Thursday, March 25, 2010
The Origin of Music
In this post, I will examine what exactly music is and how it might have evolved. Then I will proceed to explain why we find music enjoyable. This will naturally lead to the explanation of why most of us (if not all of us) find the major pentatonic scale and its derivatives to be naturally "happy". I will also be able to explain why, for instance, most of the popular chart-busters have simple rhythm patterns.
Sound
Men (and animals) have developed the capacity to hear for various purposes, one of the most important of them is to sense danger. For example, a hiding animal about to pounce and attack is detected by the man, who might be out of sight, using his ears -- the sound produced by the pouncing animal being the auditory cue. Likewise, rocks eroding and caving in (after perhaps some kind of land-slide) onto a man's house produces a series of sounds, which the man has to quickly perceive and react. Thus sound is mainly a cue for danger to which men have to react quickly to prolong their lives -- which is why men are highly receptive to sound. Let us examine the characteristics of sound that signifies danger. It is either a sudden short sound, as it is when an animal pounces or can be a series of sounds at random intervals and of random volume as it is when rocks are caving in.
First music -Rhythm
Now let us imagine that man A suddenly uses his hands and starts producing a periodic repeating sound. Man B (out of sight) upon hearing the first few sounds would sense danger initially and his body would ready itself to react to it (by producing appropriate hormones etc.). However, as man B continues to listen to it, he senses that there is something strange to this sound, in that, it is of uniform volume and is periodic; and it does not match any of the patterns of the sounds that indicate danger. Curious, he goes towards the source of the sound slowly and finds that it is actually man A generating it. Suddenly, the curiosity changes to relief and joy as he realises the safety in the situation. In other words, he experiences a series of emotions, namely fear-->curiosity-->joy, for what essentially constitutes the simple rhythm.
Music : Ratios in Time and Frequency
Why is it that the man B found the rhythm to be safe? Just because of the fact that the rhythm played consisted of sound at non-random times...In other words the pauses between the sounds bore simple ratios. This makes it highly unlikely that the sounds could have been produced by a natural cause; which in turn leads the man to a sense of safety and joy. Thus I claim that the simple periodic rhythm might have been the earliest music.
The different notes of music can be analyzed in a similar fashion. The different notes in music constitutes a simple ratios of the frequencies. For example if C (Sa) is 256 Hz, then G (P) is 3/2 of the original frequency which is 384 Hz. These simple ratios are those that make the probable source of the music non-random, which in turn causes emotions of safety and joy.
Applying this theory:
With this theory we are now in a position to explain several things which are empirically observed:
1. Sometimes it takes time, in terms of repeated listening, to fully appreciate a new tune.
This is a commonly observed phenomenon. For e.g. it is alleged that Rahman's songs take multiple listening to get used to it. I had called this as the attack time in my previous post. This can be explained by the fact that the listener initally does not understand the patterns involved in the new tune, which means the emotion stays in the curiosity part while he is still getting used to the pattern. Once, the listener finally understands the non-randomness involved in the tune, joy is finally caused. Now, this time is clearly the function of the musical experience of the listener. The listener who has already been exposed to a large volume of tunes, is able to quickly decipher the non-randomness involved in the new tune and hence appreciate it faster.
2. People get bored of songs on repeated listening.
I had called this decay in my previous post. Once the listener has listened to the song sufficient number of times, he becomes so used to the progression that the patterns do not anymore lead to the necessary uncertainty and curiosity into the listener to lead to joy.
3. Most popular music consists of the simple rhythm
The large majority of population has a brain which is hardwired to react to noise; the simple rhythm is the simplest kind of sound that introduces non-randomness into the noise and can therefore be easily understood and appreciated by the large majority and is thus popular.
4. The pentatonic scale is common across most musical forms.
The pentatonic scale (or its variants) is common across various types of music -- for e.g. chinese music, Greek , Celtic, classical, Hungarian, and Indian music etc. I claim that it is common across most musical traditions because of the simplicity of the ratios of the notes in this scale. For e.g let us examine the notes of the major pentatonic scale (known as Mohanam or Bhupali in Indian music). The notes in this scale are:
- C (Sa) : Ratio 1
- D (Ri) : Ratio 9/8
- E (Ga) : Ratio 5/4
- G (Pa) : Ratio 3/2
- A (Da) : Ratio 5/3
As we can see the notes involved in the scale involve simple ratios. This enables the listener to infer the patterns and the relations between the notes relatively easily. Remember, that the easier it is for the listener to understand the relationship between notes (the ratios), easier it is for the listener to understand the non-randomness and thus easier it is to appreciate the music.
To extend this idea one step further: the easier it is for the listener to understand the relationship between notes, the "happier" the feeling aroused. This may also explain why the pentatonic scale and its variants are generally perceived as "happy" sounding.
