prof: all right. let's get started. here we go again. going to have some fun againtoday. 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'smost demanding class, but one thing we do ask you todo is come to the lectures and come to section.
you may know if some day youare in fact ill that you'll get an e-mail message from me abouta half hour after class is over: "so sorry to hear that youwere sick this morning. hope you're feeling better verysoon." so we do look after thesethings. such an e-mail went out lasttime, but i'm preaching to the converted because you're--youguys are already here so good for you. let's continue with thediscussion of the elements of
music. we're going to be working todaywith harmony. so far we've had two sessionsspecifically on rhythm, two sessions specifically onmelody, and today we come to harmony. harmony is one of the twothings that really distinguishes the music of westerncivilization--western classical music, western pop music. what are the two things?
well, as mentioned before,this dependence upon heavy usage of written musicalnotation-- not so much in the pop musicbut certainly in the classical music--writing it all down, being able to manipulate it inthat fashion, so that's one thing thatdistinguishes western classical another aspect that we'retalking about today is harmony. stop and think about it. think about the melodies ofchina and japan,
virtually every--and islamiccountries-- virtually every musicalcivilization around the world has more sophisticated melodiesthan we do in the west. ours are very blunt in a way. they go from one discretefrequency to another discrete frequency to another discretefrequency, and they're not making use ofall of the material in between in any sort of nuanced way. maybe it's because we're sodependent on the keyboard here.
so that's important to keep inmind. then let's talk about rhythmfor a moment. is western rhythm particularlysophisticated? i was listening as i was comingin this morning--wmnr. they had a strauss waltzplaying there, >. how sophisticated is thatrhythmically? think of african music whereyou have one downbeat and one pattern working against anotherdownbeat and another pattern.
caribbean music--africaninfluence, the same kind of thing. it's worlds ahead in terms ofsophistication with regard to rhythm. but the one thing that'sdistinguished western music is this idea of harmony,this concept of superimposing multiple pitches. interesting idea that you havethis sound <
, then you put another one withit, > , then put another one with it,another one, > , something like that,and you can play with these and manipulate these in interestingkinds of ways. so piling up soundssimultaneously-- this idea of harmony--is whatmakes western music very special,and what we end up with here--i just reached for anything in myoffice--
here is the overture to a scoreof a mozart opera. and look here,how many parts we have playing simultaneously. some of them may be repeatingpitch names so somebody may be playing a c here and somebodyelse a c up there, that sort of thing. they may be duplicating pitchnames, but you could have anywhere upto ten-- well, in this case aboutfifteen--different sounds going
at once,and you don't get that in other musical cultures. let's talk for a moment aboutchords. what's a chord? well, a chord is just asimultaneous sounding of two or more pitches. and that's a very basic generaldefinition of a chord. and a chord can be,of course, consonant or it can be <
dissonant. so let's stick with> just consonant chords. we'll be working with consonantchords today and the most fundamental of the consonantchords 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 ofpop music today and there'll be--we'll be pointing out triadsthere in this pop music. so what's a triad? well, obviously you get theidea of three pitches. how does it work? let's go over to the keyboardand the staff here. let's say we've got a scale andwe do have a scale, c, d, e, f, g,a, b, c, and i wanted to construct a triad above each ofthese 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 letternames--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 inthat fashion. notice, as we've said before,we've got the scale, we've got some notes ratherimportant in the scale. tonic is very important,we've said, the-- the leading tone is importantso with chords and triads.
some are very important. the tonic is very important andthis dominant--what we call the dominant. it's not really the mostimportant. it sort of leads into,pulls into--particularly important setting up the tonic. it's the next important. right below that is thesub-dominant. it often pulls into thedominant which then pulls into
the tonic in that fashion. so we would get this idea ofhere 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 littlebit. 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 fromthe tonic or go down from the tonic. generally speaking,composers are more likely to go down from the tonic and thencome back up to the tonic and then they aren't likely to gothe other way. so we've got these three basicchords that we're going to talk about.
there are others there thatwe've built on the second and the seventh degree of the scale,but these are the most important. and it's surprising how muchmusic these three basic chords can accommodate and all of thethings-- <
it's a good teaching piece and ithought 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 onehundred 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 heardthat.
one, two, three--well,a few people. so it's a cowboy song. "as i walked out in thestreets of laredo, as i walked out in laredo oneday, 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 iwas 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 wedo that? why do we have to change thesechords? any ideas? why do we--why don't we justsay, > "as i walked out in thestreets of--" why do we change chords? yeah.
