplitudes of the forward-going and backward-going pressure waves, P+ and P-. Power spectra (|P++P-|2 vs frequency) for several types of branched and non-branched open-input resonators are computed and then compared to experimental spectra obtained from a Fourier analysis of the acoustic pressure at a position inside the resonator recorded during excitation by a localized sound source placed just outside the resonator. Agreement is good for both one-end-closed polyvinyl chloride chimney pipes and a modern flute set up with a variety of lip, keywork, and open/closed tonehole configurations, although fits for very short straight tubes appeared to require unphysically high wall losses. Input impedance derived from the computed values of P+ and P- at the flute's embouchure hole appears consistent with directly measured input impedance data in the literature.

Single Crystal Flexible Electronics Enabled by 3D Spalling.

Flexible and stretchable electronics are becoming increasingly important in many emerging applications. Due to the outstanding electrical properties of single crystal semiconductors, there is great interest in releasing single crystal thin films and fabricating flexible electronics with these conventionally rigid materials. In this study the authors report a universal single crystal layer release process, called "3D spalling," extending beyond prior art. In contrast to the conventional way of removing blanket layers from their substrates, the new process reported here enables 3D control over the shape and thickness of the removed regions, allowing direct formation of arbitrarily shaped structures of released film and locally specified thickness for each region. As an exemplary demonstration, silicon flexible tactile sensors are fabricated with sensitivities comparable to those of high performance sensors on rigid substrates. Finite element modeling indicates that the size and thickness of the selectively released features can be tuned over a wide range.