MUSI 112: Listening to Music

Lecture 2

 - Introduction to Instruments and Musical Genres


This lecture provides an introduction to basic classical music terminology, orchestral instruments, and acoustics. Professor Wright begins with a brief discussion of the distinctions between such broad terms as “song” and “piece,” briefly mentioning more specific terms for musical genres, such as “symphony” and “opera.” He then moves on to describe the differences between a “motive” and a “theme,” demonstrating the distinction between the two with the use of music by Beethoven and Tchaikovsky. Following this, he calls upon three guest instrumentalists on French horn, bassoon, and viola to give a brief performance-introduction to each instrument. He concludes the session with a discussion of acoustics, focusing on the concept of partials, and then brings the lecture to a close with commentary on Richard Strauss’s tone-poem, Death and Transfiguration.

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MUSI 112 - Lecture 2 - Introduction to Instruments and Musical Genres

Chapter 1. Distinguishing “Songs” from “Pieces”: Musical Lexicon [00:00:00]

Professor Craig Wright: Okay. Good morning. Over the weekend, you were assigned material from chapter one of the text and it dealt really with three famous beginnings of pieces of classical music. Somebody tell me at the outset: what were those three famous pieces? Young lady down here.

Student: The first was Beethoven’s.

Professor Craig Wright: Okay, Beethoven’s Fifth Symphony. What was the second one?

Student: I believe it was Tchaikovsky’s Piano Concerto Number One.

Professor Craig Wright: Yeah, Piano Concerto Number One of Tchaikovsky, and the third one?

Student: [inaudible]

Professor Craig Wright: Yeah, this piece by Richard Strauss with this funny sounding German name. We’ll just call it Zarathustra, this prophet, Zarathustra. So those are the three pieces and the issues there had to do with musical genre that we’re going to talk a little bit more about in a moment, and the instruments. And you went ahead and worked with the Listening Exercises nine through eleven to engage the musical instruments a bit in those particular exercises, and we have performers here today that are going to, as you can see, demonstrate some of these instruments for us. Let’s make one point very clear at the outset. Oftentimes I get student papers that refer to “Beethoven’s fifth song” or “Tchaikovsky’s first piano song.” Is that right? No, that’s not good at all. Are these songs? What do you have to have to make something a song?

Student: Lyrics.

Professor Craig Wright: Lyrics. You’ve got to have a text and so we don’t have — in eighty percent of classical music — we don’t have lyrics; we don’t have a text. Well, yes, with opera of course, but the other eighty percent is purely instrumental music. It works its magic, again, through purely instrumental means, so we can’t really call those songs, and this puzzled me. One day I was sitting there at iTunes and I wanted to buy an interior movement of a Mozart serenade so I was all set to purchase this and it said, “Buy song.” Boom. That told me the answer. That’s where this terminology comes in to play because on iTunes we buy songs. It could be purely instrumental but it’s called “buy a song,” but we don’t want to use that sort of parlance.

We want to be more — a bit more sophisticated than that, if you will, and use other terms, so we’ll talk generally about Beethoven’s composition or Beethoven’s piece or Beethoven’s work or his master work or chef d’oeuvre or however fancy you want to get with it.

We could also go on and be a little more precise and say it belongs to a particular genre. We could use the name of a genre, and I’ll be talking a lot about genre in this course. “Genre” is simply a fancy word for “type” or “kind” so what genre of piece is this by Beethoven?

Well, it’s a symphony. Symphonies generally have four movements. What’s a movement? Well, a movement is simply an independent piece that works oftentimes — if there are multiple movements in a symphony or concerto — works with other movements. They are independent yet they are complementary.

