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  • Prof: All right.

  • Let's get started.

  • Here we go again.

  • Going to have some fun again today.

  • Notice, of course, we have the sign-in sheet when

  • you come in every morning, a great thing to do.

  • As we say, this is not Yale's most demanding class,

  • but one thing we do ask you to do is come to the lectures and

  • come to section.

  • You may know if some day you are in fact ill that you'll get

  • an e-mail message from me about a half hour after class is over:

  • "So sorry to hear that you were sick this morning.

  • Hope you're feeling better very soon."

  • So we do look after these things.

  • Such an e-mail went out last time, but I'm preaching to the

  • converted because you're--you guys are already here so good

  • for you.

  • Let's continue with the discussion of the elements of

  • music.

  • We're going to be working today with harmony.

  • So far we've had two sessions specifically on rhythm,

  • two sessions specifically on melody, and today we come to

  • harmony.

  • Harmony is one of the two things that really distinguishes

  • the music of Western civilization--Western classical

  • music, Western pop music.

  • What are the two things?

  • Well, as mentioned before, this dependence upon heavy

  • usage of written musical notation--

  • not so much in the pop music but certainly in the classical

  • music-- writing it all down,

  • being able to manipulate it in that fashion,

  • so that's one thing that distinguishes Western classical

  • music.

  • Another aspect that we're talking about today is harmony.

  • Stop and think about it.

  • Think about the melodies of China and Japan,

  • virtually every--and Islamic countries--

  • virtually every musical civilization around the world

  • has more sophisticated melodies than we do in the West.

  • Ours are very blunt in a way.

  • They go from one discrete frequency to another discrete

  • frequency to another discrete frequency,

  • and they're not making use of all of the material in between

  • in any sort of nuanced way.

  • Maybe it's because we're so dependent on the keyboard here.

  • So that's important to keep in mind.

  • Then let's talk about rhythm for a moment.

  • Is Western rhythm particularly sophisticated?

  • I was listening as I was coming in this morning--WMNR.

  • They had a Strauss waltz playing there,

  • >.

  • How sophisticated is that rhythmically?

  • Think of African music where you have one downbeat and one

  • pattern working against another downbeat and another pattern.

  • Caribbean music--African influence, the same kind of

  • thing.

  • It's worlds ahead in terms of sophistication with regard to

  • rhythm.

  • But the one thing that's distinguished Western music is

  • this idea of harmony, this concept of superimposing

  • multiple pitches.

  • Interesting idea that you have this sound <<plays

  • piano>>

  • , then you put another one with it, >

  • , then put another one with it, another one,

  • >

  • , something like that, and you can play with these and

  • manipulate these in interesting kinds of ways.

  • So piling up sounds simultaneously--

  • this idea of harmony--is what makes Western music very

  • special, and what we end up with here--I

  • just reached for anything in my office--

  • here is the overture to a score of a Mozart opera.

  • And look here, how many parts we have playing

  • simultaneously.

  • Some of them may be repeating pitch names so somebody may be

  • playing a C here and somebody else a C up there,

  • that sort of thing.

  • They may be duplicating pitch names,

  • but you could have anywhere up to ten--

  • well, in this case about fifteen--different sounds going

  • at once, and you don't get that in other

  • musical cultures.

  • Let's talk for a moment about chords.

  • What's a chord?

  • Well, a chord is just a simultaneous sounding of two or

  • more pitches.

  • And that's a very basic general definition of a chord.

  • And a chord can be, of course, consonant

  • >

  • or it can be <<plays piano>>

  • dissonant.

  • So let's stick with >

  • just consonant chords.

  • We'll be working with consonant chords today and the most

  • fundamental of the consonant chords is this idea of the

  • triad-- this figure that we call the

  • triad.

  • It's the building block, really, of all our harmonies,

  • whether it's pop or classical.

  • And we're going to use a lot of pop music today and there'll

  • be--we'll be pointing out triads there in this pop music.

  • So what's a triad?

  • Well, obviously you get the idea of three pitches.

  • How does it work?

  • Let's go over to the keyboard and the staff here.

  • Let's say we've got a scale and we do have a scale,

  • >

  • C, D, E, F, G, A, B, C, and I wanted to

  • construct a triad above each of these notes of the scale.

