By: Derek Martinez
When listening to music, you have likely heard a pitch that just sounds displeasing. It’s not the tone, or timbre, it’s the actual pitch itself that sounds out of place and harsh to the ear. These types of phenomena are called dissonances, and are seen in both physics and music theory. Their counterparts, consonances, are harmonies or pitches which sound pleasing to the ear. Dissonances and consonances are processed in two different centers in the human brain, which in turn are wired to different emotional centers of our brain, explaining why some dissonances are displeasing and consonances are pleasing. However, which pitches go to which center vary from person to person.
So, why does this happen? Why do we dislike some frequencies, and like others? This phenomenon has been studied for centuries, but there is still not a direct answer. However, there are multiple theories for this, and there have been experiments where the results may point towards a more clear understanding.
Acoustic approaches towards consonance and dissonance have been studied since Greek scholar Pythagoras' work. Acoustic theories suggest that consonance and dissonance can be looked at through acoustic signals such as instruments and musical scales. Using an instrument called a monochord, Pythagoras examined ratios of string lengths and music intervals to categorize consonant and dissonant sounds. He discovered that dissonance occurs when the length of string ratios (frequency ratios) are far from/are not integer numbers. Some of these ratios include major seconds (8:9), major sevenths (8:15), and tritones (32:45). If you were to put these ratios into decimal form, it would be clear that these intervals are far from integers since they are repeating decimals. Consonant ratios include unisons (1:1), octaves (1:2), and perfect fourths (3:4), which are much closer to integers and can be expressed as whole percentages. With Pythagoras’ discoveries, we can suggest that for an interval to be considered consonant, the ratio of the frequencies must be a non repeating number.
Cognitive theories examine expectation and learning. What this means is that something that would be considered a dissonant interval outside of musical context could be heard as consonant. This happens if the intervals preceding it are much more dissonant. This also means that medial and imperfect consonances can be perceived as more dissonant, if the intervals preceding it are absolute or perfect consonances. Cognitive theory can also be examined from a more long term perspective throughout a person’s lifetime. In the west, popular music follows a method called “common practice harmony” which was also practiced in the 18th century. This tonal method avoids dissonant intervals as much as possible. So, if someone who grew up listening to only western music listened to Balinese music, they would perceive the pitches as much more dissonant and displeasing since Balinese music is created to intentionally have dissonant intervals. This is also seen in the classical era of western music, where certain pieces were heavily criticized and confused audiences since the composers did not follow the traditional common practice method. One example of this is Mozart’s 19th String Quartet, which diverged from consonant intervals so much that it received the infamous nickname “Dissonance.”
The examples presented in cognitive theories can also fall under the category of cultural theories. Balinese music is typically perceived as dissonant by western listeners, which is due to instruments being tuned to different frequencies within Balinese ensembles. A person from Bali would be much more accustomed to this type of music and would not perceive a dissonant interval as largely unpleasant, whether it is in the context of Balinese music or not.
Biological theories, as the name implies, look towards physiological and biological reasoning to explain perception of sounds. These theories suggest that perception of dissonance and consonance is learned at birth (nature) rather than something that a person becomes accustomed to (nurture). One experiment that largely supports this theory is Marcel Zentner and Jerome Kagan’s study on infants. In this investigation, infants were exposed to consonant and dissonant intervals, and their physical reactions to the sounds were observed and evaluated. The results showed that the infants were more likely to show a negative reaction (vocalization, fretting) towards dissonances, suggesting that there is some natural tendency in humans to favor consonances.
So, what can we get from this? Though this concept can be very confusing, it is important to notice that we may be biased towards one certain tonal system/method. Perhaps these theories can encourage you to appreciate the artistic decision to include dissonant intervals, rather than avoiding them.
A visual depiction of a monochord with equal-tempered intervals.
Q: What is the consensus on interval quality perception? Is there a consensus at all?
A: There is no single theory for how we as humans perceive consonance and dissonance. However, each theory presented in this article has evidence to support it, meaning that perception could possibly depend on biological, acoustic, and cognitive aspects.
Q: What exactly are dissonant intervals? Consonant intervals?
A: Dissonant intervals are simultaneous pitches which are displeasing to the ear, and have ratios in their frequencies which are very far from integer numbers.
Loy, G. (2006). Musimathics: The Mathematical Foundations of Music
Monochord ET, @Hyacinth, Wikimedia Commons https://commons.wikimedia.org/wiki/File:Monochord_ET.png