Monday, June 23, 2008

"Mind" -> The Scale Of Music Part I

Music and religion make up large parts of my life. Recently, Matt Petersen, friend of the family, made some comments about the trinity and music. He suggested that the trinity could resonant like a perfect chord. Interestingly, Matt is not the first person to think about this, and the fundamentals of music and the Godhead have been related for many years in the Christian faith.

The only problem is that what you might assume is true is not. And what isn't true needs some explanation. Hang onto your hat, we're going on a musical journey.

The fundamental step of music theory is really understanding the scale. I have remarked about this before, but I have never spent a lot of time on this in the blog.

So, what is a scale? A scale is simply a series of notes. Therefore, we must ask, "what is a note?"

A note is nothing more than a sound wave that is periodic. For our examples, we'll take about sound waves that are made by a string. If a string goes up and down that is termed "one cycle." As the string moves up and down, it creates little ridges of pressure that we hear as a sound wave to our ear.

The number of cycles in a second is call Hertz, like in the rental car. 60 Hertz is how fast the electricity in your wall swing from positive to negative. However, we are not concerned about electricity. We want the musical scales.

So, let look at our vibrating string. There are a bunch of instruments with strings, but for me, the easiest thing to describe is the piano, since this is a very straightforward instrument. If you go to a piano player, he or she should quickly point out the "C" note that is in the middle of the instrument. This is called "Middle C" because it is musically in the middle of the treble and bass clefs in musical notation. It is in the middle of the piano keyboard.

Now, when you hit a note, the string will vibrate. The vibration of the common middle C in most tunings is 261626 (2,6,1,6,2,6). Now, I've left out a decimal point to make the point that the number is very interesting. With the decimal point, we get 261.626 cycles per second or 261.626 Hertz. If you go and make the vibrations twice as fast you will get 523.251 Hertz. However, this is a bit difficult to remember, and since musicians want to play music and not memorize numbers, many instruments are tuned against concert A, which is the "A note" above middle C. This has a very nice 440 cycles per second, and no decimal points.

However, let's go back to middle C. If you can get a string vibrating at a nice interval of this vibration, it will "sound in tune." The easiest ratio to get is another vibration running either twice as fast or twice as slow. If it is twice as fast, it is an "octave" above the note. If it twice as slow, it is an octave below the note. So, if you hear a note, you can quickly find the octave above or below simply by knowing that it vibrates twice as fast or twice as slow. And it doesn't stop there, if it vibrates three times as fast, it is two octaves above the middle C.

In Western Modern Music, we simply say that this note that is exactly twice as fast is call "C" just like the note that was originally played. It is the same note, only played 1, 2, 3 or 4 times slower or faster. From a mathematical prospect, this makes a lot of sense. Music and math are very related, and a good mathematician often make good students of music theory.

You don't need to know what an octave sounds like. I am simply trying to get you understand that any note (which is just a vibration at a given frequency) can go a even integer faster or slower, and this new vibration is an octave. (For purposes of this post, "note" "tone" and "pitch" will be used to mean the same thing, although strictly they may not be.)

The octave is a new development in music theory. We use it extensively today to explain the whys and hows of music. However, the fathers of music is not the modern world but the Greeks. Things get a little confusing here, if we go far enough back in time, because the Greeks made all of their music around the "tetrachord."

What was the tetrachord? The musical instrument of choice was the lyre, and it had 4 strings. The top and bottom strings were four (tetra) notes apart. So a perfect fourth divided by two middle notes is a tetrachord. However, it quickly apparent to Western Music that the octave was to be the hero of our music. (Even the Greeks knew about the Octave, but it was simply considered the interval between two tetrachords and a spacer note.)

In the middle ages, the "perfect" scale was considered the Ionian scale, which is often called the major scale. There were 7 notes in this scale, and these notes were named by the monks.

These notes are very familiar to those that have seen "The Sound Of Music."

They are

1 Do
2 Re
3 Me
4 Fa
5 So
6 La
7 Ti

Which will bring us finally back to "Do." As we describe previously, C that is twice as fast as the original C is still called C. Therefore, if you have a Do twice as fast as the original Do, it is still called Do.

It is commonly recognized that Guido of Arezzo invented the modern musical notation around 1000 AD, and he was the father of the these notes as called out as Do, Re, Me. (Commonly thought to be derived from a Latin Hymn.) Before our good friend Guido, it really wasn't possible to know how exactly any song went. However, Arezzo invent the familar musical notes and staves that we use today (or pretty close to it).

The beauty behind a good musical notation is that music that was written 300 years ago and then just discovered can be played exactly as if the author demonstrated it. Although we might not personally know Mozart, by having his written music, we can hear exactly what he wrote. Arezzo was a genious.

So, we have a little background and history of the scale and the Ionian or Major scale of Western Music. Yet, we have hardly scratched the surface.

But this will need to wait for a later post.


Matthew N. Petersen said...

Uncle T,

Thanks for the post.