Think of, for example, a sculpture garden. You might have four independent sculptures in there, but they relate one to another; they make some sort of special sense one to another. So symphonies have these four movements and they usually operate in the following way: A fast opening movement; a slower, more lyrical second movement; then a third movement that’s derived from dance; and then a fourth movement that’s sort of again “up tempo,” fast, emphatic conclusion. Let’s see how these play out by means of a quick review of Beethoven’s Fifth Symphony so all we’re going to do here is going to go from the beginning of the track for the first movement to the second movement and so on, and well, let’s just start here. Let’s just, by way of refreshing our memory, the beginning of Beethoven’s Fifth Symphony.

Chapter 2. Genres, Motives, and Themes [00:04:24]

[music playing]

Let’s pause it there, and as we said last time, it operates [music playing] in that fashion, and that beginning gives us a good opportunity to make a distinction between two types of melody, between this idea of a motive and a theme. Both are sort of subsets of melody, if you will.

As I say in the textbook there, the beginning of the Beethoven Fifth is something like a musical punch in the nose. Right? [hums] Sort of grabbing you here, hitting you in the face, whatever, musically. It’s not a very long idea. How many notes is in this opening gambit here? How many pitches? Four, [hums] short, short, short, long. Okay. So that’s a classic example of a motive. A motive is just a little cell, a germ, out of which the composer will build other musical material.

Now let’s contrast that with what happens in the second movement of Beethoven’s Fifth Symphony where we have a lyrical, long, flowing theme. Okay? [music playing] Okay. We’ll stop there. All right? So that went on — If we heard the whole thing, it actually goes on for 32 notes as opposed to just four so motive versus longer theme. Themes tend maybe a little bit more lyrical.

Now let’s go on to the third movement. We said the third movement was dance derived, but in this case with Beethoven it’s a very strange dance if it is dance derived. It’s just a little bit different than most of these third movements, but let’s listen to it anyway because I’d like you to — when the brasses come in — think about what you’re hearing and think about that vis-à-vis the first movement, so let’s hear the third movement now. [music playing] Okay. So what happened there when the brasses came in? How did that relate to the first movement? Yes?

Student: Four notes?

Professor Craig Wright: Four notes, something as simple as that, [hums], same rhythmic idea, so that’s the use of a motive there and that’s how these movements are tied together a little bit.

Let’s go on to the finale now, and as we listen to the finale let’s think about what we heard at the very beginning and talked about last time, [music playing] about the mood that the beginning of the Fifth Symphony created for it. We have these adjectives up here, “negative,” “anxious,” “unsettled.” Well, how do we feel now about the finale and why? [music playing]

So why do we feel differently about that? I think we do. What do we feel there? Well, sort of upbeat, positive. What’s turned all of this around, what specifically? Well, with the first movement we said he’s generally going [music playing] and that kind of idea, but now it’s [music playing] and we’ll explore this when we get to harmony, this idea of major and minor so we’re going [music playing] and now [music playing] and that’s a change from the dark minor to the brighter major. We were going down in the first movement. Now we’re going — [music playing] It’s going up and instead of having just the violins playing we have the trumpets, the heroic trumpets, so it sounds very triumphant. So in this 40-minute interval we’ve gone sort of through an emotional musical journey here from despair, despondency, uncertainty, to whatever- to personal triumph, and in a way that mirrors some of the things that were going on in Beethoven’s life.

Okay. Let’s go on to talk about the second piece. We finished with this idea of the genre, of the four movements, so then let’s go on to talk about the piano concerto. Concertos are generally in three movements. The concerto is another genre. It’s a genre in which a soloist will confront the orchestra and there’ll be a kind of give and take — a spirited give and take — between the two. So now we are going to listen to the beginning of the first movement of Tchaikovsky’s Piano Concerto. You’ve worked with this already so you’re a little bit familiar with it, and at the outset here I have two questions for you. Is the beginning here played by the brasses or the strings? In other words, what — or the woodwinds — what family of instruments is playing here and is Tchaikovsky using a motive or is he using a theme at the very beginning of this concerto? [music playing]

So what about that? Theme or motive at the beginning?

Student: Motive.