  • Well, I take-- well, this happens to be a C,

  • middle C here, so a triad is going to have

  • three pitches.

  • You--and it spans five letter names--and we go one letter

  • name, two letter names, three letter names,

  • four letter names, five letter names.

  • We take one, three, and five.

  • Here I'm taking C, skipping D, taking E,

  • skipping F and taking G, and it gives me this three-note

  • aggregate.

  • Take one, skip, take one, skip,

  • take one, >

  • and we can do the same thing >

  • and so on right up the scale in that fashion.

  • Notice, as we've said before, we've got the scale,

  • we've got some notes rather important in the scale.

  • Tonic is very important, we've said, the--

  • >

  • the leading tone is important so with chords and triads.

  • Some are very important.

  • The tonic is very important and this dominant--what we call the

  • dominant.

  • It's not really the most important.

  • It sort of leads into, pulls into--particularly

  • important setting up the tonic.

  • It's the next important.

  • Right below that is the sub-dominant.

  • It often pulls into the dominant which then pulls into

  • the tonic in that fashion.

  • So we would get this idea of here is a chord here,

  • >

  • there is the tonic, here is the dominant,

  • >

  • there's the sub-dominant, >

  • and there's the tonic.

  • We can flip this just a little bit.

  • We can say, "All right.

  • Here's our tonic up here" >

  • and go that way.

  • Tonic, sub-dominant, dominant, tonic,

  • >

  • >

  • that way.

  • So we could go--come up from the tonic or go down from the

  • tonic.

  • Generally speaking, composers are more likely to go

  • down from the tonic and then come back up to the tonic and

  • then they aren't likely to go the other way.

  • So we've got these three basic chords that we're going to talk

  • about.

  • There are others there that we've built on the second and

  • the seventh degree of the scale, but these are the most

  • important.

  • And it's surprising how much music these three basic chords

  • can accommodate and all of the things-- <<plays

  • piano>>

  • dominant, tonic, dominant, tonic,

  • finally sub-dominant, tonic, dominant,

  • tonic.

  • So a lot of music is made in that fashion.

  • One of my favorite pieces, and I thought it was because

  • it's a good teaching piece and I thought it was known just to me

  • and other old codgers, is an old cowboy song called

  • "Streets of Laredo," but last night I looked it up

  • on You-- not on YouTube,

  • on iTunes, and there are one hundred thirty-nine recordings

  • of that that you can buy now-- Johnny Cash,

  • Arlo Guthrie, but I'm interested--

  • >

  • anybody ever heard that before?

  • Raise your hand if you've heard that.

  • One, two, three--well, a few people.

  • So it's a cowboy song.

  • >

  • >

  • "As I walked out in the streets of Laredo,

  • as I walked out in Laredo one day, I spied a cowpoke who was

  • dressed in white linens, dressed in white linens as cold

  • as the clay."

  • And as I was singing that all I was doing underneath was playing

  • the basic harmony, the chords, and they consist

  • just of two chords.

  • >

  • >

  • As I--dominant, tonic, dominant,

  • tonic, dominant, in that fashion.

  • Why do chords have--why do we do that?

  • Why do we have to change these chords?

  • Any ideas?

  • Why do we--why don't we just say, >

  • >

  • "As I walked out in the streets of--"

  • Why do we change chords?

  • Yeah.

  • Student: The melody changes.

  • Prof: The melody changes >

  • and because the melody changes and you keep banging that same

  • aggregate against it it's going to create what?

  • A dissonance and we don't want--we don't like dissonances.

  • If we're going to have dissonances, we got to control

  • them.

  • >

  • If--unless I change that chord underneath when I get up here,

  • >

  • that's very dissonant.

  • It doesn't sound very silent for "Silent Night"

  • there, so I need to switch to another chord <<plays

  • piano>>

  • and then switch back to the original.

  • And so we change chords to make the harmony consonant or to make

  • the harmony harmonious.

  • All right.

  • So that's something that we need to keep in mind.

  • Here's something else that's--we're going to ask you

  • to focus on and that is the rate of harmonic change.

  • We're really going to be asking you two things.

  • Is the harmony changing? Okay?

