The post is more technical than usual ones, please bear with me and read on. Hope you enjoy it as much as other posts.
Thanks to Aditya T., I came across this wonderful video of Bobby McFerrin demonstrating how we have the pentatonic scale imbibed in us :
The pentatonic scale in Western notation is – C D E G A C (Sa re ga pa dha sa)as opposed to the regular heptatonic scale scale – C D E F G A B C (Sa re ga ma pa dha ni sa)
For Indian classical music aficionados, this is the Bhoopali raga of Hindustani and Mohanam of Carnatic music.
As the video will tell, no one is tone deaf or musically challenged. During a recent meeting with some friends, we discussed how humans from different continents with no contact with each other whatsoever ended up with the same 7 notes as the foundation of their respective musics. This seems to point out that we all have the basic knowledge of music. In more technical terms, our brain responds to frequencies that form the musical scale. Even more specifically, our brain is tuned to the logarithmic scale.
First, what is a logarithmic scale.
In our linear scale, the numbers form the sequence 1, 2, 3, 4, 5, 6 and so on. This is the scale we interact with on a daily basis.
In a logarithmic scale, the sequence would be 1, 2, 4, 8, 16, 32 and so on. Did you see what happened ? Each number is multiplied by 2 to get the next number. This is a logarithmic scale in base 2. Similarly, you can guess what a logarithmic scale in base 10 would look like. 1, 10, 100, 1000 and so on. Cool ?
Now for those who don’t know, frequencies of musical notes are logarithmic in nature. I’ll try to explain in simple words :
If a standard C note plays at 256 Hz, the next C — the higher C — the C of the next octave — plays at 512 Hz. The next C would be at 1024, 2048 Hz and so on.
From one C to its next higher C, are 12 intervals (C -> C# -> D -> D# -> E -> F -> F# -> G -> G# -> A -> A# -> B -> C)
Given a factor of two between the two extreme C’s, the factor between each individual interval is the 12th root of 2.
So the (frequency of C)*(12th root of 2) will give you the frequency of C#.
Then the (frequency of C#)*(12th root of 2) will give you the frequency of D.
Do this 12 times, you’ll get the higher C, which is exactly twice the lower C.
Update : As Pranav points out in the comments, this means each note is higher than the previous one by 6%. Hope that helps simplify things.
All this to show that the musical scale is logarithmic in frequencies.
During the discussion, a friend mentioned that babies respond to the logarithmic scale naturally. When they are shown a set of objects of increasing sizes (like 1 apple, 2 apples … and so on), they identify changes in the logarithmic scale i.e. the neurons of the brain that fire up on seeing these sets have peaks at logarithmic points (like 1, 2, 4, 8 and so on). I am not sure if the base of the logarithm is 2 or 10 though, I could confirm if someone is interested.
You can always contact me offline for a more practical explanation if none of this made sense.
P.S. : The choice of fruit was incidental.
Ever heard of Okinawan music?
They too follow a pentatonic scale, but its slightly different. It has “C”, “E”, “F”, “G”, “B.”
Wikipedia says,
A pentatonic scale, which coincides with the major pentatonic scale of Western musical disciplines, is often heard in min’yō from the main islands of Japan, see minyō scale. In this pentatonic scale the subdominant and leading tone (scale degrees 4 and 7 of the Western major scale) are omitted, resulting in a musical scale with no half-steps between each note. (Do, Re, Mi, So, La in solfeggio, or scale degrees 1, 2, 3, 5, and 6) Okinawan min’yō, however, is characterized by scales that include the half-steps omitted in the aforementioned pentatonic scale, when analyzed in the Western discipline of music. In fact, the most common scale used in Okinawan min’yō includes scale degrees 1, 2, 3, 4, 5, 6, 7,
I didn’t really get what they are trying to say though. I guess a mathematical explanation (like this one, with numbers!) would help.
For your reference, some awesome examples:
[http://www.youtube.com/watch?v=h9Lg3dHFfsM]
[http://www.youtube.com/watch?v=3hS2g9Pzx7g]
By: Ady on November 12, 2009
at 4:35 am
@Ady : Given your explanation and the wiki description, I think this is just the normal major scale, which is why it is so popular (is it ?).
The second video has something going on in the notes, but I don’t have any instrument here at work, so will check and let you know later.
By: Deepak Iyer on November 12, 2009
at 9:41 am
Well…Yes it is very popular. The examples I gave are JPOP versions of Okinawan music though. The real thing is a bit too heavy for me to handle.
I did confirm with a jap friend here, he says its not the (okinawan) pentatonic scale in both these songs. He claims to have made something which follows the okinawan pentatonic scale
Sunrise
http://www.myspace.com/mario5115
Also would like to you to check out Hajime Chitose
http://www.fuzakeruna.com/blog/2009/08/176/
By: Ady on November 12, 2009
at 7:38 pm
>The pentatonic scale in Western notation is – C D E G A C (Sa re ga pa dha sa)as opposed to the regular heptatonic scale scale – C D E F G A B C (Sa re ga ma pa dha ni sa)
>For Indian classical music aficionados, this is the Bhoopali raga of Hindustani and Mohanam of Carnatic music.
Since the post is technical i wish to add this –
To say that Sa re ga pa dha sa is raga Bhoopali would not be correct. One of the principal differences in ICM and Western classical is that – in ICM notes might look the same on paper but sound differently when played in a Raga. A raga cannot be defined by the names of the notes. The lagaav might be different even if names are the same. For eg. Komal Gandhar(KG) in a Bhairavi is different than the one in Todi, although on paper one would write both as KG(since shrutis aren’t generally mentioned in the notation). A better way to put it is to say ‘these are the notes used in Bhoopali’, lest someone reading this should misconceive the important point.
>As the video will tell, no one is tone deaf or musically challenged
Did not get this :-/
>This seems to point out that we all have the basic knowledge of music.
There is a long going debate in the scientific community about this.
Another tiny addition towards simplification would be – 12th root of 2 is approx equal to 1.06. Thus, in WCM, one semitone higher = roughly 6% increase in frequency.
Thanks.
By: Pranav Peshwe on November 14, 2009
at 8:26 pm
@Pranav – I did feel a small pinch when I just wrote Bhoopali, but in the spirit of simplification, I went ahead anyway.
I could’ve said Deshkar instead of Bhoop for the same notes, but Bhoop is more popular even for a naive listener.
Tone deaf — I don’t know if you’ve seen the Music and Passion video by Benjamin Zander (it is posted here : http://iyerdeepak.wordpress.com/2009/09/20/music-and-passion/). The people here weren’t necessarily musicians, and as McFerrin says, it would work anywhere. I’ve myself seen that in a chorus, people’s tones tend to converge to one, because you feel something is ‘wrong’ when you are at a different note. As far as tone deaf is concerned, if you can drive a geared car, you aren’t tone deaf [;)].
I would go ahead and say it anyway — all humans have some basic knowledge of music. I’ve seen it in the happen, I had zero inclination or knowledge of music until my 9th, and then as I learnt things started sounding intuitive.
6% — Sure, why not. In the spirit of simplification [:)]
By: Deepak Iyer on November 14, 2009
at 8:40 pm