6-2 Young People's Concert: Musical Atoms: A Study of Interval

Welcome back, everybody to a new season, and to a new hall — practically new. The walls have been

changed, the seats are new, the plush is gone, the warmth of wood replaces the old dark blue, and all

sorts of things have happened to improve the sound of our hall. And at last, I am happy to say, it works.

And so, to start off, we're going to let you hear the new sound of Philharmonic Hall, by playing for you a

short brilliant piece — the prelude to the 3rd act of Wagner's opera "Lohengrin." Those of you have seen

a recent film called "Help" may recognize this as the background music for one of those wild fight scenes.

Others of you may simply recognize it as the exciting Prelude to the 3rd act of Lohengrin;

[ORCH: Lohengrin, Prelude to Act III]

One more welcome I'd like to make before we get to business is to our new solo flute player, Mr. Julius

Baker. Mr. Baker, would you favor us with a sample of your art?

[FLUTE plays short D, 9th above mid. C]

Now that's a very pretty sound, you'll admit, but what was it? A note. Was it music? Not at all. One simple

note all by itself is not music — not even a single molecule of music, not even an atom. It's more like a

proton or an electron, which, as you know, is meaningless all by itself; you need at least one of each — at

least two atomic particles — to create an atom. And in exactly the same way you need at least two notes

before you can begin to have an atom of music. Because with that one lonely note, isolated, nothing is

happening, [FLUTE]; it's just floating in space. But once you have two notes [FLUTE] you suddenly feel a

relationship between them, like an electrical tension. There's already the beginning of a musical meaning.

And with three notes, that meaning increases — [FLUTE] — and before you know it,

[ORCH: J. Strauss - Blue Danube]

You see what happened: those musical protons and electrons —the separate notes that is — have

combined together forming atoms, which then combined into molecules, which finally combined into

recognizable matter, like this wood or this hair, or that Blue Danube Waltz. So it turns out that an atom of

music is not a single note at all, as you might think, but at least two notes; and that two-note relationship

is called an INTERVAL. A very important word, "interval", because it's the heart and soul of music. You

see music is not made out of notes by themselves, but out of the intervals between one note and another.

That's why it's so necessary for us to understand this word, interval.

Everyone knows the word in daily speech as meaning a span of time between two events. For instance,

they say in the British Theatres, 'Between Acts I and II, there will be an interval of fifteen minutes" — by

which they mean an intermission. So an interval usually means a measurement of time.

In music we measure time, as you know, by breaking it up into meters and rhythms and bars and tempos;

but we also measure other things in music - especially pitches, those separate tones we were just talking

about. And that's how we use the word interval in music: to measure the distance between one note and

another.

Now how do we do this? Let's say we think of all the pitches there are, marked out on a long measuring

tape, that I just happen to have here, that reads from zero to infinity - zero being any very low note, and

infinity being those high, high notes that only dogs can hear. Now we section off this tape in feet - one

foot, two feet, three feet, and so on, each foot being that lowest note repeated over and over again higher

and higher.

For instance, let's take C as our lowest note - the 'zero' mark on the tape;

[CONTRABASSOON]

You hear that? Good. And as we unreel one foot of tape we arrive at the next c,

[BASSES, BASSOON]

an octave higher. Another foot brings us to the next;

[CELLI, BASS CLARINET]

and so on all the way up:

[ORCH]

See how it works? Thank you, Mr. Corigliano. Now each of those sections, one foot long a piece, let's say

that is equal to what musicians call an octave. It comes from the Latin word octo meaning eight; because

there are eight scale tones between any note and its next highest appearance. I'm sure you know what I

mean. [PLAY AND COUNT] That's a span of eight notes. And that span of an octave [PLAY] is called an

interval. And any smaller section within that octave is also called an interval; for instance, if it spans seven

notes [PLAY AND COUNT] it will be called a 7th; if it spans six notes [PLAY AND COUNT] it's a 6th,

sound likes this, and so on. If it covers only two notes [PLAY AND COUNT] it's called a 2nd.

Let's try something and see if you can sing these easy intervals back to me. It should be easy because

you already know that the interval between the first note of the scale [PLAY] and the second note of the

scale [PLAY] is an interval of the second. [OBOE]. Now let's hear you sing it using the words "New York"

just for instance. Let's hear it [AUDIENCE]. Perfect. Alright, you've just sung a second. Marvelous. Now

the first note to the third note makes an interval of a third [HORN]. Let's hear you sing that. New York.

[AUDIENCE] Fine. Now let's hear you try a fifth. Listen to a fifth, to a, uh, no what are we up to? A fourth.

