Why do some intervals sound better than others?

Question

Why do some intervals sound so good (e.g. a perfect fifth: seven semitones), whereas others sound so awful and diabolical (e.g. an augmented fourth: six semitones)? Is this phenomenon dependant on one's musical culture or could it be our brains are "hard wired" to perceive sounds in such a way?

Answer 1

Good and Bad are completely subjective, but what does exist are the relative concepts of consonance and dissonance.

What this has to do with are the frequencies of the two pitches that make up the interval. As a very simple example, 200hz and 300hz approximate an interval of a perfect 5th (in real life, those frequencies are close to G3 and D4). The ratio between those two frequencies is 2:3.

If you tune that D down to an in-tune* augmented 4th above the G, you'll be at 281.25hz, which compared with the 200hz note gets you a ratio of 32:45.

The reality is much more complicated when you start considering systems of temperament and then harmonic series, but what it comes down to is that intervals that approximate ratios made of small whole numbers sound more consonant ("good"), and intervals that have ratios made of large whole numbers sound more dissonant ("bad").

For further reading, consider the following:

• How does the harmonic series affect consonance?
• Difference between equal temperament and just intonation
• https://en.wikipedia.org/wiki/Interval_(music)
• https://en.wikipedia.org/wiki/Just_intonation
• https://en.wikipedia.org/wiki/Equal_temperament

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^{* "In tune" according to 5-limit just intonation. See links above.}

Answer 2

This has been the subject of some debate for some years. My view is probably a bit controversial. I'm not sure that "good" or "bad" are the proper terms for the sounds of intervals; "good" and "bad" tend to be value judgments not musical judgments. For example, augmented fourths (or diminished fifths) moving to perfect fifths is a component of a perfect authentic cadence. The reverse movement often signals the start of a composition (or part thereof.) In Common Practice Harmony, dissonance (like augmented fifths or major or minor seconds or major or minor sevenths) tends to signal movement; consonance (unisons, fifths, octaves, major and minor thirds, major and minor sixths) tends to signal stasis. (The fourth is treated a bit unusually.) The art of composition consists of the judicious combining of various consonances and dissonances. Of course, this is to some extent just my opinion.

Note that one may use different musical sounds to express different emotions. Take some movie scores for example. "Gone With the Wind" did use a lush, opera-like sound to express the idea of a saga. "Psycho" has a harsher score.

There is also debate over whether consonance or dissonance or good or bad sound are physiological or cultural. I tend to think it's mostly cultural. There are differences in Arabic, Chinese, Balinese, European, other musical material.

Answer 3

Is this phenomenon dependant on one's musical culture...

Yes

...or could it be our brains are "hard wired" to perceive sounds in such a way?

No

It is a simple as that.

Music is art, art is culture.

Some people attempt to explain consonance and dissonance in mathematical terms and reference to the harmonic series, but that does little to explain music other than show a root position major triad is acoustically "resonant", which is 'neither here nor there' regarding how we feel about it. It is a bit like saying gravity pulls down, therefore we are hard-wired to prefer classical Greek architecture. One simple physical phenomenon does not generate a complex cultural aesthetic.

Answer 4

On the side of "hard-wired" look up "Lissajous figures" on you tube. These show that pleasing sounding intervals produce pleasing patterns on an oscilloscope. This would suggest a more objective reason regardless of culture.

Answer 5

The ebb and flow of melodies as notes are arranged to compose a song as well as rhythm and instrumentation preferred by the listener is largely influenced by culture.

But there is some biological basis to explain why certain intervals seem to sound more pleasing together that do not depend on cultural influence or prior exposure to music of a particular type.

Some notes sound "good" together. This is an example of what we call consonance. Some notes do not seem to sound good together. We call that dissonance.

In simple terms, certain notes blend well together because of the way the sonic frequencies merge together and complement one another. Our brains will instinctively have a desire to gravitate towards complementary frequencies that will blend together to form pleasing sounds. The relationship between the sonic frequency of two notes is described in music theory as an "interval" which is how far apart the sonic frequencies are - commonly measured in what we call semitones (with one semitone being the smallest step in a Western Music chromatic scale).

Different sounds produce wave forms in different frequencies. A particular note will produce a particular and unique sound print based on how fast the waves move up and down which is measured as “frequency”. The mathematical relation of these frequencies to one another, account for the fact that some sets or groups of notes are harmonious with one another (sound good together) while others sound dis-harmonious (don’t seem to go together).

To further expand from math to biology and physics, we need to understand that a sound is heard because of SOUND WAVES which travel through the air to our ears. Sound waves are created by vibrations and these vibrations are detected by our ear drums or more particularly - the basilar membrane in our inner ear.

When two notes are consonant and the peaks of their sound waves (frequencies) blend together harmoniously, the corresponding vibrations in the basilar membrane are balanced and pleasing to the “processing center” in our brain. If the two notes are dissonant because their frequencies overlap instead of blending together, they create an uneven (offbeat) vibration inside our ear and the brain feels unsettled.

