Last time we worked through this idea of the scale and how

you can build triads on each of the members of the scale.

And we talked about a triad being a configuration of three

pitches where you take the first, the third and the fifth.

The first of the triad--this is a term that we'll be going over

today--is called the what?

The root of the triad so if we have >

C, E, G, the C is the root of the triad.

The lowest note of this aggregate of three is the root

of the triad.

So we can build triads on each of the members of the scale,

and we said that some of these chords tend to be used a lot

more than others, that the tonic (I) is very

important, the dominant (V) is important,

the sub-dominant right next to and below the dominant is

important, and we're going to be talking

about the VI chord today.

We could give that a name.

We could call it the sub-mediant but that's probably

getting too technical.

We'll just call it the VI chord.

So we've got a I chord built on the first degree of the scale,

a V chord built on the fifth degree of the scale,

a IV chord built on the--a IV chord built on the fourth

degree, and a VI chord built on the

sixth degree.

Now I had an interesting discussion in section this past

week and a couple of really good questions were asked.

I started by saying, "Could you come up with

any kind of-- well, you tell me in fifty

words or less what I said in lecture yesterday about harmony.

How does harmony work?

Can you come up with a visual image of how harmony

works?"

So we tried out a couple of things.

One of the things that we discussed was this type of

imagery here where you have vertically these pillars,

if you will, or we could even call--

the more I sort of looked at this--sort of call them tree

trunks almost.

And these tree trunks were the chords and at the base of each

of these chords at least conceptually,

theoretically, is this thing called the root.

So I like this tree metaphor here.

So we've got the root here of the--and then the trunk and then

up above, of course, this florid canopy would

musically be the what?

The melody. Okay.

So we might think about that.

Now in the course of this, a student asked a very good

question that I should have pointed out a long time ago,

and that is: when an orchestra plays or an

ensemble plays and they're looking at their music and

they're reading their music, do they play a chord?

Does the violin play a chord and are the trumpets--each

trumpet playing a chord and the viola--is it playing a chord?

What do you think?

No.

It's just playing one note--one note of a chord.

And once again we, our ears, hear this aggregate

of sound and then we say, "Oh, it's got that,

that, that, that," and we extrapolate out of that

information that it is this particular chord.

But if you were to look at what the YSO has on its stands

nobody's playing the chord.

They're just playing individual notes that all together form a

chord.

And we pointed out, however, that one individual

has a-- the music that has all of these

parts on it-- and that, of course,

is the conductor who has the full conducting score--

the full score--in front of him or her.

So that was one interesting question that came up,

so keep this in mind if you're wondering about this idea of

chords.

So we could say this is the root, maybe this is the third

and that's the fifth.

These other instruments are filling in these things at

various spots to produce this aggregate of the chord.

Supposing this--we mentioned this also, this idea--supposing

we had other things kind of running around there.

Without those other things running around we would have a

good sort of model of homophonic texture, sort of block chords

changing in that fashion.

If you put in other little strands of melody,

it changes it more toward polyphonic texture.

Let's review another point and I'll get to a second question

that was asked.

Why do we have to change chords?

We talked about this last time.

Why do we change chords?

Yeah.

Student: >

Melody?

Prof: Because the melody changes and not all harmonies

are concordant with every note.

Someone asked me, "Well, why are some notes

consonant and why are other notes dissonant?"

And the answer has to do with ratios and string sizes and

lengths of pipe and things like that,

but generally speaking, pitches that are right next to

each other-- very close to each other--are

dissonant.

If you get a highly irrational ratio like nine to eight,

which is the whole tone, or seventeen or eighteen to

seventeen-- which, just depending upon your

internal tuning, is the half step--those

irrational ratios are very dissonant,

>

or >

that kind of sound, but if you allow a little space

in there-- Let's say you go to a

three-to-two ratio or a six-to-five--

even a six-to-five ratio, it gets more consonant.

Let's see how this would play out.

