Section 4: The Chords at the Center of the Universe
Until now, I've concentrated almost exclusively on the properties of the major and minor scales in terms of melodic intervals - that is, I've talked about tunes and fragments of tunes. But most of the music you're likely to listen listen to involves more than just melodies. So the time has come to tackle the formidable topic of what happens when we hear more than one pitch at a time.
At this point, we need some more basic terminology. Whenever two or more pitches occur simultaneously - or, to be more precise, when your brain thinks it's perceiving two or more pitches simultaneously - those pitches form a chord. Two note chords are more commonly called harmonic intervals; if you don't want to count them as genuine chords, it's all the same to me. Harmony is the study of how chords are constructed and, especially, how they interact with each other.
I think a few words of caution and/or reassurance are in order before we proceed. Hearing harmonic intervals as two individual pitches - let alone identifying the intervals specifically - is much more difficult than hearing them as melodic intervals, that is, as consecutive pitches. (And, if you've had no previous practice at doing it, identifying melodic intervals is no trivial task either.) Hearing three or more simultaneous pitches as separate entities is harder still.
To be sure, there are plenty of people - many of whom do not even have absolute pitch - who can hear a complicated chord and immediately identify its component intervals. I myself have good days and bad days. On a bad day, I'll confuse simple melodic intervals, but even at my best, I don't have that kind of aural facility.
Luckily, as far as I'm concerned, this is not a skill necessary to enjoying music and understanding how it works. The important thing about chords, for me anyway, is the psychological effect they have as a whole. Chords are what give melodies their ability to move us so deeply, their musical "meaning." The musical architecture of a large, complex piece like a Beethoven symphony is supported by - or even better, simply is - the relationship of chords. I'm hanging my hat on the belief that you're already sensitive to their effect; my aim to make you more aware of what you're already hearing and responding to.
To be sure, there are plenty of people - many of whom do not even have absolute pitch - who can hear a complicated chord and immediately identify its component intervals. I myself have good days and bad days. On a bad day, I'll confuse simple melodic intervals, but even at my best, I don't have that kind of aural facility.
Luckily, as far as I'm concerned, this is not a skill necessary to enjoying music and understanding how it works. The important thing about chords, for me anyway, is the psychological effect they have as a whole. Chords are what give melodies their ability to move us so deeply, their musical "meaning." The musical architecture of a large, complex piece like a Beethoven symphony is supported by - or even better, simply is - the relationship of chords. I'm hanging my hat on the belief that you're already sensitive to their effect; my aim to make you more aware of what you're already hearing and responding to.
Let's start with a phenomenon you've probably heard many times, the sound of harmonic thirds.
Major and minor seconds - steps within the scale - occur most naturally as melodic intervals; a very high percentage - I'm guessing at least 80% - of the intervals in most tunes are scale steps - major or minor seconds. Thirds, however, are especially well adapted to being played simultaneously as harmonic intervals, and many melodic lines benefit from the addition of another voice a third away. Here are the two forms, melodic and harmonic, of a major third,
Example 1:
Example 1:
and here is an example of parallel thirds you have probably heard many times.
Example 2:
Example 2:
You might say parallel thirds are like musical ball bearings; the sonority they create helps music glide along with a sound that many people find to be particularly sweet and euphonious. It's a sound musicians and composers have used again and again; here are a few examples.
First, the Everly Brothers singing "Bye bye love."
Example 3:
First, the Everly Brothers singing "Bye bye love."
Example 3:
Since they're so common in this style of music, I should mention parallel thirds' close cousins, parallel sixths. If you take parallel thirds and move the upper voice down an octave, like so,
Example 4:
Example 4:
(or the lower voice up an octave) you create parallel sixths, which, for most people, have the same harmonious quality as thirds. I often get them confused.
Here's an ironically sweet passage from Mozart's opera Così fan tutte. In the duet "Ah, guarda, sorella!," the sisters Dorabella and Fiordiligi swear, in parallel thirds, their undying love for their fiancees, whom they will betray in modern sit-com style as the opera runs its course.
Example 5:
Example 5:
A fabulous performance, don't you think? Here's a link to a YouTube of the complete version of the duet.