student: the melodychanges. prof: the melody changes> and because the melody changesand you keep banging that same aggregate against it it's goingto create what? a dissonance and we don'twant--we don't like dissonances. if we're going to havedissonances, we got to control them. if--unless i change that chordunderneath when i get up here, that's very dissonant.
it doesn't sound very silentfor "silent night" there, so i need to switch toanother chord <
we're really going to be askingyou two things. is the harmony changing? okay? can you--is the harmonychanging 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 thesame amount of time. let's go back to "streetsof 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 thebass to make it more
interesting,but let's strip that down just to the fundamental chord that'sunderneath of that so we're-- _>. we're sitting here on the tonicchord and we'll go , and we could even count itout: > one-two, two-two,three-two, four-two, one-two, one-two,one-two, two-two, one-two, two-two,one-two, one-two. so some chords there areholding for--
i guess four measures--fourbars--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 askingyou is-- are we--"what chord do wehave here," and expect you to saysub-dominant or "what chord do we have you,"--here and expect you to say we're going to be working withmore fundamental things. is the harmony changing?
is it changing at a regular orirregular rate? notice i was playing up here> a little "jinglebells." so what is it in music thatsets the harmony? what part? who--what's the foundation ofharmony? what instrument plays it? where in the texture is it--arewe talking high, low, middle?
low. it's the bass. the bass--it's like thesepillars. think of architecture. you get-your--you put thesepilings 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 thepiling. that's just--i could> in that fashion. that would be simple,from dominant to tonic, or i could make it a littlemore interesting. and that's kind of what bassplayers do whether they're playing electric bass in a rockband-- maybe in an even moresophisticated way-- an acoustic bass in a symphonyor a double bass in a bluegrass
band. and who is the world's mostfamous 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 kindenough to loan me. it was something put togetherby kentucky public television so
let's bring up this screen. so here's the setup. we've got a dvd from kentuckypublic 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 undergraduateand she's telling us how she
tried out for the yale symphonyorchestra, and she was designated as an alternate. and she was crestfallen,but she then saw this ad where some people wanted her to playin a bluegrass band. so let's watch what happens. "--trapped in a classicalviolinist's body, so i guess they were kind ofpessimistic about my playing-- you know, they wanted realfiddle player, so she was like 'you're fromwest virginia.
you should go on down there andaudition for that!' and so luckily,no other fiddle players showed up, they were like> mozart? --so they were very kind to letme kind of, you know, get my training onthe job and so i started playing with them at that point and it'sjust been great ever since." so our mystery bass player ispeter salovey,
the new provost. and i sent him an e-mail--isaid, "peter, look. we're teaching bass over here. why don't you come in and bringyour bass in and you can demonstrate this stuff." "oh, i'm a little bit busy> at the moment but i got thisdvd. you can have this dvd and dowhatever you want to it."
so what's he doing there? and he's working around these> particular notes in thisparticular 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 fleshingout that subdominant chord, dominant chord and tonic chord,and it's--and we can all hear
this. do we see--is this guy playingoff the music? again, get across thepoint--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 themtoo. anybody out there hearing thesechords? 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 wholecourse on bluegrass music. it could really be good 'causea lot of interesting ethnic issues involved there. so let's continue here--andi'll sort of bang on the piano--sing the basic pitches ofthe bass.
and i hope you'll join with mehere. if you don't like bluegrass,you don't have to sing but if you like bluegrass sing alongwith me here. here we go. now i think this is craigharwood, who actually went through our ph.d. program. he's the dean of one of thecolleges around here. what college?
what? davenport. so he's very good--playing themandolin here. he also runs a klezmer band. i don't know. is this too goofy--or stay withthis > or ditch this? i think it's wonderful but youseem less excited by it than i. let's talk about how thesebasses--
we said that the bass note issort of the foundation and then you add these other things upabove it, and they produce these chordsand the chords are tonic and dominant and so on. sometimes if you're have a soloinstrument the--you can play the bass as just a chord> or you could play it> --the same notes but spinningthem out. and we call that anarpeggio--probably 'cause the
harps play this a lot,a sort of arpeggio, --taking the notes of the triadand just spinning them out in succession. and arpeggios work particularlywell with--on triads with pieces that happen to be in three. "as i walked out in thestreets of laredo," --one, two, three,one, two, three. so that's an arpeggio--just achord with the notes played successively to create anarpeggio.
it works less well--thesetriadic arpeggios--with pieces in two. that's not so good. right? kind of a metrical train wreckthere. so what we would do with thatwould be to find another pattern. and one of the favoritepatterns ever since the eighteenth century was thisthing called an alberti bass.