[VIOLINS] Try that. [AUDIENCE] Great. Now a fifth. [TRUMPET] [AUDIENCE]. Great. A sixth. [VIOLAS

AND CELLI] [AUDIENCE]. A seventh. That's hard. [CLARINET] [AUDIENCE] Marvelous. And now an

octave. [ORCH] [AUDIENCE]. Oh, divine. Well, you've just sung all the intervals in a scale. Great.

As a matter of fact, the intervals actually go on even after that: there's such a thing as a ninth, [PLAY] and

a tenth [PLAY] and so on; but we don't have to worry about them today.

Let's just stay inside our one little octave - that one foot of measuring tape. Now don't forget: these

intervals don't always have to start on the first note of the scale where we've been starting; they can start

anywhere. I can begin somewhere inside the octave, let's say on E and span three notes up to G [PLAY

AND COUNT] and that also makes an interval of the third. "New York". Or from that same G, four notes

up to C [PLAY AND COUNT] makes an interval of a fourth.

Now of course: these intervals don't always have to go up; they can be descending as well as ascending.

That interval of the fourth I just played you can be turned upside down, into a descending fourth [PLAY].

"New York". That's the same interval, only backwards. It's also called a fourth. And in fact, intervals don't

have to be either ascending or descending: they can be simultaneous, the two notes played together.

That's exactly the same fourth, only a simultaneous one. And here's a simultaneous third, and a second.

Now this is interesting because we're getting away from melody, where notes follow each other in time,

one after another, and into the new region of harmony, where notes sound at the same time. And these

simultaneous intervals are the stuff of which chords are made; you take that fourth I just played and add

another note to it, this sound, and you've got a chord. You see.

So you see, intervals work both ways: they work horizontally, you see that, which means melodically one

note going to another, and vertically which means harmonically at the same time. Thank you, gentlemen.

That's very important to remember; because if you understand that point, there is nothing in music you

won't be able to understand. Let me give you a tiny example of how this horizontal - vertical thing actually

works.

Here is a set of intervals, all of them descending seconds; [PLAY G F E D]. Those are horizontal melodic

intervals. Now I'm going to play that set three times, each time with different vertical intervals underneath,

that is, different harmony; and I'm sure you'll recognize immediately how the musical meaning of that set

changes each time [PLAY]. Does that sound familiar to anybody in this house? Well, it should, It's the

pattern of our old friend "Help!" as sung by the Beatles

[SING: Lennon/McCartney - Help]

So on ... Nobody dared to sing? I thought you'd all come in with it. Well, you had your chance. And I've

had my chance at the piano, so I think it's about time the orchestra played something. And what they're

going to play is one of the great classics of all time — the first movement of Brahms' Fourth Symphony.

This giant step that we're taking from the Beatles to Brahms is actually not such a big jump in terms of

intervals themselves. Because after all, both kinds of music are made of intervals - the same intervals.

And if you could recognize the descending seconds in "Help!", there's no reason why you can't recognize

them in Brahms' Fourth Symphony.

There's only one other thing which you should know before you can really appreciate the Brahms, and

that is the idea of Inversion, the inverting of intervals. This is a bit tricky, so listen closely. To invert

something means, as you know, to turn it upside down or backward, so you'd think that to invert an

interval — let's say, this ascending second [PLAY] — would mean simply to play it backwards [PLAY] —

a descending second. But that's not what inversion means at all. To invert an interval you may play the

two notes either forward [PLAY] or backward [PLAY] as you choose, but in the opposite direction. Does

that seem too hard? It isn't really. Just look. Here are those same two notes, C and D [PLAY], an

ascending second. Now, we invert that interval by playing the same two notes, in the same order only

descending [PLAY] in other words C to the D an octave lower — and what has happened? It's not a

second any more! The interval has changed into a seventh [PLAY].

Now supposing we had started with the same interval, only backward — D to C [PLAY] — and again, it's

turned into a seventh. Now what does this mean? Simply that whenever you invert an interval, it becomes

a different interval. And, by the way, the new interval, the inverted one, can always be discovered by

subtracting the original one from the number 9. Isn't that an amazing fact? As we just saw, a second

inverts to a seventh; and 2 from 9 leaves 7. You follow that. In the same way, a third [PLAY] inverts to a

sixth [PLAY]. 3 from 9 is 6. And a 4th [PLAY] will invert to a — what? [AUDIENCE] Right. A 5th [PLAY],

because 4 from 9 is 5. And vice versa, a 5th will invert to a 4th, a 6th to a 3rd, and a 7th to a 2nd. You get

it. Those are all components of 9.