Professor Craig Wright: Motive. All right. So here it was I think. [music playing] How many notes in our motive? [music playing] Same as in the Beethoven. Why isn’t it the same? Well, we’ve got a skippy Beethoven [music playing] but here with Tchaikovsky he’s coming down, just straight down, [music playing] down consecutive intervals there for the most part. And both of them are, however, minor. [music playing] With the Tchaikovsky they — all the intervals are the — the durations are the same, [hums] but with the Beethoven, [hums] short, short, short, long. So Tchaikovsky is a little bit more neutral in terms of the rhythm. Okay. So then we go on and the piano enters. What is the piano doing? So let’s hear the piano come in just a bit. [music playing]

So what’s the piano up to? Well, the piano is just playing chords, [music playing] playing them in octave successions, and we’ll talk about that a little bit more too. So what do we have here in this next section? Do we have a theme or do we have a motive and which do this — are the violins playing? Are they — Do they have the theme or the motive or does the piano have the theme or the motive? Let’s listen. [music playing]

So was — what the — what were the violins playing? Theme or motive? Theme. What was the piano doing?

Student: [inaudible]

Professor Craig Wright: Yeah, just the same chords [music playing] [hums] in that fashion. I’m singing the melody. They’re playing a chordal accompaniment against it. All right. Let’s listen to the next iteration of this theme. We’ve identified this as a theme. Who’s got the theme now? Is it exactly the same? And what are the strings up to in terms of string technique here? [music playing]

So who had the theme? The piano now, but was it exactly the same? Not really. It was kind of noodling around with it, varying it a little bit. What were the strings doing? They were playing the accompaniment, and what string technique were they using? I think we mentioned that in the first chapter of the book there. Yeah, you’ve got it. Nice and loud please?

Student: Pizzicato.

Professor Craig Wright: Pizzicato. Good. Okay, pizzicato. We could write that — Did we write that as a term up — Yeah. Okay. We’ve got it up there, pizzicato. That’s a help. So in that particular case we’ve switched the roles around. We’re going to move this along just a little bit here. As we come back in to this, I think we’ve got a situation where the piano keeps playing the four-note motive, [music playing] the part like he was building it up for tension. Then there’s a cascade and then the theme comes back. Let’s see what happens here, [music playing] just the motif, one, two, three, four, three four, one two, [music playing] and then the theme. [music playing] The piano is playing [music playing], ornamenting.

All right. So that’s an introduction to a three-movement piano concerto. It happens to be the first of these three movements and it’s pretty spectacular music. I hope you like that music. It’s one of the great melodies of all time. It’s a wonderful example of a theme.

Having talked just a little bit about genres, we could conclude by saying there are other kinds of genres in music of course. We’ve been introduced to this idea of the tone poem. The Strauss Zarathustra is a tone poem. That’s a one-movement work in which the composer tries to tell a story or play out an historic event or, in the case of the Strauss, to give us the beginning of the contents of a philosophical novel through music. So tone poems are one in movement, and we have got other kinds of genres in music. We’ve got opera. We’ve got cantatas, sonatas, ballets, things such as this, and we’ll get to each of those in turn. So that’s the end of the discussion of genre.

Chapter 3. Introduction to the French Horn and Partials [00:16:52]

Let’s go on now to talk about instruments and how instruments produce sound. Eva Heater, come on up. This is my friend, long-time colleague, music librarian extraordinaire and professional French horn player, Eva Heater, who will demonstrate here — Come on over here right in the center. Gene Kimball is in the basement somewhere recording all of this.

Eva Heater: Oh, my.

Professor Craig Wright: Oh, yeah. It’s very exciting here. What a time to be alive, huh?

Eva Heater: Yeah.

Professor Craig Wright: So Eva is going to just demonstrate the physical process of playing the French horn.