One more example, from Franz Schubert's String Quintet in C major - a quintet because Schubert adds an extra cello to the cello, viola, and two violins of a standard string quartet. Here, the two cellos, very high up in their range, start on the same pitch; one cello creeps down a major third and then, harmonizing in thirds and sixths, the two play what I (and many others) rate as one of most gorgeous melodies ever created.
Example 6:
Example 6:
Thirds are sexy when they are used, as they are in these examples, to add richness to a melodic line, but that's not the only reason I've given them so much attention. Thirds are also the essential building materials of most of the chords you hear.
When I say building materials, I actually mean something quite simple: the simplest sort of three-pitch chord, which is not surprisingly called a triad, is built by taking a harmonic third and adding another third either above it or below it, like so:
Example 7:
Example 7:
If you've read Section 3, that should sound familiar. It turns out that Section 3 was really all about triads, except that there I discussed thirds as separately occurring pitches within the major and minor scales, and here I'm concerned with the effects of playing those pitches simultaneously. So you already know - and, as far as the rest of this discussion is concerned, can immediately forget - that triads can be major or minor, depending on the arrangement of major and minor thirds.
I'll come back to triads in a moment, but I want to give you a taste of the exotic effects that can be created by continuing to stack thirds on top of each other.
Here's a minor triad extended by the addition of three more thirds; you'll hear the component pitches separately and then together.
Example 8:
Example 8:
And here's that extended triad in the context of the jazz standard My Funny Valentine.
Example 8a:
Example 8a:
Many would say the following excerpt from Igor Stravinsky's Rite of Spring, as notorious as much for its rhythm as for its harmony, contains the single most revolutionary chord of the 20th century,
Example 9:
Example 9:
but, despite the fact that it sounded so barbaric in 1913, it too consists of stacks of thirds - actually, two stacks of thirds that violently clash with each other.
Example 10:
Example 10:
Back to triads.
If this were a conventional harmony course, I would now embark on a detailed analysis of the possible variants of Example 7. I assure you, your eyes would glaze over. Moreover, such a discussion would have almost no connection with your actual musical experience.
Nevertheless, triads, sometimes with modest extensions but more often than not in their simple three-pitch form, are ubiquitous in classical music, in jazz, in country, in rock, in techno - in practically any style you can name. You just can't get away from them. Why is it, then, that no matter what music you listen to, you only occasionally hear anything that sounds like Example 7?
If this were a conventional harmony course, I would now embark on a detailed analysis of the possible variants of Example 7. I assure you, your eyes would glaze over. Moreover, such a discussion would have almost no connection with your actual musical experience.
Nevertheless, triads, sometimes with modest extensions but more often than not in their simple three-pitch form, are ubiquitous in classical music, in jazz, in country, in rock, in techno - in practically any style you can name. You just can't get away from them. Why is it, then, that no matter what music you listen to, you only occasionally hear anything that sounds like Example 7?
The answer is the subject of Section 1, octave equivalency. To repeat what I said near the beginning of that section, everything that we generally understand to be music depends on it in some way. Most explanations of triads completely ignore the phenomenon, and thus don't take into account how triads sound in the real musical world.
To refresh your memory of what I mean by octave equivalency, all pitches an octave apart have the same name. This is the pitch C,
Example 11:
To refresh your memory of what I mean by octave equivalency, all pitches an octave apart have the same name. This is the pitch C,
Example 11:
and so are all these.
Example 11a:
Example 11a:
Recall from Section 2 that the scale repeats cyclically each octave, like so.
Example 12:
Example 12:
Since major and minor triads are just a subset of the scales they belong to, triads also repeat cyclically.
Example 12a:
Example 12a:
So when I use the term triad, I do not mean only a chord consisting of three pitches separated by thirds as in Example 7; I also mean any chord consisting of the octave equivalents of those three pitches, distributed however one likes across the audible range from bass tuba to piccolo, each pitch duplicated at the octave as many times as is practical and/or suitable to a particular musical situation.
The beginning of Beethoven's "Appassionata" Sonata furnishes a spectacularly dramatic illustration of this expanded definition of triad.
Here's a simple minor triad.
Example 13:
Here's a simple minor triad.
