Sunday, July 06, 2008

"Mind" -> The Scale Of Music Part VI

We've covered a lot of ground, and on many of these subjects, we've hardly have scratched the surface. On just the subject of scales, some people spend the rest of their lives thinking about this. Once you discover that our basis for a scale is made up, you can change your assumptions and create a whole separate music system. So we have the field of micro-tonal music, where some strange people are pulling out new bases for scales, and creating new music. It is my observation of this music is that this music is horrible, since we are already programmed to a musical scale early in life. You can no more hear a new musical scale than you can hear phonemes once your brain has gone past plasticity.

So, what have we found out up to now? What we have found out is that there are 12 candidate notes, and the major cultures selected notes for their scale. We've found out that their are pentatonic scale and heptatonic scales.

In Western music, we picked the heptatonic scale that we call "The Major Scale." Now, most of Western Music is based around fourths and fifths.

If you remembered the previous posts, we found out that the fifth was very popular. It vibrates 150 percent faster than the base note. The fourth is a fifth below the root that has been shifted up one octave. While the fourth and fifth isn't in every culture, it is certainly in ours. Due to something called overtones, these sound pleasent to our ears.

So lets draw out our scale again:


The gap between C and F is a fourth. The gap between C and G is a fifth. The gap between F and G is called a whole note. When we look at the whole note, it is found almost always between any two notes on a Major Scale. This would be great, but there is one issue with the whole step. There is not an even number of whole steps between the tonic note and the dominate note (between C and G). You need to go three and one half steps to go from the tonic note to the dominant note.

Now, this is a very big deal. Remember that the reason that we have three and a half notes is because there is a whole step between the forth and fifth note on the scale. These three notes are the notes that sounds good.

However our nice scale system falls apart below the subdominant note (F in our case), because we need 2.5 notes to get back to the tonic note. The answer is very simple. We need to take two whole steps and one half step. We've been writing about the major scale and the major scale picked that the step between 3 and 4 would be the half step. If you go back to our post on cutting the string down to find different notes

So, we find out that the major scale goes like this to the fourth

C to D (whole step), then D to E (whole step), then E to F (half step). This is a very important series of notes. This is so important that we've given it a name, the "tetrachord" and western music is built around it. A tetrachord is a chord made up of 2.5 steps to get to a fourth.

We say that the major scale, up to the fifth is as follows: Whole, Whole, Half, Whole, or 3.5 steps.

Once we have gotten to the dominant note (G in our case), we need to climb all the way up to C.

How much higher is the C than the G note? It is a fourth higher. Now, we just found out that the fourth is made up of 2.5 steps and is called a tetrachord. We are going to reuse our tetrachort, and use the exact same interval steps in our last fourth.

G to A (whole step), A to B (whole step), and finally B to C (half step).

The octave, in this system, is built around two tetrachords separated by a whole note.

CDEF is a tetrachord made up of whole, whole, half steps.
GABC is a tetrachort made up of whole, whol, half steps.

There is a space of 1 whole note between these two tetrachords.

Let's look at a piano keyboard. You can see that I've labeled the keys on the keyboard.

You may have remembered, if you look piano lessons at any time, that if you start on C, the scale is just the "white notes." I remember when I was a kid, the other kids saying things like, "Wow, the black notes, I don't even know what those things do."

Once you start to understand the scale, you'll start to understand that each key on the keyboard is spaced exactly the same amount apart (on a decibel scale, that it, which we won't get into now.) Thus any time that you cross a line, you will go up exactly a half step. The interesting this about the scale, as we've just learned, is that the scale for Western Civilization has a couple of tricky things about it. Again, look at the photo. To go from the E note to the F note is just a half note because it only crosses one line. Even if you are extremely musical, most people do not hear just a half note between E and F. What they hear is the next step on the scale. This is an auditory illusion. While it may sound as if each step is equal, in reality, the jump from E to F (or in our other terminology the move from the submediant--the third note--to the subdominant--the fourth note) is just a half of step.

Now we are going to take that exact same picture that we showed above to graphically point out what I've stated before. A scale is just two tetrachords. There is a tetrachord between C and F. Then there is a whole note--which I've removed from the picture. The gap from G back to C is a fourth, and without the note in the way, you can see that it is a mirror image of the bottom of the scale. So, in our music, the octave goes as follows:

Whole Step, Whole Step, Half Step

Whole Step Breather

Repeat the Whole Step, Whole Step, Half Step sequence.

Once you start thinking about this, it becomes very strange. If you were going to logically put together a keyboard, and all the notes were exactly half steps apart, why wouldn't you simply place each key exactly a half step apart? If this keyboard, instead of being a nice white key for F, you would simply make the F a black key and continue to alternative White and Black keys.

This exact keyboard and others have been made. These are called the bilinear keyboard, and a bit more strange, but heralded when introduced, the Janko keyboard, looked at this.

In both cases, the keyboard failed because of resistance by the public. We'll look at this in a future post.

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