I must say I am deeply disturbed by the above post. I kept quiet all these days, because, as I said earlier, I did not want to discuss very serious and technical musical stuff here in this forum and also do not want to offend anybody. I also hope that the soul of Ali Akbar Khan forgives me for raising these issues again in a thread related to him.
However, the fact remains that I do not agree with the general message contained in gobble's post, although I agree with certain things there.
It is mentioned that very early in the Indian philosophy the 'numerical ratios of musical intervals' were appreciated. In this context, you have also mentioned Western music has only very simple relationships like major and minor etc.
Now I like to ask you, do you know what these ratios are? Can you tell us the frequency ratios of all the notes used in the ragas you have mentioned in the post (Sindhu Bharavi, Mohana, and Kalyani)? Or, have you seen these ratios mentioned in any text?
I can give you the answer: a resounding NO. But I'll try to give you some these ratios as much as possible within the limited scopes of this forum.
The most basic ratio is 2:1 (called the Octave or Saptaka) in any music anywhere in the world. The combination of notes related by octave relationship is a pleasing one, because the even harmonics of a freq f, i.e., 2f, 4f, 6f etc, are the same as all the harmonics of the note 2f, i.e., 2f, 4f, 6f etc.
Similarly the ratio 3:2 is also a pleasing combination. In Western world this called a Consonance relation, we call it Samvada. The reason in terms of harmonics is the same. Next comes the ratio 4:3, but it comes from a combination of the Octave (2:1) and the Consonance (3:2), because the higher octave of a freq f, ie, 2f has a frequency 4/3 times the frequency of the consonant to f, ie, 3/2f.
Similarly come the ratios 5:4 and 6:5, respectively the major and minor thirds.
Now, I shall show you how one obtains the notes of the Raga Mohana, mentioned by you, because it's the easiest. The other ragas are more complicated, and hence it would be difficult for me to explain within a limited space.
Step 1: Tune the 4-string tanpura in the traditional way, ie, the first string to Pancham (P), the next two to higher octave Sadja (S) and the last one to lower octave Sadja (S). Remember if the lower octave S has frequency f, it automatically fixes the freqs. of the higher octave S at 2f and the P at 3/2f.
Step 2: By the major third (5:4) relationship, the freq of Gandhar (G) is fixed at 5/4f. Note that this also makes a minor third relationship of the G (5/4f) to P (3/2f) because 3/2:5/4 = 6/5.
Step 3: Now get a new note (in this case the Dhaivata, D) by using the consonance relationship with the Gandhara (G) so that the G becomes 3/2 times the freq of the D. Obviously that D belongs to the Octave lower than S at freq f, it has the freq = (2/3)xfreq of G = (2/3)x5/4f = 5/6f. To get the the freq of D in the middle Octave, we just need to multiply that by 2. So the freq of D is 5/3f. Note that D-S-G forms a minor traid and S-G-P forms a major triad and the notes S-G are interspersed in both the triads or Khanda-merus. The whole combination D-S-G-P has been called the Meru or Matrika in certain literature.
Step 4: There is a 5th note in Raga Mohana. In general, there are two ways to get the freq of that 5th note: (a) Choose it so that D becomes the consonant note (ratio 3:2) to this one (would be called Rishava, R) so that the freq of R = (2/3)x(5/6f) = 10/9 f; (b) Choose it so that it is consonant with the Panchama P (it will then be higher than 2f and would belong to the octave higher than upper S). Dividing by 2 to bring the freq to the middle octave, one gets the freq of R = (1/2) x (3/2) x (3/2)f = 9/8 f. So we get two different frequencies of the note R, depending on from which context we arrive at the note.
So finally we have the frequencies of all the notes in Raga Mohana (or its variation, by using the method (b) above). The variation (a) is called in the North Indian lingo the Raga Bhupali or simply Bhoop, and the variation (b) is called Raga Shuddha Kalyan (Mohana Kalyani in Karnatic, I think) although Shuddha Kalyan uses two other notes (called Shuddha Nishad and Teevra Madhyam) peripherally and only while sliding (called Meend) in the Avarahi (descending) pattern. I can discuss also how these two extra notes help enhance the freq (9/8 f) of that particular R, but this is not the place.