Example 13:
Here's the opening of the sonata, in which that triad is played as a melody, doubled by the right and left hands two octaves apart (a sonority Beethoven loved to use in his piano music). The melody itself takes the triad over two octaves. Despite all the piano keys that get pressed, this passage uses only three pitches and their octave equivalents.
Example 13a:
Example 13a:
A little but later, this is what happens.
Example 13b:
Example 13b:
This is about as much octave duplication as two human hands can produce, but, as thunderous and massive as this passage is, it still consists of exactly the same triad as Examples 13 and 13a, using the same three pitches and no others, duplicated over many octaves.
Here are Examples 13a and 13b in their actual context. The pianist is Vladimir Horowitz.
Example 14:
Example 14:
With this expanded definition of triads in hand, I'll now try to answer the question you might well be asking about now: Why is Coren expending so much effort on triads anyway?
We've already seen how a scale mysteriously imposes a hierarchical order on the pitches comprising it, how it creates the sense of being in a key - specifically, how it makes the first note of the scale sound like a sort of home base. So let's see what happens if we try to distribute the pitches of the scale efficiently as we can among some triads.
It turns out that if we build triads on the first note of the scale,
Example 15a:
We've already seen how a scale mysteriously imposes a hierarchical order on the pitches comprising it, how it creates the sense of being in a key - specifically, how it makes the first note of the scale sound like a sort of home base. So let's see what happens if we try to distribute the pitches of the scale efficiently as we can among some triads.
It turns out that if we build triads on the first note of the scale,
Example 15a:
the fourth note of the scale,
Example 15b:
Example 15b:
and the fifth note of the scale,
Example 15c:
Example 15c:
we use up every step of the scale, with two of the steps appearing in more than one of these three triads. (3 x 3 = 9; there are seven pitches in the scale.) For reasons that will become apparent in a bit, it will be helpful if we extend Example 15c by an extra third, like this:
Example 15d:
Example 15d:
I am not going to burden you with knowing which scale steps appear in which chords and why, even though the logic involved is extremely simple; all I care about is that you hear how these triads work together.
If we now take these three chords and distribute their pitches over a few octaves, we get little musical fragments like this
Example 16a:
Example 16a:
or this
Example 16b:
Example 16b:
or this, a very abridged version of a tune from a Beethoven piano sonata.
Example 16c:
Example 16c:
I could go on with little formulas like this forever. They're all different, but what they have in common is, at least for our current purposes, much more important: they all consist entirely of the chords of Examples 15a, b, and c; the notes of the major scale are distributed evenly among the three chords. Most important of all, working together, the three chords demonstrate a new, efficient way of doing the work of the major scale: they create the same sense of home base, of being in a key. In fact, these chords are the scale, arranged in a new way.
It's time to give a name to this phenomenon of melody and harmony working together to create a sense of being in a key, so here it is, bolded, upper case, underlined, and in italics:
T O N A L I T Y !!!
That might as well be the actual title of this site. Everything I've written so far has been about tonality as will, I imagine, virtually everything l write here in the future.
Let me again, for the umpteenth time, emphasize the importance of context. In isolation, a single triad has no particular properties other than just being a triad. Like the pitches in a tonal melody, the three triads in Examples 16a, b, and c create their effect only by working together. And allow me also to reiterate that nobody knows - nobody is close to knowing - how this all works in the brain.
I swore at the outset not to subject you to obscure jargon, but we cannot proceed beyond this point without some of music's most unfortunate terminology: tonic, dominant, and subdominant. The terms describe not the chords of the previous examples themselves, but the roles that they assume in relationship to each other, that is, their function within a key.
Example 15a is the tonic in its simplest, most abstract form; 15 b is the subdominant; 15c and its extension 15d, the dominant. The last three chords in each of the previous three examples (Examples 16a, b, and c) are subdominant-dominant-tonic. At the risk of sounding cornily over the top, the three terms could aptly be termed the Three Pillars of Tonality. (I wanted to say the Three Pillars of Musical Wisdom, but that is a bit much. )
Example 15a is the tonic in its simplest, most abstract form; 15 b is the subdominant; 15c and its extension 15d, the dominant. The last three chords in each of the previous three examples (Examples 16a, b, and c) are subdominant-dominant-tonic. At the risk of sounding cornily over the top, the three terms could aptly be termed the Three Pillars of Tonality. (I wanted to say the Three Pillars of Musical Wisdom, but that is a bit much. )
The terminology is unfortunate, first, in that the words do not have any obvious connection with the normal, non-musical English meanings of dominant and tonic and, second, that attempts to explain them tend to generate particularly impenetrable prose. (The Wikipedia definition of the musical sense of "dominant" is especially extreme. ) Wish me luck in doing better.