Here is an example to help illustrate the tendency of our brain to prefer an evenly spaced rhythmic flow. Imagine walking down a path on square pavers (like stepping stones) that are evenly spaced about two and a half feet apart. Your pace is steady and even and you don’t even have to think about it. You could say your gait is natural. Now imagine walking on a similar path – only now the pavers are irregularly spaced. Maybe one foot apart, then three feet apart then two feet apart then two and a half feet, then one foot 8 inches – you get the picture.

You don’t like this because there is not a natural even flow – like there is when you walk or run down the sidewalk (unless you are trying to avoid the cracks). Two notes that blend are like the evenly spaced pavers. Maybe one wave hits every five feet (every second block) and the other hits every two and a half feet(every block), but they come together and create a harmonious flow of motion. The uneven blocks are like two notes that never blend together.

If you have ever rolled two windows down at the same time in a moving car you may have experienced the effect of air waves that collided together and created an unpleasant vibration. So in simplified terms, two notes who’s sonic frequencies do not blend together, will create an unpleasant irregular vibration in the inner ear. And our brain does not like it.

Music in Western Culture is divided into scales and each of these scales is commonly divided into seven notes which makes it a “diatonic scale”. Any given diatonic scale is based on subdividing an octave into seven notes. An octave is the note that is exactly double the frequency or half of the frequency of the starting note. From C to C is an octave and the ratio of the sound waves from the root note and the corresponding octave note is 2:1 The octave is the most consonant sounding interval and is common to music from every culture.

To over simplify it, the notion of dividing the octave into seven notes is based on mathematical principles that determine that dividing an octave into seven notes yields the most harmonically pleasing ratios between the intervals that can be formed with seven divisions.

So to a great extent, our brains are in fact "hard wired" to prefer certain intervals.

Answer 6

I think it's true that some intervals are more consonant than others for reasons already explained in several of the answers above. Also, "good" and "bad" are quite subjective viewpoints, as several others have pointed out. Perhaps slightly less subjective adjectives could be something like "bright," "peaceful," "mellow," sounds vs. "dark," "disturbing," "tense" sounds.

Having said that, I think there's only a limited utility to focusing on the consonance/dissonance of individual intervals when it comes to understanding the overall mood of a piece of music. An edgy or dark tone that gets beautifully resolved can have a very pleasing and satisfying effect in the overall scheme of things. On the other hand, if you dwell on darker, more disturbing intervals for longer periods of time before resolving them, or if you choose not to resolve them, it makes the music more heavy.

If you stop to think about it, the minor seventh has a much simpler ratio to the tonic (5:9) than the major seventh does (8:15). To my mind, therefore, the major seventh has an edge and aggression to it compared with the more mellow minor seventh. And yet, in Western music, the major scale (which includes the major rather than the minor seventh note) is considered happier, brighter, more positive. As for the augmented fourth, it has the same intervallic relation to the perfect fifth as the major seventh does to the octave, so I think they are somewhat similar in that respect.

In Indian music, the augmented fourth (tivra ma) is commonly used both in ragas that are bright and happy, and ragas that are more disturbing or pathos-filled. Some happy ragas featuring this note are Raag Yaman, Raag Kedar, and Raag Bihag, while Raag Marwa and Raag Todi are darker.

Answer 7

To give some balance from the other side, there is a large body of academic work that suggests we are hardwired to prefer certain intervals. As one example, our auditory system is extremely fast and precise. We can localise stereo sounds using differences as little as 10us in time. Our detection of pitches is similarly fast and free of conscious effort, which suggests we have some dedicated processing power there.

I'd start by referencing "The Neural Code of Pitch and Harmony" (2015) by Gerald Langner (1943-2016). By combining observations from neurobiology of the auditory system in mammals, along with results from music psychology experiements he suggests a framework that might explain how we come to find certain sounds to be consonant. If I were to try and summarise, he suggests that we have multiple "periodicity circuits" which are each tuned to a narrowly filtered portion of input from the cochlea. The circuits have multiple paths to allow the detection of pitch in different ways and these meet up at a "coincidence neuron" at the end of the circuit. If both pathways are strongly triggered and their activations occur close together in time, the coincidence neuron is maximally triggered (causing a strong perception of pitch at that frequency band). This produces something like a train of neural spikes which is undergoes further processing. Consonance comes into play when you consider that each of these circuits will also respond to integer multiples (aka harmonics) of their main frequency. It's a fascinating area of research and I recommend anyone to look into it, although the jumps between neurology, signal processing and music theory can be tough!

There are other academics (like Josh McDermott) who argue that the phenomenon of consonance is mostly, if not entirely cultural. See https://www.nature.com/articles/nature18635 for an example of his work. While I agree that searching for counter examples is a good idea, I think that (ironically) the fact that music exists in nearly all cultures suggests that there is a mechanism by which we appreciate it. What makes culture amazing to me is the possibility that we start with the same neural hardware but we use it in different ways. To me, that seems like something to be celebrated instead of dismissed.