Eva Heater: The horn obviously is a brass instrument and what makes the sound is a vibrating column of air. In this case, the basic column of air is twelve and a half feet long and there are something called “partials” or the “harmonic series” that happens in anything, on a string instrument or whatever, but on the horn it’s very distinct and that’s what makes the different notes. Let me demonstrate to you the harmonic series. [music playing] Now I didn’t use — no hands — that was just the notes that are naturally on the twelve and a half-foot length of vibrating air. That’s the harmonic series that’s on that, and what the valves do is they shorten and lengthen that vibrating column of air very much like the cello string on the fingerboard. A cellist is always shortening and lengthening the strings. I’m doing the same thing. I’m just doing it with a series of switches instead of a fingerboard, which we obviously don’t have —

Professor Craig Wright: Okay. That’s fine. That’s great. That’s the principle, and when she said she was “overblowing” what that means is, and we’ll keep emphasizing this point today — these partials — that when a sound is made you have not just one sound but that tube is dividing up into sections, and all kinds of little sections of that one tube are sounding, not just the big sound but the partials or the overtones, the intervals in the harmonic series. So it’s a whole series — when we listen to a single tone it’s a whole series, and what Eva was doing there is playing out the notes in that series successively, and we’ll keep banging on that. Now if you would, Eva, play just the beginning of the Zarathustra or the trumpet part. Can you do that?

[music playing]

Go, Eva. Go.

[music playing]

One more time. [music playing] Okay, and that’s another note. Thank you very much. Thank you. Thank you. Okay. Now Eva has another gig out in Gilford this morning so she’s going to run off, and I’m going to show you, maybe, if we can get our slides up, this overtone series stuff. Okay?

Eva Heater: Okay. It’s a mathematical thing too. It’s all math.

Professor Craig Wright: What we’ve got here is the following, this idea of partials that Eva was talking about with ratios, two to one, three to two, four to three, five to four, six to five and so on, and the point here is that the way we differentiate between instruments. Can anybody tell me this, why — You tell me this. It’s always better when students answer. Why does a trumpet — If I asked a trumpet to play this pitch, a trumpet played, and then I asked an oboe to play it, the sound would be very different. Why is that the case? Gentleman here?

Student: Different overtones?

Professor Craig Wright: Different overtones. Well, actually they all have the same overtones in a way, the same frequencies will sound, but you’ve got it — ninety-nine percent of it. It’s which partials are particularly prominent, have extra punch or extra volume to them. The oboe may have the seventh partial very strong and the third partial very strong whereas the trumpet — I’m just making all of this up of course — the trumpet may have the second partial and the fourth partial and the sixth partial. So it’s which of these partials are sounding within each of these instruments, and the physical properties of each of these instruments are different. It’s the particular blend.

Here’s a really dumb analogy. Any Scotch drinkers in here? No, of course not. You’re way too young to do that, but think about a blended Scotch. You’ve got a little of this, a little of this, a little of this, and it makes up whatever it is that you end up with, the particular recipe for that liquid. Well, we have a particular recipe for instrumental timbre or instrumental color and it’s the intensity of the overtones with — or partials — within each particular instrument that creates that. Okay.

Chapter 4. The Bassoon and the Viola [00:23:03]

Now we’re going to go on and talk about a woodwind instrument here so Lynda, come on up. Lynda is a bassoonist. This is Lynda Paul who will be one of our principal TAs here. She is a PhD candidate in the department of music, just passed her qualifying exam with flying colors, so here she is to demonstrate the bassoon for us, lowest member of the woodwind family.

Lynda Paul: All right. So you probably read in the book that the bassoon is a double reed instrument, and so just to show you what that looks like — You’ve probably seen it but if you haven’t, two pieces of wood vibrate together when I blow through them. [music playing] I always check it out before I play any notes. And, as you will probably suspect, by the length of the bassoon it can play very low notes [music playing] and if I put a little rag in the top I can get it even a little bit lower than that — I didn’t bring one — but actually, amazingly, it’s a very versatile instrument and can also play very high notes. As you can see, there are a lot of keys in it. There are nine keys for my left thumb alone so I’m kind of switching between these on the back here and many others, and because of that I can go very high and I’ll just demonstrate that. [music playing] So that’s just to give you a sense of the range. Because of the sort of particular character of the bassoon sound, it’s often used to play sort of funny, little low-note characters in the orchestra. For example, if you’re familiar with Peter and the Wolf, the different instruments play different characters. The bassoon is the grandfather. [music playing]

Professor Craig Wright: Cool. Okay. Great. Thanks so much. That — That’s really fun. Now Jacob Adams is a professional violist here in New Haven. What’s the name of your quartet, Jacob?

