Tuesday, July 01, 2008

"Mind" -> The Scale Of Music Part IV

We have really been focusing on theory and not on practical issues. However, before we leave the system of scales, we are going just a little bit farther and today we want to discuss the two great civilizations that drove what we call technology: The West and China.

Before we get there, let's do just a little bit of review of where we have been already.

We found out that our scale has seven notes. In the course of this series of posts, I have called out these notes as several different names. For the most part, I have called them

Do or C
Re or D
Me or E
Fa or F
So or G
La or A
Ti or B

This is the basis of all Western music. These series of notes make up the diatonic scale, or the Ionian scale. The key to the diatonic scale is the tonic note. This is call Do or C in our example. If C is called the tonic, the perfect fifth note, which is Sol or G in our example, is call the dominant note, since this is an extremely attractive note in most music. We often build to this note. If we almost get to this note, we call this the subdominant note.

So we can take our scale and find a couple of key intervals.

Do (or C) is the tonic note
Fa (or F) is the subdominant note
So (of G) is the dominant note

Now, there is a secret about the subdominant note. That secret is that it is very much like the dominant note only in reverse. If we layout the scale, we'll see that the dominant note is 5 steps above the C. However, we know that on most all instruments, we can find any note and go below this note. The subdominant note is exactly one fifth below C.

See here:


What I have done is layout a series of notes. You can see that if we started playing at F on our scale, we would need to go up five steps to get to C. Once we're at C, we need to go up 5 notes to get to G. So in any scale, the note that is five below the dominant note is called the subdominant note. However, since we can always double the frequency of the note, and make it go up an octave, the subdominant note is in two places. One place is a perfect fifth below the current note. The other place is a perfect fourth above the current note. You will also note, pun intended, the dominant note is both a perfect fourth below the fifth and a perfect fifth above.

So the fourth is a fifth, and the fifth is a fourth. Sounds confusing? Well is it is a bit. When we find out about overtones, we'll see that these types of relationships are extremely important. Music basically goes around and around in a circle.

However, we don't want this post just to focus on review, we wanted to talk a bit more about the derivation of scales.

We understand that seven notes is the derived scale that we use in Western Music. Let's review what we learned here.

The first tuning of 7 notes was probably done with Just Tuning.

Just tuning was when some musician somewhere took a string and started to cut it down. We found out that cutting it in half gave you an octave. An octave, for lack of a better word, is boring. If you cut the string by a third, you got a perfect fifth. If you cut the string by a fourth, you got a perfect fourth. If you cut the string by a fifth, you'll get a third (almost). We have just found the tonic, dominant and subdominant notes of the scale, and we've thrown in a third for good measure. For a variety of reason, cutting things into 3s, 4s and 5s is obvious. After you do this, you also find out that the sounds just "sound" like they are working with each other. (Up coming lesson on overtones to address this fact.)

So finding Do, Me, Fa, So on any stringed instrument seems pretty obvious. However, we have just found 4 notes. There are 3 missing in action.

I have been calling our 7 note scale as the Ionian or diatonic scale. The diantonic scale is just a special case of having 7 notes. Many cultures will pick different numbers of notes in there scale. However, we have a special name for all scales that have 7 notes. All of these scales are call Heptatonic scales.

There are a few more cases of these types of scales.

Heptatonic means 7 notes
Hexatonic means 6 notes (you might recongize this as the blues scale)
Pentatonic means 5 notes (this is the basis of a lot historical Chinese music)

Let's write a bit about the pentatonic scale. This is the scale of a billion Chinese. We were fortunate enough in the West to have a more complex musical system than many different cultures. While I am calling our scale "heptatonic" in reality is is chromatic. (We'll get to this later.) Our current musical instruments can replicate closely many different musical systems.

On the Pentatonic scales, they come in two types:

1. Anhemitonic
2. Hemitonic

Sound like big words? Yes, but they have simple meanings. An anhemitonic scale simply means that you can pick 5 notes off of our diatonic scale, and play this music just find. If you were playing Chinese music on a piano, you would only use C, D, E, G, and A.