Labels: music
Monday, February 19, 2007
Are all art-forms algorithms?
It's absolutely impossible to improvise. Making a movie is a mathematical operation. It is like sending a missile to the moon. It isn't improvised. It is too defined to be called improvisational, too mechanical. Art is a scientific operation, so I can say that what we usually call improvisation is in my case just having an ear and eye for things that sometimes occur during the time we are making the picture.
-- Federico Fellini , Italian Director
In Computer science, an algorithm is a set of instructions for accompishing a task. Furthermore, if the instructions are executed correctly the task will be accomplished in finite time.
Is there an algorithm for each and every art form?
I think so. I strongly subscribe to fellini's notion of all art actually being science. I think there are several reasons for art being separated and given a different status.
(1) The general quest of people to experience something incredible, amazing i.e some performance that does not have any apparent "algorithm" for they themselves accomplishing it.
A classic example is magic. People are attracted to magic just because they do not know the "algorithm" behind the trick. But do note that every magic trick has a plausible explanation. If the explanation is known to the public they will not want to pay and watch the show.
I think all art forms are like "magic" in that they have a well defined procedure for accomplishing the art form, which if known to people will diminish their amazement about the art form.
(2) In most art forms the algorithms are complex because of which the performer is not aware that he is merely executing an algorithm; His subconcious self is obviously aware of the algorithm which is why he is able to perform in the first place
(3) The randomized nature of most art forms gives as impression of improvisation. In most cases the actual algorithm may be a randomized algorithm. For example each time a singer executes a raaga aalapana (of the same raaga), it is different. If a batsman faces identical deliveries (pace, length, line, conditions are identical) he may yet play two different shots. Note that a randomized algorithm is still an algorithm.
As a proof of concept, here is a very simple algorithm for music composition.
Inputs: The emotion of the song. (Eg happiness , pathos etc...)
Output: The composition
-------------------------------------------------------------
Algorithm:
1. Consult look up table and obtain raaga, tempo.
If there are more entries for the emotion, pick randomly.
Note the look-up table is of the following form:
Mood Raga Tempo
death Subapanthuvaraali 40BPM
...
happiness Mohanam 120 BPM
happiness shankarabaranam 160 BPM
.....
.....
2. Chose a tala at random.
3. Emit notes from the raga randomly such that it fits the tala.
---------------------------------------------------------------------
Thats all...we are done. My intuition says that this ridiculously simple algorithm is enough for composing "good" songs. Ofcourse, the algorithm's caomplexity can easily extended/increased in practice.
I need to try and build this software and get the general public's opinion on the "quality" of music.
-- Federico Fellini , Italian Director
In Computer science, an algorithm is a set of instructions for accompishing a task. Furthermore, if the instructions are executed correctly the task will be accomplished in finite time.
Is there an algorithm for each and every art form?
I think so. I strongly subscribe to fellini's notion of all art actually being science. I think there are several reasons for art being separated and given a different status.
(1) The general quest of people to experience something incredible, amazing i.e some performance that does not have any apparent "algorithm" for they themselves accomplishing it.
A classic example is magic. People are attracted to magic just because they do not know the "algorithm" behind the trick. But do note that every magic trick has a plausible explanation. If the explanation is known to the public they will not want to pay and watch the show.
I think all art forms are like "magic" in that they have a well defined procedure for accomplishing the art form, which if known to people will diminish their amazement about the art form.
(2) In most art forms the algorithms are complex because of which the performer is not aware that he is merely executing an algorithm; His subconcious self is obviously aware of the algorithm which is why he is able to perform in the first place
(3) The randomized nature of most art forms gives as impression of improvisation. In most cases the actual algorithm may be a randomized algorithm. For example each time a singer executes a raaga aalapana (of the same raaga), it is different. If a batsman faces identical deliveries (pace, length, line, conditions are identical) he may yet play two different shots. Note that a randomized algorithm is still an algorithm.
As a proof of concept, here is a very simple algorithm for music composition.
Inputs: The emotion of the song. (Eg happiness , pathos etc...)
Output: The composition
-------------------------------------------------------------
Algorithm:
1. Consult look up table and obtain raaga, tempo.
If there are more entries for the emotion, pick randomly.
Note the look-up table is of the following form:
Mood Raga Tempo
death Subapanthuvaraali 40BPM
...
happiness Mohanam 120 BPM
happiness shankarabaranam 160 BPM
.....
.....
2. Chose a tala at random.
3. Emit notes from the raga randomly such that it fits the tala.
---------------------------------------------------------------------
Thats all...we are done. My intuition says that this ridiculously simple algorithm is enough for composing "good" songs. Ofcourse, the algorithm's caomplexity can easily extended/increased in practice.
I need to try and build this software and get the general public's opinion on the "quality" of music.
Labels: algorithm, art, compose, music