  • Can you--is the harmony changing or is it static?

  • And if it is changing, is it changing at a regular or

  • irregular rate?

  • By regular rate, every time a chord sounds it

  • will be holding for exactly the same amount of time.

  • Let's go back to "Streets of Laredo."

  • >

  • Conduct.

  • --three, one, two, three

  • >.

  • What do you think?

  • Regular or irregular?

  • Regular. Okay?

  • But no--well, okay.

  • So that's regular.

  • Let's go on to another one.

  • >

  • Okay.

  • I'm doing a lot there in the bass to make it more

  • interesting, but let's strip that down just

  • to the fundamental chord that's underneath of that so we're--

  • _>.

  • We're sitting here on the tonic chord and we'll go

  • >

  • >

  • , and we could even count it out: >

  • >

  • one-two, two-two, three-two, four-two,

  • one-two, one-two, one-two, two-two,

  • one-two, two-two, three-two, four-two,

  • one-two, two-two, one-two, one-two.

  • So some chords there are holding for--

  • I guess four measures--four bars--and some for two and some

  • for just one, so that's an irregular rate of

  • harmonic change.

  • So we're not going to be asking you is--

  • are we--"what chord do we have here,"

  • and expect you to say sub-dominant or "what chord

  • do we have you,"-- here and expect you to say

  • dominant.

  • We're going to be working with more fundamental things.

  • Is the harmony changing?

  • Is it changing at a regular or irregular rate?

  • Okay.

  • Notice I was playing up here >

  • a little "Jingle Bells."

  • So what is it in music that sets the harmony?

  • What part?

  • Who--what's the foundation of harmony?

  • What instrument plays it?

  • Where in the texture is it--are we talking high,

  • low, middle?

  • Low.

  • It's the bass.

  • The bass--it's like these pillars.

  • Think of architecture.

  • You get-your--you put these pilings in and then you can

  • build other things around it.

  • Well, those basic notes: >

  • the tonic note, the dominant note,

  • the sub-dominant note, they're sort of the pilings,

  • and you can ornament around the piling.

  • >

  • That's just--I could >

  • in that fashion.

  • That would be simple, from dominant to tonic,

  • >

  • or I could make it a little more interesting.

  • >

  • >

  • And that's kind of what bass players do whether they're

  • playing electric bass in a rock band--

  • maybe in an even more sophisticated way--

  • an acoustic bass in a symphony or a double bass in a bluegrass

  • band.

  • And who is the world's most famous double bass player in a

  • bluegrass band?

  • Anybody know?

  • Well, think here at Yale.

  • Well, we'll see.

  • Now what we've got here--let-- This is one that this world

  • famous bass player was kind enough to loan me.

  • It was something put together by Kentucky Public Television so

  • let's bring up this screen.

  • So here's the setup.

  • We've got a DVD from Kentucky Public Television involving,

  • as you will see, some people that may look

  • familiar.

  • Does this person look familiar?

  • Does anybody know this person?

  • She's a student around here.

  • She was a Yale undergraduate and she's telling us how she

  • tried out for the Yale Symphony Orchestra, and she was

  • designated as an alternate.

  • And she was crestfallen, but she then saw this ad where

  • some people wanted her to play in a bluegrass band.

  • So let's watch what happens.

  • >

  • "--trapped in a classical violinist's body,

  • so I guess they were kind of pessimistic about my playing--

  • you know, they wanted real fiddle player,

  • so she was like 'You're from West Virginia.

  • You should go on down there and audition for that!'

  • And so luckily, no other fiddle players showed

  • up, they were like >

  • Mozart?

  • --So they were very kind to let me kind of,

  • you know, get my training on the job and so I started playing

  • with them at that point and it's just been great ever

  • since."

  • >

  • Okay.

  • So our mystery bass player is Peter Salovey,

  • the new provost.

  • And I sent him an e-mail--I said, "Peter,

  • look.

  • We're teaching bass over here.

  • Why don't you come in and bring your bass in and you can

  • demonstrate this stuff."

  • "Oh, I'm a little bit busy >

  • at the moment but I got this DVD.

  • You can have this DVD and do whatever you want to it."

  • So what's he doing there?

  • >

  • And he's working around these >

  • particular notes in this particular piece.

