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.

Math and Music - Part II

Hello All !

In my previous posts, I had emphasised the importance of mathematical patterns, predictable sequencesand symmetry in music. It would not be fair to say that applying these forumula in music alone will make a musical hit. However, it plays a big role and I wish to talk about one such formula today, that I call "Break the sequence".

Here is an interesting sequence -
131 131 131 421
The interesting part here is the sequence "1 3 1" is repeated over and over again and the sequence is deliberately broken in the last by "4 2 1". The repetition of sequence and breaking it gives birth to melody. Illayaraja has used this pattern in 100s of his songs and I want to highlight some famous ones:

"ABC Nee Vaasi So Easy Un Raasi Vaa Rosi" song from Oru Kaidhiyin Dairy. If you assign Sa = 1, Ri = 2, Ga = 3 and so on, the swara sequence goes like this:

312 312 312 312 521

"Vaanile Thenila Aaduthe Paaduthe Vaanampadi" song from "Kaakki Chattai"
The sequence goes like this:
121 121 121 121 1442

"Vizhiyil Vizhundhu Idhayam Nuzhaidhu Uyiril Kalandha Urave"
The sequence goes like this:
888 777 555 444 111 001

Wow!!! Mere avarohanam played in a sequence of "Sudha Dhanyasi" scale. Oh God! I can't believe, he created a magical with such a simplicity. The beauty and melody lies when the sequence breaks at "Urave".

The super famous "Thakida Thathimi" has a sequence:
123 123 123 123 1 2 3

This is a different way of breaking the sequence. Not in swaras, but in the time signature. If the first 4 sets has a quarter note signature, the last part broke the sequence by a half note!

Another variation of the sequence in "Solai Poovil Maalai Thendral Paadum Neram" from "Vellai Roja":
88 88 88 88 7 6 7 8
We can go on and on by illustrating several sequences Raaja has employed in his hundreds of songs. Some of the others include:

Siriya Paravai Siragai Virithu Thudikiradhe
Naan Enbadhu Nee Allavo Deva Devi
Raathiriyil Poothirukkum Thaamarai Thaan Penno
Oru Kanam Oru Yugam Aaga
Kaalam Kaalam Aaaga Vaazhugindra Kaadhalukku Nangal Arpanam
Vidiya Vidya Nadanam Sandhosham
Arumba Arumba Saram Thodutha
Poovil Vandu Koodum Kangal Moodum Vandhu Odum
Iru Vizhiyin Vazhiye Nee Dhaan Ingu ponadhu
Innum Ennai Enna Seyya Poogirai
Iravum Pagalum Ulagai Rasikka Ninaithathu
Aalapol Velapol
Onnu Rendu Moonu Naalu

I will meet you all in my next post with different patterns that Raaja has used.

Math and Music - Part I

Mathematics and music are so interrelated and homogenous that ordinary ears can hardly see it as two separate entities. In general, the likeability of music or any piece of artwork by an ordinary person firstly depends on how easily he/she can comprehend and predict.

Though may not be true in all the cases, I believe it is true in a majority of cases. Once a person is able to comprehend and predict the piece of artwork, he is able to associate it with other pieces of artwork stored in the form of millions of nuerons. Now, at his will, he is able to retrieve the piece of artwork from his data bank. There stays your piece of artwork in his mind!

If you are still not with me, here is a real life example. You like a person who is compatible to you. (i.e.) who you can understand, comprehend and predict what he/she will do on an occassion.

So, one of the aspect to make an impression of an artwork in the minds of viewer is making it easy to comprehend and add a secret formula of predictability. Before you jump into any conclusion of what I am going to talk about, have a look at the two pictures:




By law of nature, most of us will be able to capture and reproduce the first picture better than the second. The reason is because, the first picture is "Symmetric". Our brain is able to comprehend, process and register the symmetric picture easily over the other. For ages, symmetry played a significant role in the artwork. You can notice in several artwork that symmetry were employed that added aesthetic feel.

Symmetry didn't stay just with painting and artwork, but also plays a major role in music. The role might not be evident to our naked ears, but, it adds that spice of "predictability" to the music.

It is not only "symmetry", but also a predictable pattern/sequence that interests people. For example, recently I got a new Palm Pre and it is simply superb. My only complain is I was not able to retain my old phone number that was very easy to remember - 734-26-26-226! Wow!! It's a nice pattern/sequence!

Music is no different from our real life. If you want to make a piece of music interesting, try employing a pattern sequence or symmetry on a scale and see the results yourself.

Well, coming to Raaja's fortress, he has exploited this aspect to its fullest extent. I will meet you all in the next post with more details.