You may wonder about my title: how could the musical scale have anything cosmic, or anything mysterious, about it? You've probably all the heard the familiar do-re-mi-fa-so-la-ti-do many times, and if you are a musician, you've played it hundreds or even thousands of times. If anything, it may even seem quite mundane.
Quite to the contrary, I find the scale to be fascinating, and an endless source of wonder in respect to how it is the life force behind all our music. (I am speaking here of the Western scale and Western music, though the same concept can be applied to other music and their scales.) It is not only the tonal material which our music uses, it is also the organizing principal, that which gives the possibility of movement and architecture to our music.
Try the following experiment: play an ascending scale, for example the C major scale, on the piano or any other instrument. Do it in the following manner. Play C (do) and then D (re). Listen to what wants to happen. Does the re want to move forward or fall back to do? I think you will find it does not yet have enough momentum to move forward, but can easily fall back to (or resolve to) do. Now play C-D-E (do-re-mi). What does that want to do? It has more momentum than the previous step, but barely enough; it can also easily fall back to re and then do. Now play all the way up to F (fa). You will hear an unmistakable difference -- a feeling of starting to travel or make progress....yet.... it is still somewhat easy for it to fall back to re, at least, if not all the way back to do. Now play all the way up to G (so). If you are really listening you will hear that feeling like you have reached the crest of the hill; there is no going back, only forward. As you play the scale up through A (la) you will feel the momentum increase. When you get to B (ti) the urgency to get to the final C (do) is very strong; you simply cannot go anywhere else. The final tone, ti, is often called the "leading tone" for this reason. (I thank the great writer/musicologist Victor Zuckerkandl for introducing me to this fabulous experiment over 30 years ago in his book The Sense of Music.)
I suppose there are two camps on this matter: one that says we hear it this way because we are so used to it operating in this way in our music, and another camp which would say it is something inherent in the scale itself. I am in the latter camp. There is something about the dynamics of the scale which cause us to experience it in this way, which is why, I believe, this particular scale took hold and became the basis for our music for so many hundreds of years. It gives a dynamism, a richness to the music that you simply don't get in, for example, a pentatonic (5-tone) scale.
The example we've just used is the scale we know as the Major scale (the Greeks called it the Ionian scale). What about the others? The minor (Aeolian) scale has some of the same feeling, but lacks the drive at the end with the leading tone. For that reason, the minor scale has been altered since about the mid 1600s (the so-called "harmonic" minor) to have a ti, or leading tone, raised to be the same as the major scale. The other scales, Lydian, Phyrigian, Dorian, etc, have to a large extent fallen out of usage (some ethnic music still uses them, and pop and jazz musicians use them as a basis for improvisation but they are rarely the basis for an entire piece of music).
Coming back to the dynamics of the scale tones, you will see that the first tone of the scale (do) feels like the center, or home. The 5th tone (so) feels as far as you can get away from the center, or home, before you feel like you are returning to it. This sets up one of the most important aspects of the scale, the polar opposites of the one/do and the five/so. You will see the importance of five in our music everywhere (the Circle of Fifths). The Greeks called the one-five relationship in music the Golden Mean or the Golden Ratio and considered it to be the "perfect" relationship. (Mathematically it is the ratio of 3:2) It was used in painting and architecture as well.
It is difficult to say whether the dynamic qualities we experience in the scale are all the result of mathematics. Some have believed so, and some believe it even goes beyond mathematics to the nature or the structure of the universe. The mystic G.I Gurdjieff (1877-1949) and his student P.D. Ouspensky believed the scale had cosmic meaning. "Ouspensky devotes pages and pages to Gurdjieff's concept of "octaves" - the
musical scale do-re-mi-fa-sol-la-ti-do taken as a sort of universal yardstick
for determining the measurements and proportions of all of nature's parts" (www.progressiveears.com/frippbook/ch07.htm).
With my beginning students, and even some more advanced students coming to me from other teachers, I always have them learn to play a scale (with simple fingering, 4 notes in the left hand and 4 notes in the right) at the very first lesson so they can begin to really hear the scale and understand how it is constructed. I make sure they understand I am not giving it as a "finger exercise" to be done over and over; it should just be done a few times, just to experience it. How sad it is that thousands upon thousands of musicians have done endless hours of scale practice, and yet perhaps never really heard or understood the magic and mystery that is our simple musical scale.