  • We're going to say here is a C, >

  • there's the subdominant, >

  • then it goes >

  • and oftentimes he's going >.

  • But again it's just fleshing out that subdominant chord,

  • dominant chord and tonic chord, and it's--and we can all hear

  • this.

  • Do we see--is this guy playing off the music?

  • Again, get across the point--not using music.

  • How are they doing this?

  • They're hearing the chords.

  • They're hearing tonic, subdominant and dominant,

  • and I think we can hear them too.

  • Anybody out there hearing these chords?

  • Can you sing along with these?

  • This is wonderful music.

  • It's great.

  • I--how many like this music?

  • It's happy music, again.

  • Is it--we should have a whole course on bluegrass music.

  • It could really be good 'cause a lot of interesting ethnic

  • issues involved there.

  • So let's continue here--and I'll sort of bang on the

  • piano--sing the basic pitches of the bass.

  • And I hope you'll join with me here.

  • If you don't like bluegrass, you don't have to sing but if

  • you like bluegrass sing along with me here.

  • Okay.

  • Here we go.

  • >

  • >

  • Now I think this is Craig Harwood, who actually went

  • through our Ph.D.

  • program.

  • He's the dean of one of the colleges around here.

  • What college?

  • What?

  • Davenport.

  • So he's very good--playing the mandolin here.

  • He also runs a Klezmer Band.

  • >

  • >.

  • I don't know.

  • Is this too goofy--or stay with this >

  • or ditch this?

  • I think it's wonderful but you seem less excited by it than I.

  • All right.

  • Let's talk about how these basses--

  • we said that the bass note is sort of the foundation and then

  • you add these other things up above it,

  • and they produce these chords and the chords are tonic and

  • dominant and so on.

  • Sometimes if you're have a solo instrument the--you can play the

  • bass as just a chord >

  • or you could play it >

  • --the same notes but spinning them out.

  • And we call that an arpeggio--probably 'cause the

  • harps play this a lot, a sort of arpeggio,

  • >

  • --taking the notes of the triad and just spinning them out in

  • succession.

  • And arpeggios work particularly well with--on triads with pieces

  • that happen to be in three.

  • >

  • >

  • "As I walked out in the streets of Laredo,"

  • --one, two, three, one, two, three.

  • So that's an arpeggio--just a chord with the notes played

  • successively to create an arpeggio.

  • It works less well--these triadic arpeggios--with pieces

  • in two.

  • >

  • That's not so good.

  • Right?

  • >

  • Kind of a metrical train wreck there.

  • So what we would do with that would be to find another

  • pattern.

  • And one of the favorite patterns ever since the

  • eighteenth century was this thing called an Alberti bass.

  • It goes <<plays piano>>

  • one, then up to the fifth note, degree of the triad--one,

  • five, three, five, one, five,

  • three, five.

  • >

  • And it sounds very classical.

  • But that's a good way of harmonizing something--making

  • something that's not very interesting sound more

  • interesting.

  • Another way of doing it is just taking a note,

  • >

  • kind of a boogie-woogie bass--if you just take octaves

  • and roll it that way.

  • Beethoven does this in the sonata <<plays

  • piano>>

  • and so on.

  • So there you can get the harmony to sound more

  • interesting simply by rolling that octave underneath.

  • So all of these little tricks sort of energize the music,

  • and, again, make it more interesting than it otherwise

  • perhaps would be.

  • Sometimes harmonies can stand by themselves.

  • Sometimes you could take just the harmony and it would be very

  • beautiful.

  • J.S.***Bach-- J.S. Bach wrote a prelude to

  • the first book of his "Well-Tempered

  • Clavier."

  • And it's a famous work.

  • It goes this way <<plays piano>>

  • and so on.

  • All it really is is >

  • a succession of chords played as arpeggios.

  • So there it sat for about--well, I would--could say

  • rather specifically about one hundred and forty years or so.

  • And the French composer in the nineteenth century,

  • Charles Gounod, came along and said,

  • "Well, gee, that's nice, but I could write a melody

  • against that."

  • So we're going to listen to this--listen to Bach's harmony

  • underneath.

  • At the same time we listen to this lovely melody that Charles

  • Gounod composed for it.