Jacob Adams: I’m a member of the “Vinca String Quartet.”

Professor Craig Wright: The “Vinca String Quartet” so keep an eye out for them. They’re based here in New Haven. So come on out, Jacob. And he is a violist, not a violinist, but the principle here is pretty much the same, so tell us about the construction of the instrument.

Jacob Adams: Okay. So obviously we’ve now seen a little bit of the brass family and the woodwind family, and the other principal section of the orchestra would obviously be the string family. The viola is very similar to the violin so anything I say about the viola applies to the violin as well, and of course you all are probably familiar with violins and the size. The violas are a little bit bigger. This particular one is about 16 inches long.

Violins are — maybe — go up about to twelve inches. They have a slightly smaller body to them but violins and violas have the same general construction. All of the sounds are produced by the strings on the instrument and how the bow is pulled across the instrument. The bow is made out of, typically, horse hair from the tails of horses. The strings are now metallic but sixteenth, seventeenth to eighteenth century they would have been made out of cat or sheep gut. That was much more common, and still some people —

Professor Craig Wright: Okay. So I’m sorry. We’ve got lots of things going on here this morning so just play a scale quickly and then vibrato, pizzicato and tremolo for us.

Jacob Adams: So again this is on a viola so it has a deeper, darker timbre than a violin but here’s a scale. [music playing]

Professor Craig Wright: Wow. You did something there at the end. Did you have too much coffee this morning? You started shaking over there. Yeah. So tell us about what you were doing there at the end.

Jacob Adams: So there are all sorts of different little technique things you can do to create different colors and sounds on all string instruments, so this applies to any of them. One of them is the technique you saw me do with my left hand where I wiggled it a little bit. It’s called vibrato. You hear it in human voices as well. You can do it on other instruments but on a string instrument it’s the difference. I’ll play a melody without vibrato and with vibrato so you can see the difference. [music playing] So that’s without vibrato, not that interesting in my opinion, so with vibrato. [music playing] And you can vary the width and the speed and the length. There’s a lot of varieties which —

Professor Craig Wright: Okay. And then just quickly play a pizzicato for us?

Jacob Adams: Sure. [music playing]

Professor Craig Wright: Okay, and then finally tremolo.

Jacob Adams: Tremolo, yes. [music playing]

Professor Craig Wright: So adds a little excitement or a little filler to the music sometimes.

Jacob Adams: Uh huh.

Professor Craig Wright: All right. Great. Thank you, Jacob, very much.

Chapter 5. Mussorgsky and the Basic Principles of Acoustics [00:29:14]

What I wanted to show you was a clip that actually my daughter brought to my attention just this past weekend. She was watching television, “America Has Talent.” Does anybody watch this, “America Has Talent”? And she said, “Dad, you’ve got to watch this. This is the most amazing thing. They’ve got these two guys on here called Nuttin’ But Strings.” So I did. I — And I went to — She sent me the link to YouTube here. [music playing]

All right. So obviously the violin is not just this stodgy old thing from the Renaissance. It has some legs today, used in folk music. Sometimes you see it in Nashville playing with country music, that kind of thing. Is this a travesty to use a violin with hip-hop here? I guess this is hip-hop. Of course not. This is wonderful. This is the best thing that has happened to the violin in the last hundred years. There will be millions of kids out there now that say “Gee, I’d like to learn to play the violin too.” So this is wonderful, this sort of cross-semination of genres here, bringing this particular instrument, the traditional classical violin, into the popular realm.

