Index of content:
Volume 116, Issue 4, October 2004
- MUSIC AND MUSICAL INSTRUMENTS 
116(2004); http://dx.doi.org/10.1121/1.1788732View Description Hide Description
In Western music, a musical interval defined by the frequency ratio of two notes is generally considered consonant when the ratio is composed of small integers. Perfect harmony or an “ideal just scale,” which has no exact solution, would require the division of an octave into 12 notes, each of which would be used to create six other consonant intervals. The purpose of this study is to analyze four well-known historical tunings to evaluate how well each one approximates perfect harmony. The analysis consists of a general evaluation in which all consonant intervals are given equal weighting and a specific evaluation for three preludes from Bach’s “Well-Tempered Clavier,” for which intervals are weighted in proportion to the duration of their occurrence. The four tunings, 5-limit just intonation, quarter-comma meantone temperament, well temperament (Werckmeister III), and equal temperament, are evaluated by measures of centrality, dispersion, distance, and dissonance. When all keys and consonant intervals are equally weighted, equal temperament demonstrates the strongest performance across a variety of measures, although it is not always the best tuning. Given C as the starting note for each tuning, equal temperament and well temperament perform strongly for the three “Well-Tempered Clavier” preludes examined.
116(2004); http://dx.doi.org/10.1121/1.1788728View Description Hide Description
An experimental and theoretical investigation of the acoustic and vibrational properties of orchestral crotales within the range to is reported. Interferograms of the acoustically important modes of vibration are presented and the frequencies are reported. It is shown that the acoustic spectra of crotales are not predicted by assuming that they are either thin circular plates or annular plates clamped at the center, despite the physical resemblance to these objects. Results from finite element analysis are presented that demonstrate how changing the size of the central mass affects the tuning of the instruments, and it is concluded that crotales are not currently designed to ensure optimal tuning. The possibility of using annular plates as crotales is also investigated and the physical parameters for such a set of instruments are presented.
116(2004); http://dx.doi.org/10.1121/1.1791717View Description Hide Description
The vocal tract resonances of trained soprano singers were measured while they sang a range of vowels softly at different pitches. The measurements were made by broad band acoustic excitation at the mouth, which allowed the resonances of the tract to be measured simultaneously with and independently from the harmonics of the voice. At low pitch, when the lowest resonance frequency exceeded the values of the first two resonances and varied little with frequency and had values consistent with normal speech. At higher pitches, however, when exceeded the value of observed at low pitch, increased with so that was approximately equal to also increased over this high pitch range, probably as an incidental consequence of the tuning of increased slightly but systematically, across the whole pitch range measured. There was no evidence that any resonances are tuned close to harmonics of the pitch frequency except for at high pitch. The variations in and at high pitch mean that vowels move, converge, and overlap their positions on the vocal plane to an extent that implies loss of intelligibility.