Math and Music - Part IV

"Axis of Symmetry" is a line that divides the figure into two halves, with either side is a mirror image of the other. In the world of music, with all the figures formed with 7 Swaras, Shadjamam and Panchamam have a special significance. If the frequency associated with Shadjamam is X decibels Hz, and the Shadjamam at the next octave is 2X decibels Hz, then, the Panchamam stands in the middle of it as an axis of symmetry - at 1.5X decibels Hz.

In short, Shadjamam and Panchamam notes are special because they act as epicenters, around which other swaras dwell. In this post, I would like to bring some interesting aspect, what I call "Sa Pa Symmetry". Play a sequence/pattern of notes with your Sa as the home key and try to play the same sequence/pattern of notes with lower/upper Panchamam as the home key. There you go!

Keeravani and Mayamalavagowli raaga offered this symmetry naturally. Raaja has used this pattern in many many songs. To highlight with a classic example, "Poovama Oorvolam" song from Chinna Thambi. Listen to the verses -
"Aranmana Annakili Tharayile Nadapadhu Nadakkuma Adukkuma
Paniyilum Vetta Veli Veyilum Ulla Sogam Aranmana Kudukkuma"

If the first line of the above stanza is centered around upper Shadjamam, the second one follows with lower Panchamam. Another example in "Poova Eduthu Oru Maala" from "Amman Kovil Kizhakkale". Listen to the verses -
"Kannadi Vala
Munnadi Vizha"

Other evident usages that comes to my mind immediately are - "Om Namaha" from Idhayathai Thirudadhe; "Poo Poo Poo Pootha Solai" and many more..

This might be one of the reason why Keeravani and Mayamalavagowli are very popular in light music and especially Raaja has used to its full potential in film songs.

Math and Music - Part III

"Octave Equivalence" is an interesting concept that I have discussed in my earlier post - http://7swara.blogspot.com/2008/08/science-of-sound.html

You can observe that in a keyboard, the keys goes like this: Sa, Ri, Ga, Ma, Pa, Da, Ni .... and it repeats with Sa, Ri, Ga, .... and so on.. The frequency of Sa in the lower octave is half of the frequency in its adjacent higher octave and so on. When the frequency doubles, it sounds similar and hence its called "Octave Equivalence". (i.e.) Sa in lower octave sounds similar to Sa in higher octave except for the fact that the frequency is higher.

You cannot imagine how music would sound in the absence of this "Octave Equivalence". As many composers, Raaja has used this "Octave Equivalence" in several hundreds of his songs. The usage of this concept automatically brings a beauty to the piece of music inadvertantly.

Let me illustrate with an example -
"Vaanile Thenila Aaduthe Paaduthe" song from Kakki Chattai movie.

The notes for "Vaanile Thenila Aaduthe Paaduthe" goes like -
P D1 P P D1 P P D1 P P D1 P

In the Charanam, the last phrase goes like this - "Maivizhi Paingodi Mannavan Poongodi"
The notes for the above phrase is EXACTLY same as pallavi -
P D1 P P D1 P P D1 P P D1 P
but, in the higher octave.

Another example -

The swaras in "Aasai Nooru Vagai Vaazhvil Nooru Suvai Va" - Pallavi is identical to the swaras used in later part of the Charanam.

"sorkam maNNil varum sondham kaNNil varum vaa"

In other words, the tune for the two parts is identical except for the fact that one is in lower octave and the other in higher. Raaja has employed this technique especially with repeating the Pallavi's tune in Charanam (in higher octave) in many songs.

You can observe the same pattern even in the recent "Kangal Irundaal" song by James Vasanthan. (Kangal Irandaal (Pallavi) - S G R G M; Unai Indri Verum Enadhillai (Charanam) S G R G)

Meet you next time with a different pattern.