Publications

Abstract

Dichoptic mixtures of equiluminous components of different wavelengths were matched with a binocularly presented "monocular" mixture of appropriate chosen amounts of the same colour components. Stimuli were chosen from the region of 490-630 nm. Although satisfactory colour matches could be obtained, dichoptic mixtures differed from normal mixtures to a considerable extent. Midspectral stimuli tended to be more dominant in the dichoptic mixtures than either short or long wavelength stimuli. An attempt was made to describe the relation between monocular and dichoptic mixtures with one function containing a wavelength variable and an eye dominance parameter.

Abstract

PHD thesis, defended at the University of Leiden

Abstract

Firstly, theories are reviewed on the explanation of tonal consonance as the singular nature of tone intervals with frequency ratios corresponding with small integer numbers. An evaluation of these explanations in the light of some experimental studies supports the hypothesis, as promoted by von Helmholtz, that the difference between consonant and dissonant intervals is related to beats of adjacent partials. This relation was studied more fully by experiments in which subjects had to judge simple-tone intervals as a function of test frequency and interval width. The results may be considered as a modification of von Helmholtz's conception and indicate that, as a function of frequency, the transition range between consonant and dissonant intervals is related to critical bandwidth. Simple-tone intervals are evaluated as consonant for frequency differences exceeding this bandwidth. whereas the most dissonant intervals correspond with frequency differences of about a quarter of this bandwidth. On the base of these results, some properties of consonant intervals consisting of complex tones are explained. To answer the question whether critical bandwidth also plays a rôle in music, the chords of two compositions (parts of a trio sonata of J. S. Bach and of a string quartet of A. Dvorák) were analyzed by computing interval distributions as a function of frequency and number of harmonics taken into account. The results strongly suggest that, indeed, critical bandwidth plays an important rôle in music: for a number of harmonics representative for musical instruments, the "density" of simultaneous partials alters as a function of frequency in the same way as critical bandwidth does.

Abstract

As a preliminary to further research on musical consonance an explanatory investigation was made on the different modes of judgment of musical intervals. This was done by way of a semantic differential. Subjects rated 23 intervals against 10 scales. In a factor analysis three factors appeared: pitch, evaluation and fusion. The relation between these factors and some physical characteristics has been investigated. The scale consonant-dissonant showed to be purely evaluative (in opposition to Stumpf's theory). This evaluative connotation is not in accordance with the musicological meaning of consonance. Suggestions to account for this difference have been given.