  • And it gives a chance to think about melody and it gives us a

  • chance to think about the sound of the cello.

  • The cello is a particularly beautiful instrument.

  • I've always said if I ever come back as a musical instrument I

  • want to come back as a cello.

  • And it's just so rich and so beautiful and it can soar.

  • So let's listen to a lovely cello line added over top of

  • Bach's original harmony.

  • >

  • Descending sequence.

  • Here the pattern shows up again but at a lower step.

  • >

  • Now it sounds as if he's going to do it yet a third time,

  • but this time he takes that melody and moves up with it.

  • >

  • Now the rest of this, he's arching for a high moment

  • and we'll get to that.

  • It's building higher and higher.

  • >

  • It comes back to the tonic after that lovely climax at the

  • top of that.

  • So we need to point out that we've got these two types of

  • chords here, the idea of the-- >

  • This was all in C major but we could turn this into C minor.

  • Let's go back and review this.

  • We have up on the board again the scale.

  • And we need to talk about these triads that are made up of

  • either major or minor thirds.

  • Here we could look at this way with this particular interval

  • and this particular interval.

  • Let's go over to the keyboard here 'cause I think it's easier

  • to show here so we're going to start here with C because C is

  • kind of revenue neutral.

  • We'll start here with C and we're going to take--skip one,

  • take one, skip one, take one, so we do C,

  • E, G.

  • Notice coming up here, we have one,

  • two, three, four half steps here.

  • This is an interval.

  • This interval from C up to E is the interval of a third because

  • it spans three letter names.

  • C up to G is a fifth.

  • It spans five letter names.

  • So we have C, D, E being a third with one,

  • two, three, four steps in it--half steps.

  • Now we're going to go from E up to G.

  • Notice here we get one, two, three--just three.

  • And that's because, as I said before,

  • we've got this arbitrary division of the octave according

  • to Greek mathematics onto which in the ninth and tenth and

  • eleventh century the Benedictine monks laid on another system

  • that didn't quite work.

  • So up here this all seems to be the same distance.

  • E to F seems to be the same distance as D to E but it's not.

  • It's only half the distance.

  • So we get this funny disjunction in the keyboard

  • here.

  • But in any event, the important thing to note is

  • that we have a major triad with the big third on the bottom and

  • the little third on the top.

  • If we switched this around now and went to C,

  • E-flat, G to give us the minor triad,

  • then, of course, we would have just three half

  • steps here and four here.-- or reciprocal angles or

  • something like that.

  • You change one--ipso facto, you change the other.

  • But that's all of this in play and we've seen this in play

  • before.

  • Just the positioning of that third will determine whether

  • this triad is a major triad or a minor triad.

  • Let's see how this works out in terms of real sound.

  • I'd like for you guys down here-- >

  • Just hold that pitch.

  • >

  • And TAs, can you sing the fifth?

  • >

  • And nice and loud, everybody, and everyone else--

  • >

  • There is the major third.

  • Work with me.

  • Everybody else sing that third.

  • >

  • Now we're going to go minor.

  • >

  • Major, minor, major, okay.

  • And it's just tweaking that middle note of the triad there.

  • That's all that's really involved.

  • And composers have tweaked this.

  • Here's a piece by Franz Liszt.

  • It was re-orchestrated by a contemporary composer,

  • called "Lugubrious Gondola"

  • in French-- or in English,

  • translated from the French.

  • Let's listen to a bit of it.

  • It starts out with a woodwind instrument.

  • What woodwind instrument is playing here?

  • And then we'll focus on the change from one triad to the

  • next.

  • >

  • So what instrument was that?

  • Did you pick that up?

  • Now everybody--yeah, it was a clarinet.

  • Now if we were doing this on a quiz or a test,

  • we'd probably play that three times so that you'd hear it a

  • lot more than just that, but it was a clarinet.

  • Now we go to this sound >

  • and watch what happens.

  • >

  • Moves to another chord, >

  • --minor, major, minor, major,

  • minor, major, minor.

  • Let's pause it there and reset that just a little bit,

  • because underneath, what's the bass doing here?

  • >

  • What's that?

  • Arpeggio.

  • Yeah, just an arpeggio underneath.