Now what does all this have to do with Brahms. Just this: that Brahms, great master that he was, built

almost the whole movement we're going to hear our of the interval of the 3rd, and its inversion, which is

the interval of the ? [AUDIENCE] Sixth. Oh, you're brilliant. It's astonishing how Brahms does it. Let me

show you a sample or two.

The beautiful main theme, right at the beginning, starts off with a descending 3rd [PLAY]; and it's

immediately answered by the inversion, an ascending 6th [PLAY]. Again comes a descending 3rd [PLAY],

and again an ascending 6th [PLAY]. Now that's a marvelous construction. Which is all very fascinating to

those mechanically inclined, but does it make beautiful music? Well, just listen;

[ORCH: Brahms - Symphony no. 4]

Quite promising, isn't it? And that's just 4 little bars of music! Now of course Brahms can't just stick to 3rds

and 6ths forever; in the next phrase, for instance, he expands the descending interval to an octave

[PLAY], then again a rising third [PLAY], again an octave [PLAY] and again a third [PLAY]. And then, as

he goes on developing his theme, other intervals come into play, 4ths, seconds, and whatnot; but the

important thing is that beginning of the theme, the first 4 bars, out of which the whole movement is going

to be made is all intervals of the 3rd and its inversion, the 6th.

Now let's jump ahead to the next theme in this movement. And what do we find? Again it's almost all built

on thirds.

[ORCH: Brahms - Symphony no. 4]

Could you hear those thirds?

[PLAY AND NAME THIRDS: Brahms - Symphony no. 4]

Those are 3rds; that's a 3rd; again 3rds, a 3rd, 3rd, more 3rds. Incredible, Almost the whole theme. Now

as this theme goes on

[PLAY: Brahms - Symphony no. 4]

we begin to feel something's wrong. Suddenly there are no thirds at all. Ah, but on closer inspection, it

turns out that the accompaniment to that tune, underneath, is nothing but a series of descending thirds.

[PLAY: Brahms - Symphony no. 4]

Now isn't that lucky? And isn't it typical of Brahms, the master builder? Now listen to how that theme and

its accompaniment of thirds sounds in the orchestra — like some great, mad German tango:

[ORCH: Brahms - Symphony no. 4]

It's simply miraculous, what can happen to a little interval of the 3rd, isn't it? And so all through this

movement, we come upon these intervals of 3rds and 6ths used in the most ingenious ways —

horizontally, vertically, upside down and inside out.

And now we're going to play for you the whole of this magnificent, dramatic movement — which is one of

the high points of Brahms' whole creative output.

[ORCH: Brahms - Symphony no. 4]

Somebody asked me this week, "Why in the world did you pick intervals to spend a whole program on?

Who cares about that stuff? But after all, didn't we decide that the interval is the atom of all music? What

can be more important, or more basic, than that? So let's forge ahead and get to know intervals better.

Now remember that measuring tape we used before to mark off the octaves? Now let's just consider out

of this measuring tape one octave - one foot of the tape. What a lucky coincidence it turns out it's marked

off into 12 inches, and there also just happen to be exactly 12 notes in an octave!

Now I don't want to confuse you; I know I said before that an octave has eight notes in it (which is why it's

called an octave); but then I was speaking of our regular major scale, which uses only some of the notes

that exist in an octave. For instance, as you know, the C-major scale, uses only the white notes of the

piano [PLAY] — eight of them. But there are black ones too [PLAY]; so all in all there are actually twelve

different notes in every octave, each note exactly the same distance from its neighbor [PLAY AND

COUNT], and with the thirteenth [PLAY] we're back again where we started.

Now the distance between any two neighboring notes is, as you know, a 2nd [PLAY], from here to here.

But, as you may not know, it is a minor second. A minor second is the smallest distance we can move

from one note to the next, in our Western musical system, which is based on the twelve different tones —

like the twelve inches of the foot rule, or the twelve minor seconds in an octave [PLAY].

Now if there is such a thing as a minor second [PLAY] there must be also such a thing as a major second

as well. And so there is [PLAY], twice as big an interval as the minor second. I know this seems to be

getting complicated, but I just want you to feel the difference between a minor second and a major

second, because the piece with which we're going to finish our program is almost totally made out of

themes built in minor and major seconds. And the difference between them is very important, as you're

going to see. This hair-raising piece is again a Fourth Symphony, only this time by the great, famous

British composer Vaughan Williams; and we're going to play only the Finale, the last movement.

