A number of hypotheses and theories have been proposed regarding the origin of consonance and dissonance. These theories can be broadly distinguished into four groups:

• Acoustic theories. These theories are based on physical properties of the acoustical signal, such as frequency ratios.
• Psychophysical theories. These theories are based on psychophysiological aspects of the auditory system, such as the influence of the basilar membrane.
• Cognitive theories. These theories are based on higher level cognitive phenomena, such as the categorical perception of musical intervals due to learning.
• Enculturation theories. These theories are based on social, cultural or stylistic norms that are internalized by listeners.

1. Frequency Ratios.* This hypothesis proposes that consonance is evoked by simple frequency ratios. Plomp & Levelt (1965) quote a charming characterization of this hypothesis formulated by Galileo Galilei: "Agreeable consonances are pairs of tones which strike the ear with a certain regularity; this regularity consists in the fact that the pulses delivered by the two tones, in the same interval of time, shall be commensurable in number, so as not to keep the ear drum in perpetual torment." Plomp & Levelt note that supporters of this hypothesis have included Leibniz, Euler, Lipps and Polak. Further discussion.
   
   
2. Harmonic Relationships.* Further discussion.
   
   
3. Temporal Dissonance.* The component of dissonance that arises due to rapid beating or amplitude fluctuations. Helmholtz (1877) proposed the notion that dissonance arises due to beating between adjacent harmonics of complex tones. Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 cycles per second. Further discussion.
   
   
4. Synchrony of Neural Firings. Boomsliter and Creel (1961) proposed the theory that consonance arises when neural firings in the auditory system are synchronized.
   
   
5. Periodicity Length. Irvine (1946) proposed that consonance and dissonance are related to the length of the periodicity of a cycle. For example, when tones are related by simple frequency ratios, the cycle of repetition for the combined signal is relatively short. When tones are not related by simple frequency ratios, the cycle of repetition for the combined signal is long.
   
   
6. Difference Tones.* Another possibility is that dissonance arises when tones produce strong audible difference tones.
   
   
7. Tonal Fusion.* This hypothesis is most commonly associated with Stumpf (1890) although there are historical precedents prior to Stumpf. Stumpf argued that tonal fusion is the basis for consonance. By "fusion" is meant the propensity for two or more tones to fuse perceptually and sound as one complex tone. The tonal fusion hypothesis argues that the most consonant sonorities are those where the components tend most to sound like a single tone. Plomp and Levelt point out that Stumpf later abandoned the tonal fusion hypothesis as unsatisfactory. Further discussion.
   
   
8. Tonotopic Dissonance. Plomp and Levelt themselves portray their work as supporting Helmholtz's idea that dissonance arises from beating harmonics. However, the Plomp and Levelt (1965) experiment links dissonance to the critical band. Specifically, this hypothesis proposes that dissonance is eliminated when pure tone components are separated by a distance greater than the critical band. The component of dissonance that arises when pure tones are separated by roughly 40% of a critical band. (Greenwood, 1961; Plomp & Levelt, 1965; Kameoka & Kuriyagawa, 1969a, 1969b). Further discussion.
   
   
9. Virtual Pitch Dissonance. The component of dissonance that arises from competing (unclear) viritual pitches. (Terhardt, 1974). Further discussion.
   
   
10. Pitch Resolution Dissonance. Depending on the signal, it has been observed that listeners may require more or less time to resolve the pitch of a signal. In the case of harmonic tones, the resolution is relatively fast. Resnick (1981) has proposed that dissonance arises when the time taken to resolve the pitches of a complex signal is relatively long. (Resnick, 1981). Further discussion.
    
    
11. Expectation Dissonance. The component of dissonance that arises due to the thwarting or delaying of a (learned) expectation. According to this view, "even a single tone may engender that urgent expectation of resolution that is the essence of dissonance." (Cazden, 1980; p.157) Cazden argued that there are three levels of expectation-related dissonance: Dissonating Tone where a nonharmonic or non-chordal tone has a tendency to resolve within the framework of an underlying chord or harmony, Dissonant Chord Moment where a chord may be dissonant to the extent that it arouses the expectation of resolving to another chord within a harmonic progression, and Tonal Center Dissonance where a passage may retain a tonic or dominant tonal center, and dissonance arises is resolved when the dominant tonal area ultimately moves to the original tonic area. Further discussion.
    
    
12. Interval Category Dissonance. The component of dissonance that arises when a two pitches form an interval that is categorically ambiguous for a listener. That is, where the interval lies near a learned categorical boundary. Further discussion.
    
    
13. Absolute Pitch Category Dissonance. The component of dissonance that arises when a pitch is categorically ambiguous for a listener posessing absolute pitch. That is, where the pitch lies close to a learned categorical boundary. Further discussion.
    
    
14. Stream Incoherence Dissonance. The component of dissonance that arises due to confusion regarding streaming. (Wright & Bregman, 1987). Further discussion.
    
    

Additional Hypotheses

Two additional hypotheses can be identified that are independent of the above theories. One hypothesis relates to the contextual or relative perception of dissonance. The second hypothesis relates to how the density of parts may influence perceptions of consonance.

1. Relative Dissonance. The component of dissonance that arises from the context of dissonant successions. A sonority might sound relatively consonant when it is preceded by by other sonorities that are highly dissonant. Further discussion.
   
   
2. Numerosity Conjecture. Huron has proposed a further factor influencing consonance -- in addition to the effect of the critical band. Specifically, Huron has suggested that consonance is positively correlated with perceived numerosity. That is, as the number of apparent sound sources is increased, the overall perceived dissonance is reduced. Further discussion.
   
   

* These five historical theories are described in Plomp and Levelt (1965).

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