I do have a couple of quick questions.

First, I listened to a tape at L'Abri about world music--I can't remember the speaker's name, he was a Zen Bhuddist who came to L'Abri as a missionary and left as a Christian--and he said that the only thing that all music systems have in common were the octave, the fifth and the forth. Is this not accurate, or is there more subtelty than I would suppose? Even Schönberg used the octave in his atonal twelve tone compositions. (The rule was that he would use each note before going back to the first. But a C' counted as a C.)

Second, I don't know I was saying the Trinity was like a perfect chord so much as a perfect chord progression. (Or perhaps more accurately a perfect fugue or canon.) And that an augmented triad can make a major chord more beautiful. (e.g. C-E-G# naturally resolves into B-D-G, and this G major chord is more beautiful than it would be without the ugly augmented triad preceeding it.)

Similarly in counterpunctual music, particularly on words for pain, two parts meet in a dissonance which is subsequently resolved into more beautiful consonance. Thus in The Messiah "stricken" from "he was cut off out of the land of the living" is disonant (I believe, I don't have a score here), but that disonance adds to the beauty when we finally get to "death is swallowed up in victory."

Or more to my point, Hugo Distler's setting of Isaiah 53:4 "Surely he has born our griefs and carried our sorrows..." (In German Fürwahr, er trug unsere Krankheit und lud auf sich unsre Schmerzen. Wir aber hielten ihn für den, der geplagt und von Gott geschlagen und gemartert wäre.") the first section of the verse is repeated several times, the second section is sung, and the song returns and sings through the first part of the verse again. The first time through, "Krankheit" and "Schmerzen" (griefs and sorrows respectively) are very dissonant (Distler was a contemporary of Schönberg so he knew dissonance) but the second time through, they become more and more consonant and the song actually "resolves" (if it resolves at all) on Schmerzen.


Matthew N. Petersen said...

I resolved that chord wrong. C-E-G# resolves to F major, C-F-A.

Theologic said...


On the octave. This is just tough to answer. In Western music theory, we can lay most of the world's scales on an octave grid, and make sense of it.

However, for the fifth and the fourth, this is definitely wrong. Even our own scale is not a fourth and a fifth, it is a tempered fourth and fifth. Now, this may be "close enough" that someone could say that it is a nominal fourth and fifth. However, then they would be ignoring pelog and slendro scales in Indonesian music, and other world music. I just don't know how you can say that fourth and fifths are common.

As I pointed out, the Greeks knew the octave but did not plan around the octave.

I think that all western derived music has 4 and 5th as there primary underpinnings. So perhaps, this is what the lecture was referring to. I may not be enough of an expert to know for sure, however.

On your second point, I am VERY in tune with the idea that the trinity is like a fugue or canon (or what might better be termed counterpoint). This is possibly one of the best analogies of the trinity. I am completely lined up with you here.

As a final point, I have no idea of how you at such a young age track things like Distler. What little I've listened to him is his Christmas stuff, and somehow it strikes me that you would like him very much. His music inspires contemplation, which seems to fit you well. I take it that you like him.

As per composers like Schonberg, I guess I will show my bias. Nobody listens to atonal music for good reason, and I personally will only listen for short periods. (Yes, I am ignore the small group of intelligentsia that listens to Schonberg). This is a bit more of a longer post, but arguing for atonal music is like making up your own language in phonemes that others can't hear. It is quite delusional.

For example: Stravinsky's "sacrificial dance" in the rites of spring is atonal worth a listen, but it is limited in scope. Contrast to the finale on Firebird. You could listen to Firebird many times and come away with a sense of hope every time.

One is beautiful and one is not. Both are by the same composer.

Matthew N. Petersen said...

Yeah, I wasn't arguing for Schornberg, only stating that even he used the octave.

I first discovered Distler when we sang Maria durch ein'n Dornwald ging for choir a couple of years ago. The director really liked him, and strongly recommended him. (His emphasis on church music really appealed to Dr. Schuler, as did his drawing on Schutz.)

Some of my favorites include:

Totentanz, a dialogue between death and various people as they die.

Die Weihnachtsgeschichte (The Christmas Story) He sets various Christmas texts to chant, interspersed with Lo how a rose ere blooming, and other choral selections. (I have a different recording so I can't recommend the recording, only the work. But since mine has terrible notes I have thought about bying this one before.)

And this CD has a number of excellent Motets. My only complaint is that there aren't English translations of the texts, but most of it is Scripture (and German is easy) so that isn't so much of a problem.

I suppose there should be fair warning that he's not like anything else. He was writing in the '30's in Germany, and is very much a '30's German composer. But his main influences were people like Schutz, so he has a very Baroque or even Renaissance feel. If at first you don't like him, give it a couple of listens so it can grow on you.

Theologic said...


Thank you. By the way, I've added you to the friends link for blogs. I hope this is okay.

Your Adoptive Uncle,

Matthew N. Petersen said...

Thanks for the link, I'm honored.