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1
Content available remote Metoda transformowania muzyki w figury 4D
PL
Przedstawiony w tej pracy system generuje figury w przestrzeni 4D na podstawie plików muzycznych MIDI. Tworzone figury w przestrzeni 4D i ich rzutowania w przestrzeni 3D dają możliwość obserwacji 4 dźwiękowych akordów, ich zależności między dźwiękowych, ich dysonansowości i charakteru brzmienia. Otrzymane figury, zbudowane z ciągłej linii, różnią się kształtem i gęstością zapętleń, które odzwierciedlają dysonanse i konsonanse w 4 dźwiękowych muzycznych współbrzmieniach.
EN
The system presented in this paper generates 4D figures based on MIDI music files. Spatial figures created in the fourth dimension space and their 3D projections, allow for the observation of 4-voice chords, their dependence on the sounds they represent as well as their dissonancity and sound character. Obtained figures are constructed using continuous line, they differ in shape and complexity, and correspond with consonance and dissonance in 4-voice musical sounds.
2
Content available remote Roughness of two simultaneous harmonic complex tones in various pitch registers
EN
The purpose of the study was to determine the dependence of perceived roughness on the frequency ratio of two simultaneous harmonic complex tones. A set of 36 dyads forming musical intervals of various tuning systems was presented in three pitch registers. Twelve sound engineering students judged each dyad for roughness by the method of absolute magnitude estimation. Results show that roughness considerably varies with the frequency ratio of the two complex tones, what is a well-known phenomenon. A new finding, being in contrast to published theories of roughness, is that some of the equally-tempered intervals are perceived less rough than their counterparts based on integer frequency ratios. This effect is attributed to slow beats that arise between the harmonics of two complex tones when the frequency ratio of the tones slightly departs from the integer ratio.
3
Content available remote Perceived roughness of two simultaneous harmonic complex tones
EN
Two experiments were carried out to determine the dependence of perceived roughness on the frequency ratio of two simultaneous harmonic complex tones. In the first experiment, the frequency ratios of the tone pairs corresponded to 35 within-octave intervals of various musical tuning systems. In the second experiment 12 intervals were used; six of them ranged from 10 cents below to 10 cents above an equally-tempered fourth and the other six encompassed a similar range centred around the equally-tempered fifth. In both experiments the amount of roughness was assessed by absolute magnitude estimation. Results show that roughness considerably varies with the frequency ratio of a pair of harmonic complex tones, which is a well-known phenomenon. A new finding, that is in contrast to published theories of roughness, is that equally-tempered intervals produce less roughness than their counterparts based on integer frequency ratios. This effect is attributed to slow beats that arise between the harmonics of two complex tones when the frequency ratio of an equally-tempered interval slightly departs from integer ratio. Such beats, heard as fluctuations, impart a smooth character to the sound.
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