But in order for you to relish it to the fullest, I want to show you a bit of what Vaughan Williams does with

these tiny little intervals in the preceding three movements. From the very opening bars of the first

movement, he is already presenting us with minor seconds, as if to say: This is going to be the subject of

my symphony.

[PLAY: Vaughn Williams - Symphony no. 4]

That's nothing but a descending minor second [PLAY] followed by a drop of an octave [PLAY]. Now to

build his theme, he repeats that minor second [PLAY] and follows it up by more minor seconds,

descending from a greater height: [PLAY next three notes]. Then, even higher, he gives us two more

pairs of descending minor seconds, and those four notes form the basic motive, or the motto, of the whole

symphony. You're going to hear it a lot in the last movement.

In the orchestra, this rugged opening theme sounds even more rugged, because while the high

instruments are playing one note of that interval, that minor second [PLAY] the low instruments are

playing the other [PLAY] — and that makes a mighty, clashing dissonance [PLAY] because when that

interval of the minor second is played vertically — you remember about vertically — meaning

simultaneously [PLAY], it makes harmony of a very bristly kind. Just listen to the whole theme now in the

orchestra with all its orchestral bite and strength.

[ORCH: Vaughn Williams - Symphony no. 4]

Pretty bristly isn't it? The very next thing that happens is again made of minor seconds, only this time

they're rising instead of descending — like a great monster rising our of the sea. It sounds like this.

[ORCH: Vaughn Williams - Symphony no. 4]

You see what can be done with minor seconds? You can have all sorts of music. And so it goes. Almost

the whole movement is concerned with those dissonant, fierce, gigantic uses of that tiny interval, the

minor second, especially in its four-note motto form, which is this

[INSTR: Vaughn Williams - Symphony no. 4]

The second movement also uses 2nds, in a slow song-like way, but it's greatest moment comes just

before the end of the movement where there's a sad flute solo mostly made of falling minor 2nds, that

sounds like this

[INSTR: Vaughn Williams - Symphony no. 4]

and underneath that flute solo harmony in the trombones consists of four very soft chords which, as if by

magic spell out the four-note motto from the first movement. Just listen.

[INSTR: Vaughn Williams - Symphony no. 4]

That's the harmony under the flute solo. Now listen to them together, the flute melody and those chords in

counterpoint; it makes a whole network of minor seconds.

[ORCH: Vaughn Williams - Symphony no. 4]

Beautiful. And what a mysterious atmosphere it makes with those tiny little intervals. Then abruptly the

third movement charges in, in high spirits, as if to dispel the mystery; but after a brief moment the old four-

note motto clangs forth again in the brass, then faster in the woodwinds, and even faster in the strings, as

if to show that this riddle of minor seconds from the first movement is still not solved. Sounds like this:

[ORCH: Vaughn Williams - Symphony no. 4]

Do you hear that? It seems as if all three movements so far are bent on solving the mystery of these

minor seconds we heard at the beginning; but now in the last movement we finally get the feeling of

having solved it, as it breaks in with this great jolly tune:

[ORCH: Vaughn Williams - Symphony no. 4]

Now what is it about that music that makes it sound so solved, so liberated? It's just this: that after all the

messing around with those crabbed little intervals of minor seconds

[PLAY: Vaughn Williams - Symphony no. 4]

that we've been hearing for three movements, we finally arrive at a triumphant tune that opens up into a

major second

[PLAY: Vaughn Williams - Symphony no. 4]

Now obviously, major seconds aren't all that wide-open [PLAY] compared to fourths [PLAY] for instance,

or fifths [PLAY] which are really wide open; but compared to the scrunchy little minor seconds, [PLAY]

which we've been hearing in every conceivable form for three whole movements, this major second

seems like the gates of Heaven itself [PLAY]. And there you have the real magic of intervals: in the hands

of a composer who's a genius, a modest, humble little major second can have a mountainous majesty.

And so, all through this final movement, you'll hear the interval of the second used for all it's worth, major

and minor, descending and ascending, in all kinds of rhythm, combined with all the different themes of

this Finale in a dazzling display of counterpoint. It's a regular festival of seconds, minor and major. It

finally works itself up to a frenzy of major and minor seconds, but at the very height of this exciting build-

up, when everything is going like gang busters, an the very last page, the composer suddenly hurls us

back into the dissonant rage of the opening movement, and with six final hammer-blows the symphony

comes to a savage end. Now why this sudden, brief, angry, dissonant ending after a whole joyful

movement that made us feel we'd solved everything at last? Well, it's as if Vaughan Williams were telling

us: Ladies and gentleman, boys and girls, that's life.

[ORCH: Vaughn Williams - Symphony no. 4]