Hi all,
Sorry again for not being able to participate more actively, for the reasons stated previously. The installation will go on for most of the week.
Firstly, let me say a few things very briefly about melody and harmony. I think you guys have mixed up harmony with harmonics. Harmonics are very useful for melody.
Harmonics:
Every musical note is actually a superposition of several frequencies. There is a fundamental frequency f (what is usually denoted as the freq of the note), but along with comes a host of frequencies which are integer multiples of the fundamental frequency. So the 2nd harmoic has a freq 2f, 3rd is 3f, and so on. An unmusical sound (for example a dog's burking, or even a human being with a harsh voice) will also consist of several frequencies with a fundamental, however, this time the other frequencies will not be harmonics or integer multiples of the fundamental frequency.
Now I'll explain why two notes may sound pleasing together (the case of harmony) or when taken in succession (in the case of melody). Say we have the frequency of Sa (called the tonic, or in our lingo the Sadaja) as f. Now, since this is a musical sound, it'll have higher harmonics and they will be 2f, 3f, 4f and so on. Now higher octave Sa by definition has a frequency 2f. The higher harmonics of the higher octave Sa are then 2x2f, 3x2f, 4x2f, ... , that is, 4f, 6f, 8f, ... etc. or all even harmonics of the lower octave Sa (the so-called tonic). This is the reason why these two notes (with fundamental frequencies f and 2f, also called the madhhya Sa and the tara Sa) when taken together or taken in succession of each other sound good (that is, not out of tune).
Extend the above logic. Take a note with fundamental frequency 3/2 f (called the Panchama or just Pa, belonging to the middle octave or the madhhya saptaka). Now you see that its upper harmonics are 2x3/2 f, 3x3/2 f, 4x3/2 f, ... that is, 3f, 9/2 f, 6f , .... . So you discover that all the even harmonics of the note called Panchama has the same frequencies as all the 3rd harmonics of the note Sa. That is why when the notes Sa (abbreviated as S) and Pa (abbreviated as P) are taken together or taken in succession, they also sound quite good (that is, in tune), This is called the first-fifth relation in Western music. Generally it's also called a consonance relation. We call it the Samvada relation. You may have heard Indian musicians calling two notoes as Samvadi to each other, for example S-P, r-d, R-D, g-n, G-N, M-S^, m-r^, P-R^, d-g^, D-G^, n-M^, N-m^ or P_-R, D_-G are all examples of the consonance/samvada/1st-5th relation (My notation here is the following:- S :Sa, r: komal Rishav, R: shuddha Rishav, g: komal Gandhar, G: shuddha Gandhar, M: shuddha Madhhyam, m: teevra Madhhyam, P: Pancham, d: komal dhhaivat, D: shuddha Dhhaivat, n: komal Nishad, N: shuddha Nishad: in addition the ^ symbol next to any note means that it's in the upper octave or tara saptak, and the _ symbol next to any note means that it's in the lower octave or the Mandra Saptak, otherwise all notes are in the middle octave or madhhya saptak). If you divide any freq by 2 it comes down by an octave, and if you multiply any freq by 2, it goes up one octave.
Similarly S-M is also a consonance relation (known as the 1st-4th in the Western world). Notice, it's not really a new relation. M-S^ is actually a 1st-5th relation.
You will find by simple algebra of ratios that this M has a frequency of 4/3 f if S has a freq of f.
So far we have found the ratios 2/1 (octave/saptaka relation or S-S^), 3/2 (samvada or S-P relation), 4/3 (another samvada or the S-M relation).
Similarly we shall find S-G relation where the freq of G is 5/4 f and the S-g relation where the freq of g is 6/5 f. The relation S-G-P is called a major triad, and the S-g-P is called a minor triad. These are also musically pleasing based on the theory of harmonics explained above. Also note that the ratio of the frequencies of G to S is 5/4 and that of P to G is 6/5 (that is the same as g to S). Examples of other major triads: r-M-d, g-P-n etc and of minor traids: R-M-d, G-P-N, P_-n_-R etc.
A scale developed in the above way is called a harmonic scale.
The scale predominant in Western music today or in any keyboard (piano, harmonium etc) is called the equal temperament. It cannot maintain these relationships based on harmonics except the octave relation, because in an equally tempered scale frequency ratios of two successive notes on the keyboard are the SAME for any two successive notes and that is the twelvth root of 2. So this way when you start from S and keep on multiplying by twelvth root of 2 and do it 12 times you reach the frequency 2f (the higher octave Sa), but you mess up all other harmonic relationships. For example the note P has the frequency 1.498... times f which is definitely NOT 3/2 f.
So in the above I have described some basics of the so-called harmonic scale on which Indian music is based, and in principle all music can be based. That is why, in Indian music, strictly, keyboards are discouraged. In all traditional music, some drone instruments are used like the tambura (in classical music) or do-tara etc (in folk music) and these are tuned usually in notes S and P with the absolute frequencies chosen appropriate for the vocalist's voice range or the type of instrument. Other than this absolute frequencies really do not have much place in music, the frequency ratios are important.
Melody is a musical piece where a succession of notes are taken one after the other so that the requirements of melody are fulfilled. Harmony on the other hand is implemented by taking more than one pitch sounding at the same time. Most harmonies are based on chords (groups of notes built on major and minor triads). Harmany can also be implemented by taking more than one independent melodic line at the same time (known as polyphony or counterpoint).
I do not know how to explain these things in a simpler way. These are much better conveyed in a lecture demonstration.
More later. BTW, during breakfast, I have listened to the song "Kalyana Then Nila" given in Sri's post # 161. Whenever I have some time, and if you people have some interest I can discuss that.
Actually these installation people went for an early lunch today, and that gave me the opportunity to write this long post. Now I am feeling very hungry. Off to lunch. I'll correct the typos later (must be many there).
Regards.
Note: Many typos corrected, one error corrected, a few lines added for more clarity.