it goes <
kind of a boogie-woogiebass--if you just take octaves and roll it that way. beethoven does this in thesonata <
sometimes harmonies can standby themselves. sometimes you could take justthe 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 <
a succession of chords playedas arpeggios. so there it sat forabout--well, i would--could say rather specifically about onehundred and forty years or so. and the french composer in thenineteenth 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 tothis--listen to bach's harmony underneath.
at the same time we listen tothis lovely melody that charles gounod composed for it. and it gives a chance to thinkabout melody and it gives us a chance to think about the soundof the cello. the cello is a particularlybeautiful instrument. i've always said if i ever comeback as a musical instrument i want to come back as a cello. and it's just so rich and sobeautiful and it can soar. so let's listen to a lovelycello line added over top of
bach's original harmony. descending sequence. here the pattern shows up againbut at a lower step. now it sounds as if he's goingto do it yet a third time, but this time he takes thatmelody 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 tonicafter that lovely climax at the
top of that. so we need to point out thatwe've got these two types of chords here, the idea of the--> this was all in c major but wecould turn this into c minor. let's go back and review this. we have up on the board againthe scale. and we need to talk about thesetriads that are made up of either major or minor thirds. here we could look at this waywith this particular interval
and this particular interval. let's go over to the keyboardhere 'cause i think it's easier to show here so we're going tostart here with c because c is kind of revenue neutral. we'll start here with c andwe'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 stepshere.
this is an interval. this interval from c up to e isthe 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 init--half steps. now we're going to go from e upto g. notice here we get one,two, three--just three.
and that's because,as i said before, we've got this arbitrarydivision of the octave according to greek mathematics onto whichin the ninth and tenth and eleventh century the benedictinemonks laid on another system that didn't quite work. so up here this all seems to bethe same distance. e to f seems to be the samedistance as d to e but it's not. it's only half the distance. so we get this funnydisjunction in the keyboard
here. but in any event,the important thing to note is that we have a major triad withthe big third on the bottom and the little third on the top. if we switched this around nowand went to c, e-flat, g to give us the minortriad, then, of course,we would have just three half steps here and four here.--or reciprocal angles or something like that.
you change one--ipsofacto, you change the other. but that's all of this in playand we've seen this in play before. just the positioning of thatthird will determine whether this triad is a major triad or aminor triad. let's see how this works out interms of real sound. i'd like for you guys downhere-- > 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 thatmiddle note of the triad there. that's all that's reallyinvolved. and composers have tweaked this.
here's a piece by franz liszt. it was re-orchestrated by acontemporary composer, called "lugubriousgondola" in french--or in english, translated from the french. let's listen to a bit of it. it starts out with a woodwindinstrument. what woodwind instrument isplaying here? and then we'll focus on thechange 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 aquiz or a test, we'd probably play that threetimes 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 resetthat just a little bit, because underneath,what's the bass doing here? what's that? arpeggio. yeah, just an arpeggiounderneath. so sometimes we take thesechords and we'll just use it as
an arpeggio to support. remember last time? that's all puccini does-- byway of a harmonic support there, just takes that tonic chord and> basically just works that outas an arpeggio underneath. so let's see how--if we canbegin to hear the distinction between a major triad and aminor triad, and for this we're going toturn to a very famous piece-- the "moonlightsonata" of beethoven,
and i ask you--if you got apiece of paper there-- i hope you do--we're going toplay nineteen chords for you and we're going to ask you which ismajor and which is minor. so, you know the piece. so i'm going to sort of stripthese down to their essence here's chord number one:major triad or minor triad? here's chord number two. here's three,> four, <
five. here's six, <
fourteen, <
let's go back and double checkthis. now that's a minor chord. i'll just tell you the answershere. 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 aminor chord? major. some of these are hard,though. major or minor? okay. that was six. here's seven. excuse me. seven is <
eight is <
sixteen, minor. seventeen, <
harmony and combine the idea ofharmony with major and minor i'm going to play a piece thati've always liked by u2. i don't really know much aboutthem but it's an interesting piece, "love isblindness." let's listen to chunks of thisand we'll see what they're doing with the harmony here. what's the meter? kind of a slow what? so for copyright reasons we'recutting this exactly short.
we don't want to go over ourlimit here. so we're going to skip aheadnow and listen to just a little bit more. i think that's kind of the beathere, kind of a slow beat. let's hear just a little bitmore and then i'll start to play along, and i want you to countthe number of bars--number of measures--in the pattern. this is a pattern that repeatsover and over. in music when that patternrepeats, we call it an
ostinato--ostinare,from the italian word ostinare:stubborn, pigheaded. so we have an ostinato harmonyhere and how many bars is in this ostinato--are there in thisostinato pattern? one, two, two-- <
prof: sixteen? you're on the right track. roger? eight, yeah. it was a sixteen-bar pattern. it was a--we played sixteenbars there, but the harmony of the second eight bars wasidentical to the harmony of the first eight bars. it was just repeating that sameharmony.