All right. So let’s put that aside. We’ve talked a little bit about sound production here. I’ve got two pieces I’m going to work with here for the end of our session. We have 15 minutes left and here are these two pieces. The first, you can see on the board up there, is by another Russian composer, Modest Musorgsky. It’s called “Polish Oxcart” from his work Pictures at an Exhibition. What happened was he had a friend. The friend died. The friend was an artist. The friend left these pictures as an homage to the painter. Mussorgsky sat down and tried to come up with, create a musical response to each of these paintings that were on display. Now this is a piece that’s always interested me because the painting is very pedestrian. It’s of an old Polish oxcart sitting on some godforsaken road in rural Russia somewhere. So how do you make that work as music? How do you turn that visual image into music? How do you turn that into a sort of live sonic-scape?

And I should say at the outset — I’m going to prejudice your listening here just a little bit. I hear this as me being in the center and this oxcart starting — It could start at either side. It doesn’t matter. Every written thing usually moves left to right so I’m going to hear this moving left to right. It comes in front of me, almost rolls over top of me, runs me down, and then disappears to my right, so as we listen to this, you think about what are the techniques by which Musorgsky creates this musical action scene. You should be able to come up with two pretty good ideas here, two pretty good answers. All right. Here we go. [music playing] Now the instrument is — that is — playing is a low tuba, a low brass instrument. It doesn’t sound much like a tuba because it’s actually playing in the higher register of the instrument, but it is a tuba. [music playing] Okay. Now the strings.

The strings come in with a counter-idea, a complementary idea. [music playing] Okay. Give me one pretty straightforward way this happened. What did he do there? Yes, young lady out here please.

Student: Crescendo?

Professor Craig Wright: Okay, crescendo. From beginning to end?

Student: Got louder, then softer.

Professor Craig Wright: Yeah, so like a giant wedge, that’s why the cart seems to move in front of you, so we’re talking about musical volume here. It started very quietly, it built up to this huge center in which we had the bass drum pounding away there and the snare drum coming in to give the effect that the entire earth is rattling at that particular point, and then as it passed by you — the thunder passed by you — and off it went into the distance, quietly into the distance. We’ll come back to that, but how did that happen? We’ll listen to the end of that in just one moment. It’s kind of a disintegration of the sound at the end. So that’s one big way this happened. That’s probably the big-ticket item here. There’s another way, a more subtle way. Any thoughts about that? Yes?

Student: The instrumentation?

Professor Craig Wright: Yes, the instrumentation. Can you elaborate on that?

Student: Yeah. It starts with low instruments and then moves to higher ones, and then back to low ones.

Professor Craig Wright: Great. Right. So there’s a kind of wedge shape with regard to the instruments too. He started with the lowest instruments and then goes to the high instruments and then back to low instruments at the end. Let’s just review — Well, no, we won’t review this. Let’s not review that. Okay? We don’t have time to review that, but let’s go on to say the following, that what Musorgsky knew there was a very basic principle of acoustics, and what is that principle? Yeah?

Student: Doppler principle.

Professor Craig Wright: I beg your pardon?

Student: Doppler principle.

Professor Craig Wright: Well, to some extent. I’m going to give an example or — example of that — of the train kind of going by you, and the sound heading off in the other direction. Yes, to some extent it is that, yes, but what I was thinking about here is this idea that the lowest sounds create the longest sound waves, and they last the longest. The lowest sounds create the largest sound waves and they last the longest. The lowest sounds last the longest. Why might this be the case? If we’re not having too much luck with our slides this morning, I went ahead and put this one up on the board here. Here is one pitch. Here is the pitch in — of — a string an octave higher so you can see it this way. As you probably know, if you take a long string and pluck it, it’s going to take that long string a long time to pass that sort of cycle, if you will, just one pass through that cycle. The string half a length will pass through that cycle two times so that you can kind of graph these up here as one long, low sound or one faster vibrating sound an octave higher, so again low sounds or low frequencies travel farther.

