Lecture 7. Harmony: Chords and How to Build Them
Yale (YouTube) · lecture · en · indexed 2026-02-08
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alright let's get started here we go again have some fun again today notice of course we have the sign-in sheet when you come in every morning great thing to do as we say this is not yells most demanding class but one thing we do ask 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 email 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 we do look after these things such an email when 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 to special session 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 harm in it stop and think about it think about the melodies of China and Japan virtually every in 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 that's important to keep in mind let's talk about rhythm for a moment is Western rhythm particularly sophisticated I was listening as I was coming in this morning the wmn are they had a Strauss waltz playing there oom-pah-pah oom-pah-pah how sophisticated is that rhythmically think of African music where you have one downbeat and one pattern working against another downbeat in another pattern Caribbean music African influence the same kind of thing it's world 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 you know that that you have this this sail and you put another one with it put another one with it another one something like that and you can play with these and and manipulate these in interesting kinds of ways so piling up sounds simultaneously this idea of harmony is what makes western music very special what we end up with here I just reach 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 somebody may be playing see here and somebody else's see up there that sort of thing they may be duplicating pitch names but you could have anywhere up to 10 well in this case about 15 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 that's a very basic general definition of a chord and a chord can be of course consonant more it can be dissonant dissonant so let's stick with just consonant chords will 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 they'll be will be pointing out triads they're in this pop music so what's a triad well obviously you get the idea of three pitches 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 F G a B C and I wanted to construct a triad above each of these notes of the scale well I take the 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 one letter name two 1183 they turn into four letter names five letter names we take one three and five here I'm taking C's skipping D taking a skipping F taking G and it gives me this three and note aggregate take one skip take one skip take one yah Tom bottom and we can do the same thing and so on right up the scale in that fashion notice as we said before we've got the scale we've got some notes rather important in the scale tonic is very important we said the Yatim the leading tone is important so with cords 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's a chord here there's the tonic here's the Dominator there's a sub-dominant and there's the tonic we can flip this just a little bit we could say all right here's our thomna cup here long bum bum bum 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 time generally speaking composers are more likely to go down from the tonic and then come back up to the tonic than they aren't likely to go to the other way so we've got these three basic chords we're going to talk about there are others there that we built on the second and 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 with all the things dominant tonic tonic finally sub-dominant tonic so a lot of 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 YouTube on iTunes and you know there 139 recordings of that that you can buy now Johnny Cash Arlo Guthrie but I'd be interested anybody ever heard that before raise your hand if you've heard that one two three well few people so it's a it's a it's a cowboy song as I walked out in the streets of Laredo as I walked down in Laredo one day I spied a cowpoke who was dressed in white linens dressed in white means as cold as the clay and as I was singing that all I was doing underneath was playing the basic harmony the chords and it consists of two chords as dominant in that fashion ah why the chords have why do we do that why do we have to change these chords any ideas why don't why don't I just say as I walked out in the street so why do we change chords yeah the melody changes and because the melody changed 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 distances if we're going to have distances we had to control them you know if unless I change that cord underneath when I get up here it's very distant doesn't sound very silent for silent night there so I need to to switch to another cord and then switch back to the original one so we change cords to make the harmony consonant or to make the harmony harmonious harmonious alright so that that's a 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 the rate of harmonic change would really 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 what do you think regular irregular regular okay but no well okay so that's regular let's go on to another one okay doing a lot there in the base to make it more interesting but let's strip that down just to the fundamental chord that's underneath of that so we're targeting we're sitting here on the tonic or we could even count it out so some chords they're holding for I guess four 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 as are we what chord we have here and expect you to say sub dominant or what chord we have you hear expect you to say dominant we're going to be working with more fundamental things is the harmony changing is it changing in a regular or irregular irregular rate okay notice I was playing up here no 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 we're in the texture is the are we talking high low middle low it's the bass the bass it's like these pillars think of architecture you get you know 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 they're sort of the pilings and you can ornament around the pilot that's just a I could go 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 an even more sophisticated way the acoustic bass in a symphony or double bass in a bluegrass band and who is the world's most famous double bass player in bluegrass band anybody know well think here it yeah well we'll see now what we've got here is Brian if you could bring up this particular video this is one that this world-famous bass player I was kind enough to loan me it was something put together by Kentucky public television so let's bring up this screen okay let's pause it here just for a second so here's the setup and we're going to turn off the lights we've got a DVD from Kentucky Public Television involving as you will see some people that may look familiar this person look for me buddy 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 bluegrass band so let's watch what happens trapped in a classical violinist body so I guess they were kind of pessimistic about finding a real fiddle player so so she is like you're from West Virginia you should go down there and audition for that and so luckily no other fiddle players showed up there like filmed around I was like Mozart so so they were very kind and let me you know kind of get my training on the job and so I started playing with them