  • So sometimes we take these chords and we'll just use it as

  • an arpeggio to support.

  • >

  • Remember last time?

  • That's all Puccini does-- by way of a harmonic support there,

  • just takes that tonic chord and >

  • basically just works that out as an arpeggio underneath.

  • All right.

  • So let's see how--if we can begin to hear the distinction

  • between a major triad and a minor triad,

  • and for this we're going to turn to a very famous piece--

  • the "Moonlight Sonata" of Beethoven,

  • and I ask you--if you got a piece of paper there--

  • I hope you do--we're going to play nineteen chords for you and

  • we're going to ask you which is major and which is minor.

  • So, you know the piece.

  • >

  • So I'm going to sort of strip these down to their essence

  • here.

  • Here's chord number one: major triad or minor triad?

  • >

  • Here's chord number two.

  • >

  • Here's three, >

  • four, <<plays piano>>

  • five.

  • >

  • Here's six, <<plays piano>>

  • seven.

  • >

  • Here comes eight.

  • >

  • Here's nine, >

  • ten, >

  • eleven.

  • >

  • Here's twelve, >

  • thirteen, <<plays piano>>

  • fourteen, <<plays piano>>

  • fifteen, <<plays piano>>

  • sixteen, <<plays piano>>

  • seventeen.

  • >

  • Here's eighteen <<plays piano>>

  • and nineteen <<plays piano>>.

  • That's nineteen.

  • >

  • So how did you do?

  • Well, let's see here.

  • Let's go back and double check this.

  • >

  • Now that's a minor chord.

  • I'll just tell you the answers here.

  • >

  • That's major.

  • This is minor.

  • >

  • Three is minor.

  • >

  • Four is minor.

  • >

  • What about that one?

  • That may be a tough one.

  • >

  • Is that a major chord or a minor chord?

  • Major.

  • >

  • Some of these are hard, though.

  • >

  • Major or minor?

  • Major.

  • >

  • Okay. That was six.

  • Here's seven.

  • >

  • Excuse me.

  • Seven is <<plays piano>>

  • major.

  • Eight is <<plays piano>>

  • minor.

  • Nine is <<plays piano>>

  • major.

  • Ten is major.

  • >

  • Eleven is <<plays piano>>

  • minor.

  • Twelve is major.

  • >

  • Thirteen is <<plays piano>>

  • minor.

  • Fourteen, minor.

  • >

  • Fifteen, minor.

  • >

  • Sixteen, minor.

  • >

  • Seventeen, <<plays piano>>

  • major.

  • Eighteen, <<plays piano>>

  • minor.

  • Nineteen, <<plays piano>>

  • major.

  • So we'll be working--this I think is fair game,

  • just to differentiate between a major triad and a minor triad.

  • And we'll be doing that on the test a week from now but we'll

  • be giving you lots of prepping in that in section this week.

  • Let's return to the pop realm and focus continually here on

  • harmony and combine the idea of harmony with major and minor

  • triad.

  • I'm going to play a piece that I've always liked by U2.

  • I don't really know much about them but it's an interesting

  • piece, "Love is Blindness."

  • Let's listen to chunks of this and we'll see what they're doing

  • with the harmony here.

  • >

  • What's the meter?

  • Kind of a slow what?

  • Okay.

  • So for copyright reasons we're cutting this exactly short.

  • We don't want to go over our limit here.

  • Okay.

  • So we're going to skip ahead now and listen to just a little

  • bit more.

  • >

  • I think that's kind of the beat here, kind of a slow beat.

  • Let's hear just a little bit more and then I'll start to play

  • along, and I want you to count the number of bars--number of

  • measures--in the pattern.

  • This is a pattern that repeats over and over.

  • In music when that pattern repeats, we call it an

  • ostinato--ostinare, from the Italian word

  • ostinare: stubborn, pigheaded.

  • So we have an ostinato harmony here and how many bars is in

  • this ostinato--are there in this ostinato pattern?

  • >

  • One, two, two-- <<music playing>>

  • Anybody able to count the number of bars in the pattern

  • just on that one little quick playing there?

  • Yeah, Betty.

  • Student: Sixteen.

  • Prof: Sixteen?