Now you’ve experienced this in your own life. You’re standing on a street corner here in New Haven. In the distance what do you hear? An automobile approaching with a souped-up audio system in it, and what sound do you hear at the very first? [vroom vroom] That kind of thing. Then maybe [d- d- d- d- d] and then maybe some kind of melody will come in and then it’ll all come together right in front of you and it’ll kind of disappear in the distance.

You’re at a football game. You’ve probably experienced this too. The band is marching on the field. Suddenly they do the Doppler effect where they turn their backs to you, in a way, and they’re marching away from you and you hear very little sound. What instrumental sound do you hear? [boom boom boom]. The bass drum and the tuba or in the marching band it would be a sousaphone they would call it, the bass drum and tuba.

So Musorgsky knew this law of acoustics because he was a professional musician and was playing off of it to create this rather unusual and remarkable musical sound-scape here.

Chapter 6. Dissonance and Consonance in Strauss’s Death and Transfiguration [00:40:31]

Okay. I have five minutes left. I’d like to do one last piece. It’s another piece by Richard Strauss. It kind of brings us to the end of Richard Strauss, our discussion of Richard Strauss. We’ll say good-bye to him here in our course. It’s called Death and Transfiguration, and I hear this as a companion piece, a kind of pendant to the Zarathustra. One sort of opens up the beginning of life here and the other closes it down through a referencing of death.

There’s an interesting anecdote about Strauss, and that is that on his deathbed he said to his daughter, Alice — He said, “Alice, it’s the funniest thing. Dying is exactly as I composed it in Death and Transfiguration.” What an odd thing to say, but in any event [laughter] here is how this works. We’ve been talking about this overtone series with Zarathustra. Eva played this overtone series. He’s basically working up to the upper partials. Now he’s going to work down the partials. He’s going to close it back down here with death and he’s going to close it back down using a process that we frequently encounter in music, and that is this idea of dissonance resolving to consonance.

Here is a dissonance. [plays chord] Here is a consonance. [plays chord ] There are precise technical reasons why these are the way they are, but let me try to cut to the chase here. With dissonant intervals they tend to be frequencies that are sounding right next to each other, very close-by frequencies. (The integers in the ratios are close to each other.) They sound dissonant. If you allow a little bit of spacing, a little more space between your frequencies, they’re a little bit farther apart, then you can move from closeness [plays chord] to [plays chord] spacing and you get the consonance. Generally speaking, dissonant intervals have ratios such as nine to eight for the whole step or seventeen to sixteen for the half step. They’re irrational numbers and these irrational numbers like to move to rational numbers; they like to move to consonances; they like to move to intervals that are based on things such as two to one and three to two or maybe four to three.

So that’s the principle of this idea of dissonance resolving to consonance. So we’re going to listen now to the end of Strauss’s Death and Transfiguration, and again we’ve got the idea of the octave, then the fifth, then the fourth. We’re working up farther and farther in these partials and we’ve got some of these notes right next to each other and they want to move to the stable notes so we’re going to be hearing a lot of a note right above the tonic wanting to pull down to that tonic note. We’re going to hear a lot of the note right above the dominant wanting to pull down to the dominant.

So let’s listen to this. We have about three minutes I think. We’ll hear it and I’ll comment a bit as we go. [music playing] Okay. First question: What string technique is being used here? Tremolo. Just sawing away there. [music playing] Now just working with the four-note motive here — [music playing] Whoah. A strange little dissonant chord there resolving to consonance. [music playing] [hums] And here it’s all just tonic, just the basic primordial note upon which all these other tones are built. [music playing] Okay. So that’s Richard Strauss’s approach to death, not particularly relevant to you young people but for older gentlemen such as Professor Kagan and myself we’re getting close to that. Right, Don? [laughs] So thank you all for staying with this this morning. I hope you enjoyed that music. We’ll see you in section starting this Thursday. If you have any questions, come up and see me or send me an e-mail.

[end of transcript]

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