at that point and it's just been great ever since the shovel is last call show okay let's closet here just for a second so our mystery bass player is Peter Sullivan the new provost and I said sending me email said Peter look we're teaching bass over here once you come in bring your bring your bass in and you can demonstrate this stuff I'm a little bit busy at the moment but I got this DVD you can have this DVD and do what ever you want to it so what's he doing there boom boom boom boom boom boom and he's working around these particular notes in this particular peach where you say here's a see yah ha ha there's the sub dum bum bum bum bum ba then go bum BA bum bum and often time he's doing bum bum bum bum bum bum bum bum bum bum bum bum bum bum bum bum bum bum bum ba bum BA bum bum bum but again it's just fleshing out that sub dominant chord dominant chord and tonic chord and it's and we can all hear this I mean do we see does this guy playing off of music again get across the point not using music how are they doing this they're hearing the chords they're hearing tonic sub-dominant and dominant and I think we can hear them too anybody out there hearing these chords can you sing along with these this wonderful music it's great I how many like this with its happy music again we should have a whole course on bluegrass music it could really be good because a lot of interesting ethnic issues involved in so let's continue here and all sort of bang on the piano or seeing the basic pitches at 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 ok here we go well nothing for me home now I could listen to this all day I don't know it's just too goofy or stay with a history or ditch this I think it's wonderful but you seem less excited about by it you know all right so let's let's turn the lights back and get back to Mozart and stuff like stuff like that 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 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 because with the harps play this a lot of sort of arpeggios taking the notes of a triad and just spinning them out in succession and our pages work particularly well with on triads with pieces that happen to be in three as I walk down the states of Lauren you know one two three one two three so that's an arpeggio just a chord notes played successively to create an arpeggio it works less well these triadic arpeggios with pieces and two that's not so good right kind of a metrical trainwreck there so what we would do with that would be find another pattern one of the favorite patterns ever since the 18th century was this thing called an Alberti bass it goes one then up to the fifth note a 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 a a something making something that's not very interesting sound more interesting another way of doing is just taking a note kind of a boogie-woogie bass you could just take octaves and roll it that way Beethoven does this in the Sonata and so on so there you can get to 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 sometimes harmonies can stand by themselves sometimes you could take just the harmony and it would be very beautiful JS Bach I should get my music up here there's my music JS Bach wrote a prelude to the first book of his well-tempered clavier and it's a famous work it goes this way and so on all it really is is succession of chords played as arpeggios so there it's sad for about well-nigh we could say rather specifically about 140 years or so and the French composer in the 19th century cha know 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 box harmony underneath at the same time we listen to this lovely melody that Charles GU no composed for it and it gives us 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 it's just so rich and so beautiful it can soar so let's listen to a lovely cello line added over top of box original harmony descending sequence here that pattern shows up again but a lower step now it sounds as if he's going to do it yet a third time this time takes that melody the rest of this is arching for high mold get to that it's building higher and higher I saw stop it there it comes back to the topic 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 mistress 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 it this way with a this particular interval in this particular interval let's go over to the keyboard here because I think it's easier to show here so I'm going to start here with C because you know 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 get ceg 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 CDE 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 I said before we've got this arbitrary division of the octave according to Greek mathematics on to which in the ninth and 10th and 11th 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 switch this around now and went to see E flat G to give us the Minor triad then of course we would have just three half steps here and four here what are the reciprocal angles or something like that you change one if so facto you change the other but that's all that's 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 trial let's see how this works out in terms of real sound I like the view guys down here YUM just hold that pitch and TAS can you sing v la and nice and louder everybody and everyone else yeah there's the major third work with me everybody else saying that their law and we're going to go miner all major major minor major and it's just just tweaking just tweaking that middle note of the trial there that's all that's really involved and composers have tweaked this here's a piece by Franz Liszt it was reor castrates by a contemporary composer called lugubrious gondola in French or in English translating from the French let's listen to a bit of it starts out with a woodwind the instrument what woodwind instrument is playing here and then we'll focus on the change from one triad to the next let's stop there there's a positive right there so what instrument was that did you pick that up yeah yeah well yeah it's a clarinet we're doing this on it on a quiz root test we probably played that three times so you hear a lot more than just that but it was a clarinet now we go to this sound and watch what happens move to another chord minor nature minor major minor let's cross it there let's pause it there and reset that's just a little bit because underneath underneath what's the base doing here what's that arpeggio yeah just an arpeggio underneath so sometimes they take these chords and we just use it as an arpeggiated 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 or paggio 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 asked you if you got this paper there I hope you do we're going to play 19 chords for you and we're going to ask you which is major and which is minor so you know the piece you so I'm going to sort of strip these down to their essence here here's court number one major triad or minor triad here's cord number two here's three four five you're six seven becomes eight here's nine ten eleven here's 12 13 14 15 16:17 here's 18 and 19 that's 19 so how did you do well let's 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 it's major this is minor three is minor four is minor what about that one that may be a tough one it's at a major quarter one major some of these are hard though major minor major okay that was six here seven my shoes make seven is major 80s minor 9 is major 10 is major 11 is minor 12 is major 13 is minor 14 minor 15 minor 16 minor 