  • Okay.

  • You're on the right track.

  • Roger?

  • Eight, yeah.

  • It was a sixteen-bar pattern.

  • It was a--we played sixteen bars there, but the harmony of

  • the second eight bars was identical to the harmony of the

  • first eight bars.

  • It was just repeating that same harmony.

  • What's the harmony?

  • >

  • Is this piece by U2 in major or minor?

  • Everybody who think major >

  • raise your right hand.

  • Sinister minor types, raise your left hand.

  • >

  • It's definitely a minor so it's one of these unusual pop pieces

  • in minor.

  • All right.

  • So that's chord one.

  • That's the tonic.

  • What about this triad?

  • Major or minor?

  • >

  • Major.

  • What about this one?

  • >

  • Major.

  • What about this one?

  • >

  • Minor.

  • Okay.

  • Then back to <<plays piano>>

  • minor, <<plays piano>>

  • major, <<plays piano>>

  • and minor at the end.

  • So that's our eight-bar pattern.

  • Now maybe even kind of sing along with this.

  • My question to you, and this is the last one with

  • this piece, is: is this an example of a

  • regular rate of harmonic change or an irregular rate of harmonic

  • change?

  • So here we go.

  • Maybe I'll just play it on the piano--just the simplest thing

  • here.

  • Ready, go.

  • >

  • So what do you think?

  • Regular or irregular?

  • How many think regular?

  • How many think irregular?

  • It's actually irregular.

  • Thaddeus, tell me why.

  • Anybody tell me why?

  • I just like to put you on the spot here but you got it right.

  • Student: Well, >

  • . Prof: Well,

  • no.

  • They were kind of falling on--they were falling on the

  • meter, okay, but there was one moment when something was a

  • little bit different.

  • Elizabeth?

  • Student: It didn't--it lasted longer.

  • Prof: Okay.

  • It lasted longer.

  • What's the "it" here?

  • Student: The chord lasts longer at the end of the phrase.

  • Prof: Okay.

  • At the end of the phrase, >

  • seven--no, six--seven-two, eight-two, so that one lasted

  • two bars: <<plays piano>>

  • one-two, two-two, three-two, four-two,

  • five-two, six-two, seven-two, eight-two.

  • So one of those chords lasted, actually--one of those chords

  • toward the end there lasted twice as long as all the others.

  • Roger, a question?

  • Student: >

  • Prof: It could conceivably be a rest but that

  • would give us kind of a seven-bar phrase and I don't

  • like seven-bar phrases.

  • I've never met a seven-bar phrase that I was really

  • comfortable with.

  • And musicians generally don't like that so it's better to go

  • with-- I've used this for the first

  • time in section the other day and I'll use it again here a

  • second time.

  • Occam's razor: if there's a simple solution,

  • go for it.

  • And so take the idea of symmetry and assume that it's an

  • eight-bar phrase and you've got one chord holding for an extra

  • chord, but theoretically that's

  • possible.

  • A question here?

  • Student: >

  • Prof: We would not get in to that but it would still be

  • considered regular.

  • All they're doing is filling between chord--like Peter

  • Salovey.

  • >

  • Okay.

  • All here's doing is >

  • and if he comes-- <<plays piano>>

  • playing other things along the way that's still regular.

  • But that's far more sophisticated than we're ever

  • going to get to.

  • We're just going to go "plunk, plunk,

  • plunk."

  • Okay?

  • So keep it very much in the straight and narrow.

  • All right.

  • We have one more idea to talk about and that is the concept of

  • key and modulation.

  • Now this piece by U2 >

  • is written in a key.

  • It's got the home key here.

  • It's an odd key.

  • It's B-flat minor: five flats.

  • B flat minor.

  • But it nonetheless is a key and the whole piece--at least the

  • vast majority of it,--is in that one key.

  • Occasionally, composers will change keys.

  • I was thinking I could play for you here the Beethoven.

  • He starts-- <<plays piano>>

  • So here we are in this minor key >

  • and here he is in a new key.

  • This is <<plays piano>>

  • a major key here.

  • So composers do change keys.

  • And when they change keys they effect what's called a

  • modulation.