If you relate to the subdominant - dominant - tonic relationship in terms of musical feeling - that is, in terms of their psychological effect - rather than as obscure terms that you might be tested on, I'm hopeful you'll find that you've known all along, if perhaps only subliminally, what they mean.
Tonic in the musical sense has the same pronunciation as the tonic one adds to gin, but if the term were pronounced with the long "o" of the word "tone" it wouldn't seem quite so arbitrary and obscure. The tonic function is easy to explain: it's the chord (or single pitch) that has the quality of home base; the final triad you hear in just about every piece of music you listen to is the tonic. Don't worry; trust your instincts. If something feels like the tonic, it almost certainly is the tonic.
But how do you know that a tonic is a tonic? Because the dominant chord tells you so; it tells you where the tonic is and makes you want to hear it. Since the function is so crucial to so much music - in the long run, next to tonality itself, the dominant is probably the most important concept I'll deal with - it's worth taking a moment to dissect a dominant chord.
Listen again to Example 15d. Here's the same chord moved down an octave.
Example 17a:
Listen again to Example 15d. Here's the same chord moved down an octave.
Example 17a:
Now, because it will help a bit in illustrating my point, I'll take the second lowest pitch and move it up an octave.
Example 17b:
Example 17b:
For me, the essence of this chord, what makes it so "dominanty," is the tension created by the top two pitches of Example 17b, the way they yearn to move to their neighbors in the scale - the top pitch up to what happens to be the tonic, the other down to what happens to be the third step of the scale.
Example 17c:
Example 17c:
Add to this the way the bottom note wants to jump down to the tonic,
Example 17d:
Example 17d:
and you get the complete picture of how a dominant chord functions.
This is not a particularly dramatic example, to be sure. I'm just showing you the bare bones of the dominant function. But at crucial junctures in large scale classical pieces, a dominant chord might make you feel like you're about to go over Niagara Falls. Take this example from Beethoven's "Waldstein" Sonata, Op. 53. Here, on steroids, is the same dominant chord as we've just been listening to, finally resolving to the tonic at the end of the excerpt. The pianist is Maurizio Pollini.
Example 18:
Example 18:
Do I have your attention now?
While the tonic may be home, it has that quality only because the dominant makes it so. (But no, I really don't believe that's why it's called the dominant. I really have no idea where the term comes from.) You don't need to hear the tonic to know where it is! It's the dominant function that determines what key we're in; the tonic is merely what the dominant promised we'd get.
While the tonic may be home, it has that quality only because the dominant makes it so. (But no, I really don't believe that's why it's called the dominant. I really have no idea where the term comes from.) You don't need to hear the tonic to know where it is! It's the dominant function that determines what key we're in; the tonic is merely what the dominant promised we'd get.
There's a specific term for a sequence of subdominant-dominant-tonic chords - or simply dominant-tonic chords - like the ones we've been talking about for the last several paragraphs: such a sequence is called a cadence. More specifically, when the sequence actually ends on the tonic, it's called a full cadence. (If it stops on the dominant, it's called a half-cadence.) It's another one of those musical terms that has nothing to do with other more common uses of the word, but using it saves me the trouble of always having to write something like "the sequence of chords that defines the tonic."
While I find it easy to talk about the dominant and the tonic, but I've never been able to find a good way to verbalize what the subdominant feels like. For now, let's be content with saying that when it participates in full cadences, typically at the end of a piece, it somehow amplifies the powers of the dominant. For me, a good, solid subdominant has the stabilizing quality of the third leg of a tripod.
Wouldn't it be nice if there were some way that all this theory could be made tangible and concrete for those of you who don't play an instrument? Well, as it turns out, the good folks at Google, apparently aware that I was going to write about this topic, have supplied us with the perfect teaching tool.