17 major 18 nineteen major major so we'll be working this I think is fair game just to differentiate between a major triad and a minor to try and we'll be doing that on the test a week from from now but we'll be giving you lots of prepping in that in section section this week let's return to the pop realm and focus that continually here on harmony and combine the idea of harmony with major and minor tribes I play a piece that I've always liked by you too I don't really know much about them but it's an interesting piece love is blind in this 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 one okay so for copyright reasons we're cutting is exactly short we don't want to go over a limit here okay so we're going to skip ahead now we'll listen to just a little bit more yacht dot I think that's kind of the beat here kind of a slow beat let's here just a little bit more and then I'll start to play along and I want you to 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 Austin RA from the Italian word Austin are a stubborn pigheaded so we have an ostinato harmony here and how many bars is in this ostinato are there in this ostinato pattern you see marry his blood Louise go steal to love is but and it's going to continue again anybody able to count the number of bars in the pattern just on that one little quick plane there yeah Betty 16 okay you're on the right track Roger eight yeah it was it was a 16 bar pattern it was a 60 week played 16 bars there but the harmony of the second 8 bars was identical to the harmony of the first eight bars it was just repeating that same army what's the harmony is this piece by u2 in major or minor how many think major raise your right hand sinister minor type Frazier left hand is definitely in liner so it's one of these unusual pop pieces in minor all right so that's cord one that's the tonic what about this tri major minor major about this one major about this one mine okay then back to minor major and minor at the end so that's our that's our 8 bar pattern now maybe even kind of sing along with this my question to you and this is the last one where this piece is is this a 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 for the simplest thing here ready go so what do you think regular irregular how many think regular how many think irregular it's actually irregular Thaddeus tell me why anybody tell me why I started to put you on the spot here but you got it right 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 okay it lasted longer what's the it here okay at the end of the phrase 7 6 7 - 8 - so that one lasted 2 bars one - two - three - four - five - six - seven - eight - so one of those chords lasted actually cool one of those chords toward the end there lasted twice as long as all the others Roger question it could conceivably be a rest but that would give us a kind of a seven bar phrase I don't like seven bar phrases I've never met a seven bar phrase that I was really comfortable with the musicians generally don't like that so it's better than better to go with you know 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 so take the idea of symmetry and assume that it's an eight bar phrase and you've got one cord holding four extra cord but theoretically that's possible question here we would not get into that but it would still be considered regular all they're doing is filling between core like Peter salivating okay all he's doing is and if he come playing other things along the way that's still regular but that's far more sophisticated and we're ever going to get to we're just going to go plonk plonk plonk plonk okay so keep it very 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 of this piece by u2 is written in a key it's got the HOME key there's an odd key it's b-flat minor ooh five flats b-flat minor but it nonetheless is a key and the pole piece at least the vast majority of it is in that one key occasionally composers will change keys I was thinking I could play right for you here the Beethoven he starts so here we are in this minor key and here is it a new key this is a major key so composers do kick change keys and when they change keys they affect what's called a modulation let's listen to an example of I think we have Copeland up next okay let's listen to an example of a pretty simple modulation affected by Aaron Copland American composer working in New York City in the 40s 50s 60s and 70s 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 he pulls off a modulation so let's listen to Copeland'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 modulations are hard to hear the only the best you can do with it often time to say this is unsettled maybe it's modulating and we I don't I'm not even sure we would ask you it has the piece modulate they're really really kind of hard to hear but let's let's try anyway so here's cope of Copeland modulation so here he is in this game closet right there I think this is where the modulation comes and he's going to bring in the sitting on this note he brings in the trombone and then the trumpet will jump off from there to a much higher he was here or and though he's modulated up to here so let's see if we can hear this modulation now here we go you or is it food so that's a modulation in music conceptually it's pretty straightforward but it's hard to hear I think I've got an a1 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 piece by the Beach Boys Beach Boys music is extremely interesting I think California airheads no no no no this is really musically just light years ahead of what everybody else was doing I guess late 50s really early 60s so what I've got here on the board is a harmonic scheme and we're going to fit one seguin for copyright reasons just take little chunks of this but you can see that it's a 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 build on G and a try it on e try out on a try out on F de and just looking at this this isn't shaping out to be 1 4 or 5 1 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 la wild modulations and then sections of Stacey's here it gets very boring and we're not going to even listen to it just going to sit there put ba ba ba ba ba ba ba I'm really hip and I'm having a great time but then the text comes back too I get around so let's lit I think that's what I've had to parse this thing out into a Frankenstein but let's let's listen to the next thing I think we go back to the idea of I get around more boring stuff 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 go ahead so they're sitting here in which so what kind of cadence have they given us they're deceptive Cain's deceptive cadence and that takes it up a half step and then it jumps now doesn't jump to the Aaron Copland Appalachian Spring but it does the same thing it does exactly the same thing it uses that in beyond Bambaataa it's going to jump up from the dominant to the tonic and then slide up one more thing so that we have now whole section in a-flat and the original was in G so he's modulated to a flat it's extremely sophisticated involving half-step modulations and things like that who would have thunk that from the beat from the Beach Boys alright we're going to stop here we've got sections this week we have two tests a week from today if you look at your emails later in the day you'll see an email for me saying that we are posting a prep sheet for the tests and it will tell you all you need to know and how to study over the weekend for the tests next Thursday so let's listen to a little bit of the Aaron Copland as you go out