what's the harmony? is this piece by u2 in major orminor? everybody who think major> raise your right hand. sinister minor types,raise your left hand. it's definitely a minor so it'sone of these unusual pop pieces in minor. so that's chord one. that's the tonic.
what about this triad? what about this one? minor. then back to <
my question to you,and this is the last one with this piece,is: is this an example of a regular rate of harmonic changeor an irregular rate of harmonic change? so here we go. maybe i'll just play it on thepiano--just the simplest thing ready, go. so what do you think? 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 thespot here but you got it right. student: well,> . prof: well, no. they were kind of fallingon--they were falling on the
meter, okay, but there was onemoment when something was a little bit different. elizabeth? student: it didn't--itlasted longer. prof: okay. it lasted longer. what's the "it" here? student: the chord lastslonger at the end of the phrase. at the end of the phrase,>
seven--no, six--seven-two,eight-two, so that one lasted two bars: <
like seven-bar phrases. i've never met a seven-barphrase that i was really comfortable with. and musicians generally don'tlike that so it's better to go with--i've used this for the first time in section the other dayand 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 ofsymmetry and assume that it's an eight-bar phrase and you've gotone chord holding for an extra chord,but theoretically that's possible. a question here? prof: we would not getin to that but it would still be considered regular. all they're doing is fillingbetween chord--like peter salovey.
all here's doing is> and if he comes-- <
we have one more idea to talkabout 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 andthe whole piece--at least the
vast majority of it,--is in thatone key. occasionally,composers will change keys. i was thinking i could play foryou here the beethoven. he starts-- <
and when they change keys theyeffect what's called a modulation. let's listen to an example of--let's listen to an example of a pretty simple modulationeffected by aaron copland, an american composer working innew york city in the forties, fifties, sixties andseventies--wrote a ballet suite called "appalachianspring." and in it he has one sectionwhere he's working through a series of variations on a folktune called "a gift to be
simple" and he pulls off amodulation. so let's listen to copland's"appalachian spring" as he proceeds,and i'll kind of try to duplicate and go crazy up hereat the piano at the moment we get to the modulation. modulations are hard to hear. the best you can do is thatoftentimes 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 tohear. but let's try anyway. so here's a copland modulation. so here he is in this key. i think this is where themodulation comes. then he's going to bring inthe-- <
he brings in the trombones> and then the trumpet will jumpoff from there <
it's a piece i like to usebecause it's just off the charts in terms of what other popularmusic was doing at that time. it's a piece by the beach boys. beach boys music is extremelyinteresting--you might think, "these californiaairheads." no, no, no, no. this is really musically justlight years ahead of what everybody else was doing,i guess late fifties, early sixties.
so what i've got here on theboard is a harmonic scheme and we're going to once again forcopyright reasons just take little chunks of this. but you can see that it's apiece that changes--uses--a lot of triads. so every time you see a g uphere 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 whereit does get very boring. it's very static at thatparticular point. and then something of interestwill happen. so let's listen to a little bitof this and there are-- it's a piece in which there arecontrasts between sections of movement with wild modulationsand then sections of stases. so here it gets very boring andwe're not going to even listen
to it. it's just going to sit there,>, "i'm really hip and i'mhaving a great time," but then the text comes back to"i get around." so let's--i think that'swhat--i've had to parse this thing out into a frankenstein,but let's listen to the next i think we go back to the ideaof "i get around." more boring stuff at this pointbut let's pick it up as we come to the end of what i think isthis boring stuff and we'll
listen to what they do there. so they're sitting here inwhich they're so what kind of cadence havethey give us there? deceptive cadence. deceptive cadence and that> takes us up the half step andthen it jumps-- <
spring" but it does thesame thing. it does exactly the same thing. it uses that>. it's going to jump up from thedominant to the tonic and then slide up one more step--so that now we have now a whole section in a-flat and theoriginal was in g. so he's modulated to a-flat. and it's extremelysophisticated, involving half step modulationsand things like that.
who would have 'thunk' thatfrom the beach boys? we're going to stop here. we've got sections this week. we have a test a week fromtoday. if you look at your e-mailslater in the day, you'll see an e-mail from mesaying that we are posting a prep sheet for the test and itwill tell you all you need to know and how to study over theweekend for the test next thursday.
so let's listen to a little bitof the aaron copland as you go out.
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