So, this seems to also answers Matt's question about some cultures without fifths in their music. All we are missing the F out of this scale. Therefore, Chinese music doesn't have a fifth, right?

Well there are two answers for this. The first answer goes back to our discussion on dominant and subdominant. Do you remember that the subdominant note is just a fifth, only it is a fifth below C? Well in music, anytime that you have a fourth, you also really have a fifth. So, one could argue this either way. You can say that Chinese music has no fifth, or you could simply say that the fifth is the one below the tonic cord. This is why I referred to Indonesian music. Their scale really lands on the cracks.

One thing that you will see about all these scales, they are bits and pieces of the western scale. For the most part we can play the Western music on these scales. You may ask why.

The reason is that the Chinese also did the trick of subdividing the string muliple times until it wrapped around. Once they got all the possible notes, they then selected just five notes, from all the possible notes, to play their music. The ancient writings of China describes creating 12 bamboo pipes, or 12 lü.

So, we have both the West and the East run into the same problem. We want to find a few notes, and a few other notes come along for the ride. What both cultures eventually ended up doing was to say, "Well there are really 12 notes that are candidates for selection. However, we don't want all of those candidates. We'll pick some from this selection. These 12 notes are called the chromatic scale, and if you go to a piano, you will find there are 12 notes between any two octave notes.

But here is the rub to plague music students for all times. The problem with having all these notes is that you actually don't end up using all of them when you are playing a piece of music. We'll have to talk about this a bit more later, but this is an important thought.

What is important is that both the Chinese and the West said "there are 12 candidates to pick from in any musical scale." They pick their playing scale from the same type of chromatic scale that we did. I find this one of the most fascinating ideas in the world. If would appear that two separate cultures, once they had explored music and figured out overtones, would both come up with a candidate list for scales. The problem is that the two different cultures picked two different list of possible candidates.

At first though, you may think the Chinese didn't have a good understanding of what they were doing. However, they seemed to be far ahead of the West.

Do you remember that we talked about Pythagoras comma? This is the bit left over when you subdivid the string to find different notes. After 12 times, the next division gets you very, very close to your original note. For the West, we said "we'll good enough, who cares about a little left over." We then went on to build a bunch of music around these 12 notes. But not the Chinese. They were curious about the left over bit.

Ching Fang, around 50 years before the birth of Christ, said that he wondered if he kept subdividing the string if he couldn't get much closer to the original C. He went on to calculate that if you divided the string 53 times, you could get exceptionally close. Since he was Chinese, we never recognized his contribution. We recognize Nicholoas Mercator's reinvention of this technique 1600 years later. We now call this Mercator's comma.

What drives a culture to different musical scales? This is unclear. However, I do believe that it is tied back into the language. The Chinese language, mandarin, is tone based language. If you are ever listening to mandarin being spoken, you will quickly be familiar that there is almost a "sing song" quality to it. Unlike western language, if you say the exact same word with a rising tone or a falling tone, it changes the meaning of the word. The joke is that the word for donkey and Mom is the same. Western's forget to say the right pitch, and they'll say that they miss their donkey. (Instead of Mom.)

Because of this, speaker of Mandarin really have much better training of scales, or a concept of perfect (or absolute) pitch. If you had to sing everything, you have a bit of an idea of what this would do to your singing skills. It would be very great.

Therefore, the Chinese-Mandarin speaker have a phenomenally high percentage of people with perfect pitch when compared to Western Cultures, as reported by Diana Deutsche, who studies these types of things.

Confusingly, this ability to deal with pitch created a less diverse scale. We'll discuss this in our next post.

In both Western and Chinese music, we recognized that there were many notes. In both great civilizations, a subset of 12 notes were taken to come up with our scales. The difference is that the West picked 7 notes, and the Chinese picked 5.

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