Inharmonic Sounds Research Articles

Consonance-Based Spectral Mappings

This article presents a method of mapping the spectrum of a sound so as to make it tonally consonant with a given specified reference spectrum. One application is to transform inharmonic sounds into harmonic equivalents. Alternatively, this method can be used to create inharmonic instruments that retain much of the tonal quality of familiar (harmonic) instruments. Musical uses of such timbres are discussed, and forms of (inharmonic) modulation are presented. A series of sound examples demonstrate both the breadth and limitations of the method. [Sound examples will be included on the forthcoming compact disc for Volume 22 of Computer Music Journal.-Ed.]

Infants’ pitch perception: Inharmonic tonal complexes

Two experiments assessed the effects of inharmonicity on 7- to 8-month-old infants' perception of the pitch of tonal complexes. A number of harmonic and inharmonic complexes were presented in a visually reinforced operant head turn procedure. In both experiments, infants demonstrated the ability to discriminate two harmonic complexes based on missing fundamental frequencies of 160 and 200 Hz. After learning this basic task, infants learned to discriminate inharmonic complexes, which were created by shifting the partials of the harmonic complexes upward by 30 Hz (experiment 1) or 20 Hz (experiment 2). Finally, three spectrally different inharmonic complexes represented each pitch, and infants attempted to categorize those complexes according to their pitches. In both experiments, infants successfully discriminated the pitches of the spectrally varying tonal complexes, but their performance deteriorated for the more strongly inharmonic complexes of experiment 1. These results suggest that, as for adults, the salience of pitch for inharmonic sounds decreases with increasing inharmonicity.

Infants' extraction of pitch from inharmonic tonal complexes

Previous research has demonstrated the infant's ability to extract the virtual pitch of harmonic tonal complexes. In the present study, we used a conditioning procedure to assess 7‐month‐old infants' perception of pitch for inharmonic tonal complexes. Infants initially discriminated a pitch change from 160 to 200 Hz or vice versa in harmonic tonal complexes, which contained eight consecutive harmonies but no fundamental frequency. After infants discriminated the harmonic complexes, each partial's frequency was shifted upward by 30 Hz to render the sounds inharmonic. All infants who discriminated the inharmonic complexes proceeded to a categorization stage in which a randomized sequence of three inharmonic complexes (containing six partials) comprised each pitch category so that the spectral characteristics of the tokens changed continuously while the pitch category changed only on change trials. The harmonic complexes were discriminated by 19 of 22 infants, while 16 infants successfully discriminated the inharmonic sounds. However, only 11 infants categorized spectrally different sounds consistently with their pitches, suggesting that infants had more difficulty extracting pitch from inharmonic complexes than from harmonic ones presented in previous research. [Work supported by NSF and NICHD.]

Consonance and dissonance of pairs of inharmonic sounds

The hypothesis that pairs of appropriate inharmonic sounds can evoke perceptions similar to conventional consonance and dissonance is examined. The inharmonicity considered is not the relatively small displacement of frequency components seen in conventional musical instruments (e.g., piano), but rather large, deliberate shifting of frequencies by a number of semitones. The hypothesis states that if there is a match between upper-frequency components of two such inharmonic sounds, consonance should be perceived. If near misses occur between upper-frequency components of the two sounds, causing audible beats, then dissonance should be perceived. The individual inharmonic sounds should have reasonably wide component spacing to avoid a noiselike timbre. This hypothesis was confirmed by experiments in which subjects chose which of two different inharmonic sound pairs was the more consonant. The sound pairs with matching frequency components were chosen more often than those with near misses. The difference was significant for the experimental subjects as a whole and was pronounced for subjects with musical experience. This last fact is important since the sound pairs with matching components were arranged to have conventionally dissonant relationships between their fundamentals, and vice versa for the pairs with near misses. It is speculated that the structures in music which have their origins in the harmonic series (intervals, chords, scales) may be alterable by electronically relocating the harmonics to inharmonic positions.