  • Let's listen to an example of-- Let's listen to an example of a

  • pretty simple modulation effected by Aaron Copland,

  • an American composer working in New York City in the forties,

  • fifties, sixties and seventies--wrote a ballet suite

  • called "Appalachian Spring."

  • And in it he has one section where he's working through a

  • series of variations on a folk tune called "A Gift to be

  • Simple" and he pulls off a modulation.

  • So let's listen to Copland's "Appalachian Spring"

  • as he proceeds, and I'll kind of try to

  • duplicate and go crazy up here at the piano at the moment we

  • get to the modulation.

  • Modulations are hard to hear.

  • The best you can do is that oftentimes is say,

  • "This is unsettled.

  • Maybe it's modulating," and we--I don't--I'm not even

  • sure we would ask you, "Has the piece

  • modulated?"

  • They're really kind of hard to hear.

  • But let's try anyway.

  • So here's a Copland modulation.

  • >

  • So here he is in this key.

  • >

  • I think this is where the modulation comes.

  • Then he's going to bring in the-- <<plays

  • piano>>

  • He's sitting on this note.

  • He brings in the trombones >

  • and then the trumpet will jump off from there <<plays

  • piano>>

  • to a much higher--he was here >

  • and now he's modulated up to here.

  • >

  • So let's see if we can hear this modulation now.

  • >

  • Here we go.

  • >

  • So that's a modulation.

  • In music--conceptually it's pretty straightforward but it's

  • hard to hear.

  • I think I've got an--one that's easier to hear.

  • It's a piece I like to use because it's just off the charts

  • in terms of what other popular music was doing at that time.

  • It's a piece by the Beach Boys.

  • Beach Boys music is extremely interesting--you might think,

  • "these California airheads."

  • No, no, no, no.

  • This is really musically just light years ahead of what

  • everybody else was doing, I guess late fifties,

  • early sixties.

  • So what I've got here on the board is a harmonic scheme and

  • we're going to once again for copyright reasons just take

  • little chunks of this.

  • But you can see that it's a piece that changes--uses--a lot

  • of triads.

  • So every time you see a G up here that means we have a chord

  • built on G and a triad on E, triad on A, triad on F,

  • D, E.

  • And just looking at this, this isn't shaping out to be

  • one, four, five, one, so it's moving around a

  • lot.

  • Then it gets to a section where it does get very boring.

  • It's very static at that particular point.

  • And then something of interest will happen.

  • So let's listen to a little bit of this and there are--

  • it's a piece in which there are contrasts between sections of

  • movement with wild modulations and then sections of stases.

  • >

  • Okay.

  • So here it gets very boring and we're not going to even listen

  • to it.

  • It's just going to sit there, >,

  • "I'm really hip and I'm having a great time,"

  • but then the text comes back to "I get around."

  • So let's--I think that's what--I've had to parse this

  • thing out into a Frankenstein, but let's listen to the next

  • thing.

  • I think we go back to the idea of "I get around."

  • >

  • More boring stuff at this point but let's pick it up as we come

  • to the end of what I think is this boring stuff and we'll

  • listen to what they do there.

  • >

  • >.

  • So they're sitting here in which they're

  • >

  • >.

  • So what kind of cadence have they give us there?

  • Deceptive cadence.

  • Deceptive cadence and that >

  • takes us up the half step and then it jumps-- <<plays

  • piano>>.

  • No.

  • It doesn't jump to the Aaron Copland "Appalachian

  • Spring" but it does the same thing.

  • It does exactly the same thing.

  • It uses that >.

  • It's going to jump up from the dominant to the tonic and then

  • slide up one more step-- so that now we have now a whole

  • section in A-flat and the original was in G.

  • So he's modulated to A-flat.

  • And it's extremely sophisticated,

  • involving half step modulations and things like that.

  • Who would have 'thunk' that from the Beach Boys?

  • All right.

  • We're going to stop here.

  • We've got sections this week.

  • We have a test a week from today.

  • If you look at your e-mails later in the day,

  • you'll see an e-mail from me saying that we are posting a

  • prep sheet for the test and it will tell you all you need to

  • know and how to study over the weekend for the test next

  • Thursday.

  • So let's listen to a little bit of the Aaron Copland as you go

  • out.

Prof: All right.

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