So, you see how the Raga scales are selected by nature, by a few basic ratios (Octave, Consonance, Major and Minor thirds) and the rest of the notes are defined using these basic relationships from a given context. If the context is different, you can arrive at slightly different frequencies of the so-called same note, as exemplified above in the case of the note R. So the context also defines which note should follow which one, quite naturally. This takes years of practice, but when a classical musician performs a particular Raga, he or she is improvising, but not randomly, but according to the natural selection of frequencies for a given raga and he or she is arriving at a given note from a previous note with a particular inherent relationship between notes. All this happens quite naturally and spontaneously, obviously after years of practice.
The above should also explain why a lot of folk music around the world is based on Mohana (or Bhupali or Bhoop) or 4 other Ragas obtained from translating the scale of Mohana (ie. making R the fundamental, then making G the fundamental and so on). This method of translation is called the "Murchhana". In the North Indian nomenclature, the other 4 Ragas are respectively called: Madhyamadi Sarang (called Madhyamavati in Karnatic), Malkauns (Hindolam in Karnatic), Durga (Suddhasaveri in Karnatic) and Dhani (I do not know of any Karnatic equivalent, I am sure there is one). I call it a natural selection because it seems nature and our brains prefer a complete consonance and tend to look for the fundamental frequency f in all other notes or their harmonics. That's why in the North Indian voice training tradition, Gurus always give a special emphasis on staying at the fundamental note (S), because without it no other notes are defined and the melody will never be created.
After all this discussion, does it matter any more what came first, or which is more superior etc? I find that part of Gobble's post largely irrelevant and potentially wrong. Even the word "Saamkhya" is a Sanskrit word (adjective derivative of "Samkhyaa") and does not have the roots from any Dravidian (pre-Vedic) language. But I agree even given the above, it still may have pre-Vedic roots, just that nowadays we may call it by a Sanskrit name. Please note that by Sanskrit I mean a language not necessarily after Panini's work. This language existed even before Panini. Panini made an order and formulated the grammer and thereafter it was called Sanskrit.
Discussions of this sort are very misleading and potentially damaging. Most references to Kapila (apparently the founder of "Samkhyadarshana"), if not all, are dated AD. It is very hard, if not impossible, to determine the age of the Vedas and even Mahabharata. You would be surprised to know that versions of Mahabharata existed even among the native tribes of India and some of them did not even have a written language. A dear friend of mine (another physicist actually) does research in that area and he keeps on telling me all these differing and fascinating variations of Mahabharata's little episodes. Right now he is working on "Harivansham", the sequel to Mahabharata.
Some even suggest that the North Indian classical music has come from the middle East and Karnatic music is the pure form of Indian classical music. Common sense would tell you that this is not true. If the North Indian music is derived from the middle East, where is the present form of that music in the middle East itself? Kerala had a long relationship with most of the middle East for as long as History can reach back, but the classical music from Kerala is mostly the Karnatic classical music. The state of Orissa had one of the least influences traditionally of outside invasions or interactions of the above kind, still the classical music prevailing largely in Orissa is in the North Indian style. Where has the use of violin in Karnatic music come from? Is it a traditional Indian instrument?
Why should we dwell on irrelevant topics? We in India have one of the richest forms of music, highly sophisticated and developed and the whole world now acknowledges that. When I taught a Masters level course on Indian classical music at the Music Department of the Ohio State University, USA, it was attended by most faculty members of the music department and some from neighboring Universities. I have seen the respect in their eyes and an attempt to embrace it. I know and can refer to many Western composers who are nowadays trying to come out of the "equally tempered" scale (fixed scale provided by the keys of the piano or the harmonium) and compose using a "harmonic" scale (which is how a scale or raga is achieved, as exemplified by the example of Mohanam above).
Actually I do not see any difference in the basics of both these classical forms of India, neither in melodic nor in rhythmic structures. Essentially the scales of our Ragas (although they are called by different names in the two styles) are the same and derived by the methods described above. Believe me, I have learnt a little, read a little and spent a lifetime on these things. The forms in which the melody is presented is somewhat different nowadays, and that may have something to do with outside influence or different ultra-local customs and cultures.
Gobble, this post is not meant to offend you. Please forgive me if it does. Just that I cannot agree with the general message you wanted to convey and I believe there is only one way of finding out about these things. Forgive me again, I do not want to spell it out.