The determinants of musical emotion
Music has two basic components:
- A prehistoric language of emotion which determines the quality of musical emotion
- An internal brain illusion which determines the intensity of musical emotion
The internal brain illusion is caused by the use of exact repetition in the basic elements from which music is constructed.
However, the language of music can only express emotion if something changes.
This makes music something that has to satisfy two conflicting constraints:
- The individual elements should, as much as possible, consist of things that are exactly the same as elements that occurred previously.
- In order to express emotion, something must change.
To resolve this conflict, we have to construct music as a changing whole, assembled from individual elements that are mostly unchanging.
Types of Exact Repetition
I will now present an account of the different types of exact repetition that can be identified as occurring in music.
But before that, a couple of notes.
Firstly, the list of repetitions that I have identified is almost certainly not complete.
Secondly, the list is very much informed by my own personal experience of modern western-style pop music, where by "western" I really mean anything with melodies mostly but not always constructed from subsets of the standard chromatic scale, with harmonies and/or chords, and beats with varying degrees of syncopation based on regular simple time signatures.
Exact repetition has to occur in music, but, it is not necessary for every type of exact repetition to appear in every musical item. It is quite possible that musical genres substantially different from modern pop music may contain different forms of exact repetition that I have not identified in this article.
Scales
The primary fact about scales is that they consist of a relatively small finite set of notes. There is the complication of octaves, and we can argue about whether the 'same' note in a different note counts as being exactly the same. Or we can resolve the argument by treating pitch and 'pitch class' as two distinct attributes, where the second attribute gets exactly repeated more often. Either way, we can identify the primary source of exact repetition in scales, which is that, most of the time, when a given pitch value occurs in a melody, it is an exact repetition of a pitch value that has already occurred at least once in that melody.
It's not just the pitch values that get repeated. Depending on the exact nature of the scale, the intervals between one note and the next belong to a finite set of possibilities. In the case of the justly-tuned major or minor scale, there are exactly two step sizes, ie 1 semitone and 2 semitones. When a tune runs up and down the scale (which a lot of them do a lot of the time), then there are basically 5 distinct possible steps, if we count up and down as separate, and also count note repetitions as 0 (ie steps of -2, -1, 0, 1 & 2 semitones).
But wait, there's more. If we abstract the scale as a series of steps, then melodic contours can be categorised in terms of scale steps, in effect abstracting away the differences between different step sizes.
So, to give a simple example, consider a melody with a phrase of C D E D C, followed by a phrase of E F G F E (which does sound a bit musical as it is). If we characterise the contour of each phrase in terms of semitones, it's [2, 2, -2, -2] and then [1, 2, -2, -1] which is not an exact repetition. But if we abstract away the different in scale step sizes, then the contours become [1, 1, -1, -1] and then [1, 1, -1, -1], which is an exact repetition.
Harmonic Intervals
If two notes are separated by a harmonic interval, and if the instrumental (or vocal) sound is a sound with integral harmonics (which for most western musical instruments is the case), then there will be exact repetition in the individual harmonics.
For example, if I have note A at pitch 440Hz, then it has harmonics at 880Hz, 1320Hz etc. If I have a note E above the A, using a pure harmonic interval, then the E would be 660Hz, with harmonics 1320Hz, 1980Hz etc. We can see that the 2nd harmonic of the E is an exact repetition of the 3rd harmonic of the A. (In practice, using just-intonation, the E will be 659.25Hz with 2nd harmonic 1319.5Hz, so the repetition will be less exact, but still pretty close.)
Rhythm and Beat
The most basic component of musical rhythm is regular beat, which, by definition, is the exact repetition of something.
But that is not the only type of exact repetition that arises from musical rhythm.
A full description of musical rhythm as it occurs in most of modern pop music is that rhythmic components in both melody and percussion are constructed from what I call nested regular beats (I invented that term because there doesn't seem to be any existing terminology), where the nesting is the nesting of a finite sequence of beat periods where each beat period in the sequence is a multiple of the following beat period.
For example, in 4/4 time, consisting of 4 1/4 notes per bar, and defining one 1/4 note as a beat period of 1, then the nested beat periods are, typically, 4 (full bar), 2, 1 (full note), 1/2 and 1/4.
Within the context of nested beat periods, we can label each note in a rhythm by the finest beat period that it belongs to. So with the previous example, there are exactly 5 labels that can be assigned to any note. So almost every note has a label which is a repetition one that has already occurred.
(To fully understand how nested regular beats are required to cause this type of repetition, we would have to extend the labelling scheme to apply to arbitrary irregular rhythms, which would involve some type of fourier analysis, and it can be shown that, in the general random case, the labels will not be exactly repeated as they are with nested regular beats.)
With nested regular beat, there is a finite set of possible note lengths, so that is another thing that is exactly repeated.
Diminuendo, Crescendo and other Smooth Gradual Changes
Diminuendo and crescendo are one type of smooth change that have always appeared in music.
However, with modern production technology, other types of smooth gradual change can appear in music – a common example is a frequency filter which is smoothly and gradually changed over some period of time (usually at least a few bars)
With a sufficiently smooth gradual change, the thing that is exactly repeating is the rate of change, in other words, it's an unchanging rate of change.
Rhyming
Rhyming seems like something that is not quite a feature of music.
For example rhyming can occur in poetry. Of course poetry can have metre, which is also a feature of music, and one could argue that maybe scanning rhyming poetry is a limited form of music.
What is certain is that rhyming is an almost essential feature of modern popular music. Song lyrics almost always rhyme.
So we should consider the possibility that the brain's response to rhyming is based on the same basic mechanisms as its response to other features of music.
Within the context of exact repetition & overall change, rhyming fits exactly – when two words rhyme, a portion of the phonetic components of the words are exactly repeated, but the words are different words with different meanings, so the meaning is the thing that changes.
The Requirement for Precision of Performance
One thing about music is that if you want to get a good result, your performance has to be quite precise.
The notes you sing have to be in tune. Your rhythm has to have correct timing.
The degree of precision required for musical performance is quite unnatural, compared to, for instance, the precision required to competently speak a natural language.
For most of the types of repitition given above, we can see that achieving maximum exactness of repetition depends on the precision of performance.
That is, if your performance is not precise enough, then the required repetitions will not be exact enough, and the intensity of musical emotion will be reduced accordingly.
(Rhyming would be one exception – rhyming could be considered an unnatural constraint on spontaneous speech, but if you've already learned the words, then saying a poem with the correct rhymes is not particularly difficult, even for someone who has not spent any significant portion of their life practising reading poetry.)
The Requirement for Change
I haven't given much detail about the second major constraint on music, that there has to be change in order to express actual musical emotion.
We can observe that very, very repetitive music does not sound that musical.
So under the assumption that exact repetition is a major determinant of the intensity of musical emotion, the fact that very repetitive music doesn't sound so musical implies the existence of some other constraint that requires overall change.
We can also observe subjectively that there is indeed often a maximum point of emotional impact when something does change, for example a chord change. So this is at least consistent with the hypothesis that the expression of musical emotion requires something to change.
In my current analysis of these hypotheses, I have not yet gone any further than these basic observations.