Here for example we have the pitch C and either note above or

below it is dissonant.

These are very close together.

Now let's play this on the piano.

So here is a C.

>

If I play the D above it, >

it's dissonant, >

the D below it, it's dissonant,

but let's say I go down to the A below it, <<plays

piano>>

allowing a little separation between the two pitches now.

>

What about that?

Consonant or dissonant?

Sounds a lot better.

What about this, now going down to the G against

the C?

>

Yeah, it sounds fine, >

sounds well, kind of bland or revving in

neutral there.

What about this?

>

Yeah, it sounds sort of nice.

What about this?

>

Yeah, not so much, but if you think about it--so

it's not that--if you--it's not that we're allowing even more

space here.

What we've done is taken this pitch and played it all the way

down an octave below it so we're actually getting back to this

configuration of the pitch right next to it,

and we could--then of course we could go down one more step

>

and we would get the octave, which is a duplication of

two-to-one.

So that's a very wide sort of ratio there.

So that's something to think about.

The closer these pitches are together, the more likely they

are to be dissonant--and the desire to have some space added

there.

Questions about that?

Okay.

Let's go on now to talk about chord progression.

Anybody want to do--what's your understanding of what a chord

progression is?

If I said "chord progression"--I think we

have that term up on the board today.

What is a chord progression?

I--let's see.

Are you going to?

Yeah.

Fire away.

Student: >

Prof: Nice and loud, a little bit louder.

I couldn't hear.

Student: A sequence of chords that sound good together?

Prof: Okay.

Good.

Excellent.

A sequence of chords that sound good together,

kind of make sense together; we could say that sort of march

along in a purposeful fashion.

>

--that kind of make sense together.

All right?

They seem to be going somewhere and there's this sort of force

of pull or gravity in music having to do with some chords

wanting to go to other chords.

So we've got a chord progression.

We've talked about the root of the triad.

>

The root of the triad is the bottom-most pitch of that triad.

>

Supposing we didn't go >

C, E, G, but we decided to start with the

>

E, G and then put the C up on top, >

C, E, G, C.

Well, that'd be what's called a chord inversion.

We're not going to get into that 'cause that takes us into

heavy-duty music theory, but it's--if we don't have root

position then we've got some other note of the triad in the

bass, and we've got some kind of

chord inversion, so that's what that particular

term means up there.

What are we going to do to hear these chords?

How do we hear chord progressions?

How do we hear harmony?

What are we listening for again?

Obviously, we've talked about it again and again and again.

We're going to be listening for the bass.

Okay?

And all of our musical experience tells us to listen to

melody; melody's beautiful--that's what

we want to hear, but now to get a sense of

harmony we're going to listen to the bass.

And we said last time we want to do two things.

We want to figure out if the harmony is changing,

and if it is changing whether it's changing at a regular or

irregular rate.

By regular rate we mean that the amount of time that each

chord holds is exactly the same; every chord holds for the same

length of time.

If one chord holds twice as long or only half as long,

then we have an irregular harmonic change--irregular rate

of harmonic change.

So let's begin with our first example here this morning.

It's from Richard Wagner.

It's the beginning of his Ring cycle and we're

going to listen to this.

Well, how do we hear the bass?

How do we tell if the harmony is changing?

What I do is try to sing the bass.

I don't know whether it's easier for gentlemen or not

because our voices are sort of in the bass,

but maybe this is payback time since ladies are always singing

the melody.

So we'll focus on the bass and we'll try to sing the bass,

and if we find that in singing the bass our voice is not

changing, probably the harmony hasn't

changed.

If we have to sing a different pitch, then probably the harmony

has changed.

So let's try that as an initial modus operandi here and we'll

see how it works.

So here's an example from Wagner.

>

See if you can find the pitch.

Sing it.

I want to hear the sound.

Louder, please.

>

Did it change? No.

He just keeps that same E-flat chord for about six minutes at

the beginning of the Overture to Rheingold,