| Popis: |
In this article, the topic of tuning and temperament is addressed mainly from an empirical point of view. After furnishing some historical background on tone systems, scales, and tunings (in a review from Greek antiquity to the 18th century), twelve major and twelve minor chords played in two well-known keyboard tunings and temperaments (Werckmeister III, Vallotti) are investigated in regard to acoustical parameters on the basis of sound recordings we made with a Kirckman harpsichord from 1766. Our analysis of major and minor chords employs signal processing methodology, in particular autocorrelation and crosscorrelation from which the harmonics-to-noise ratio (HNR) is computed in the time domain as a measure of the periodicity in a signal. HNR readings vary for different chords relative to the justness of interval ratios and the different degrees to which partial frequencies converge in signals representing several complex harmonic tones such as contained in musical chords. The HNR thus can be taken as an indicator for the relative quality of a particular tuning. In addition, data from two experiments are reported in which listeners judged perceptual qualities as well as the goodness of intonation for various tunings implemented on digital synthesizers or realized by means of a computer. Our study intends to provide empirical data that can help to substantiate discussions of musical tunings and temperaments. |