On June 9th, to celebrate what would have been the 96th birthday of the late jazz guitar pioneer Les Paul, anyone doing a Google search was greeted with this display of virtuoso web programming. This little toy guitar toy has proved so popular that Google has given it this permanent website.
On June 9th, to celebrate what would have been the 96th birthday of the late jazz guitar pioneer Les Paul, anyone doing a Google search was greeted with this display of virtuoso web programming. This little toy guitar toy has proved so popular that Google has given it this permanent website.
Simply passing your mouse over a string in this display simulates plucking it. If you fool around a bit, you'll notice that there is a musical logic to the way the strings are arranged. In fact, you'll find that the keys are neatly arranged into our three cardinal tonal functions. The three strings on the upper left are the subdominant; the four strings on the bottom left are the tonic; the four strings on the right are the dominant.
For those of you who are interested, I've labeled the scale steps of each string.
Each step of the major scale is present and, as a bonus, the guitar also includes the higher octave equivalents of steps 1, 2 , and 3. It's worth repeating that, unless you have absolute pitch, the names of the pitches don't matter, just their collective effect. But just for the record, this guitar is in G major - that is, the tonic, step 1, is G.
Note that even though the tonic isn't represented by a full triad - only steps 1 and 3 are present -
those two pitches (supplemented by their octave doublings) still sound, at least to me, like an unequivocal tonic.
Note that even though the tonic isn't represented by a full triad - only steps 1 and 3 are present -
those two pitches (supplemented by their octave doublings) still sound, at least to me, like an unequivocal tonic.
You can even play actual melodies on this guitar, albeit in a very clunky fashion, by using the numerical keys at the top of the keyboard. But as nifty as Google's musical gift to the world may be, I wouldn't be surprised if after fooling around with it a bit you begin to get frustrated - if you weren't frustrated already - by the feeling that by now we've spent a lot of time paddling around the shallow end of the swimming pool.
Yes, we certainly have. I've so far been very careful not to stray beyond the boundaries of the scale, mostly the major scale, and I imagine you're fully aware that in the open ocean of actual musical experience, things are quite a bit more complicated.
Yes, we certainly have. I've so far been very careful not to stray beyond the boundaries of the scale, mostly the major scale, and I imagine you're fully aware that in the open ocean of actual musical experience, things are quite a bit more complicated.
In classical music, one spends a lot of the time wondering where the hell the tonic is. Moments of absolute clarity like the ones in Example 16 and 18 are relatively rare, but getting to one of them is more often than not the point of an entire piece, the denoument of the sort of elaborate abstract musical drama composers like Mozart, Beethoven, Chopin, and the rest created. So I'll conclude with such a moment, a passage near the end of Chopin's Nocturne Op. 27, No. 2 in D-flat major.
The heart of this passage uses this cadential sequence of five chords: 1: tonic, 2: subdominant, 3: a subdominant-dominant blend, 4: dominant, and 5:tonic.
Example 19:
Example 19:
That doesn't sound like anything special, especially plunked out on this dumb MIDI keyboard, but listen to what Chopin does with it.
At the beginning of Example 20 (below), Chopin unexpectedly takes what appears to be a turn into the remote wilderness of tonality; in the context of the entire piece, one might well wonder how he's ever going going to find his way home.
At the beginning of Example 20 (below), Chopin unexpectedly takes what appears to be a turn into the remote wilderness of tonality; in the context of the entire piece, one might well wonder how he's ever going going to find his way home.
But suddenly, out of nowhere, there's a series of descending sixths and it's as if we've come around a bend and found ourselves on our front doorstep. Chopin writes "appassionato" over his expanded version of Example 19 (starting at 0:55); the second chord is, for me, the essence of subdominant feeling, like hitting a ball on the sweet spot of a tennis racquet, and I find the big flourish over the third chord in Example 19 to be one the most ecstatic expressions of the joy of knowing the we're about to get home to the tonic.
Example 20:
Example 20:
The pianist is Lang Lang. I know some folks are put off by his theatrics, but for me, it's as if he channels the composers he brings to life. Here's a video of Lang Lang talking a bit about the piece and then playing it in its entirety.