Volume 116, Issue 4, October 2004
Index of content:
- 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/10.1121/1.1791717View 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.