Proof for weighted sum of fibonacci squares

Ashwin's proof for weighted sum of fibonacci squares

Raga Malayamarutham

Raga Malayamarutham evokes the morning moods (pensive/meditative) similar to other ragas such as Bhoopalam, and Bowli. Malamarutham is a janya of malakarta raga Chakravaham (or Vegavahini per the Dikshitar school). The pensive nature (can come as across as plaintive for some listeners) seems to be a characteristic of ragas in this cluster (Mayamalavagowla, and Chakravaham being adjacent melakarta ragas).

Here is an older tamil song "Thendral ennai muthamittadhu" set to Malayamarutham by music maestro Illayaraja sung by relative unknowns:

I stumbled upon another Malayamarutham sung by S.Janaki and SPB called "Neela Kuyile Unnodu" also set to Malaymarutham by Illayaraja.

Turns out Malayamarutham is still in vogue: a recent R.Madhavan's movie Dum Dum Dum featured the song "Ragasiyama Ragasiyama" sung by Hariharan and Sadhana Sargam.

Of course, the classical prototype Malayamarutham is by none less than Saint Tyagaraja -- kriti "Manasa Etulo" by Carnatic Saxophonist Kadri Gopalnath.

All time greats of Carnatic Music

Here are some of the all time greats of Carnatic Music:

The Carnatic Music Trinity (Mumoorthigal):
In a typical modern day carnatic concert, it is a safe bet to assume more than 50% of the kritis/songs rendered would have been authored by one of the trinity. In particular, Thyagaraja seemed to have been a prolific composer with more than 20,000 kritis to his credit.
Thyagaraja
Shyama Shastri
Muthuswami Dikshitar

Purandara Dasa
Annamacharya


Great Carnatic Musicians of the 20th century:

Semmangudi Srinivasa Iyer

Raga Dharmavati and Madhuvanti

Dharmavati (aka Dharmavathi) ragam is one of the seventy two melakarta ragam like Kalyani, Shankarabharanam etc. This raga has been employed by both old and contemporary film music directors. At first glance, several phrases occuring in Dharmavati based compositions remind us of Kalyani.

Here is a Oothakadu Venkatasubbayyar's kriti Oododi Vanden Kanna in Dharmavati ragam rendered by Madurai T.N. Seshagopalan. Incidentally Oothakadu Venkata Subbayar had composed a set of songs in the praise of Lord Krishna (Krishna Ganam) some of which are exceedingly popular (to have made it into movies -- the song Alai Payuthey in Kanada ragam from the eponymous tamil movie is probably the best representative).

An old tamil song "Kathal Kathal Enru Pesa Kannan Vanthaano" from the movie Utharavinri Ullae Vaa is a good example of Dharmavati ragam.

An old SPB song "Nanda Nee En Nila" is based on Dharmavati ragam :

Mid-80s Kamala Hassan's movie Vikram also had a Dharmavati based song "Meendum Meendum Vaa" composed by Music Director Ilayaraja :

The early-90s featured Dharmavati by the contemporary music director A.R.Rahman in the song "Ottagatha Katikko" from the tamil movie Gentleman:

There is a detailed exposition of the use of Dharmavati (and other ragams) in tamil film music at Classical Ilayaraja.

The ragam Madhuvanti closely resembles Dharmavati (in fact, Madhuvanti is a janya raga of Dharmavati). Most classical musicians tend to sing/play Dharmavati elaborately whereas Madhuvanti is usually relegated to "tukkada" status. Notwithstanding that (or perhaps because of that), there are several short pieces of very nice Madhuvanti renderings both in classical carnatic and film music.

Here is a beautiful Thillana (carnatic form typically employed for dancing) in Raga Madhuvanti composed and played by one of the greatest carnatic violin maestros of all time, Lalgudi G. Jayaraman.

The theme song for a recent tamil movie "Kanda Naal Mudhal" is based on Madhuvanti ragam:

Here are couple of Hindustani renditions of Raga Madhuvanti: