Music Theory
So I've been crazy stressed dealing with grad school stuff, from GREs in October, to apps in December-February, to waiting on decisions and trying to make my own decision now. Last week I traveled to one school to check it out, this evening I'm flying out to another. The thing for this one I'm going to, though, it's for a music cognition program, though officially I'll be doing music theory/composition, if I pick it. Whether I go will be based at least partly on funding, for which I'm applying for a teaching assistantship. And for my application, I have to make a video, a mock-lecture to demonstrate that I can, in fact, teach.
Only I've never taught. I mean, I've done one-on-one stuff, peer tutoring and carillon instruction and small stuff like that, but not actual teaching, and certainly not actual teaching of music theory. Well, after much angsting, I have at least written a text for the video, though when and how I'm going to make it I still don't know. Anyway, I was hoping to test the actual recording out on people, but that's just not gonnna happen, so I thought I'd at least stick the text up here and see if anyone will read it and tell me what they think.
It's 1600 words, and it's going to have musical examples which I have to play on the keyboard, when the time comes, but for now it's just text:
Chromaticism, Tonicization and Modulation
Music has an hierarchical structure; it also has an iterative structure. What happens at a top level of organization often happens or could happen at each subsequent level, down to the level of greatest detail. We see the same processes in the overall formal content of a piece as we do in the relationships between individual notes, in each unit of musical time.
One instance of this phenomenon that you are all familiar with is the relationship between I and V. At the note level, we have the simple chord progression I-V-I, a progression which immediately establishes key in a very straightforward way. At a much wider level, we have, for example, the sonata form. There, the entire theme journeys from tonic to dominant, through a ladder of many other keys, and back again.
To travel to other keys is called modulation, and to do this requires a departure from the diatonic scale.
So you've got your scale, in a key that you've established. Seven notes, in a set pattern of whole and half steps. Nice, comforting, familiar. We all know it, feel pretty much at home there. But you noodle around, and it gets a little boring. You can do a lot with just the diatonic notes, but it's like spending your whole life playing in your own backyard. After a while you know every square inch of the yard a little too well. You want to open up that gate, walk down the path, and see what else is out there. Going into the world enriches your experience of home when you return.
Enter what we call the accidentals. The non-diatonic notes. Extra sharps, flats and naturals that aren't in the original scale, joining us mid-journey. They're not just there to trip up beginning piano students. Let's leave aside the various minor scales for the moment, which have their own reasons for some accidentals, and look at why we use them most of the time.
Equal temperament is a powerful thing. Equal temperament allows us to roam by leveling the playing field in key-relationships, like a very successful civil rights movement or road-paving project. (It does this by making the very smallest intervals in western tonal music--the interval of the second--the same.) It makes chromatic harmony possible.
Chromatic harmony is what this is all about. The next big step. All the juicy stuff.
The term 'chromatic' comes from chroma, color. And, especially at an early level, that's what it is. The most simple insertion of chromatic notes stems from voice-leading practice. A passing tone--what's a passing tone?--bridges the gap between two chord tones, facilitating the movement of the line, and a chromatic passing tone towards an especially strong, emphasized note, will greatly intensify that movement. In the grand scheme of things, though, the effect of this most basic instance of chromaticism is slight. It really does provide color more than function, almost like a decorative sconce with no weight-bearing properties.
Take chromaticism a little further, and you have another level of organization exhibiting the same sort of process. Let's look at whole chords now. Even here, the load-bearing duties of the chromaticism can be light. Who can tell me what a secondary dominant is?
The circle of fifths: Start in D major, the fifth of that is A; the fifth of A is E; the fifth of E is B. And so on. If you're in the key of A major, and you see an E chord, generally followed by a B chord, that E is a secondary or an applied dominant, a dominant on top of a dominant. It's a momentary hop into another key, the key of E major, or the fifth, achieved by using its fifth to temporarily tonicize E, turning it into I. It doesn't last very long, but while it's there it lends flavor to a harmonic progression; sometimes it's for interest, sometimes it's for emphasis, sometimes it complements some motion in the voice leading.
You'll recognize tonicizations because of their brevity. They only last for a few chords. Pretty soon, you're back in the original key again, and you might not really feel as though you have gone to another key at all. Tonicizations also tend to happen in the middle of phrases, at moments of less rhythmic importance in order to support that fleetingness. And, as a teacher of mine once said, you can go around tonicizing all kinds of chords. Secondary dominants are a primary type of tonicization, but they're not the only kind. There are also, for instance, the various kinds of sixth chords, really juicy. Their function, as is the function of basically all harmonic progressions, when you come down to it, is prolongation of V/delay of I.
Okay, so we have passing melodic chromaticism, and brief harmonic chromaticism. That's two levels; what's next? Another level. What if the chromaticism wasn't so brief? What if the change in key is much more definite? What do we call it when we move into another key for a while?
Modulation can happen on a wide range of scale, of scope. It's really a continuum from the three-chord tonicization and back again, to the whole-section modulations that structure entire movements and pieces. Coming back to sonata form, modulations happen for the second statement of the expositional theme (generally in the dominant) and throughout the development, which is really all modulation, before returning to the tonic. It's basically like a novel in music. The main character, who is hopefully pretty dynamic, experiences his whole plot, be it a romance, an action-adventure, a coming-of-age story, whatever, and through his experiences is changed, even though he's still recognizably the same person. He's enriched and colored by having gone through his journey, just as our experience of the theme is enriched by having gone through all the modulation, the chromaticism! Juicy. Some people would say it's like life. I'll let you decide that for yourself.
So how do modulations work? They're a little bit different from what we call tonicizations, though, again, it's a continuum from one to the other. Modulations usually happen at rhythmically significant places and last for at least an entire phrase, making them much more noticeable, more definitely going somewhere. There are several actual ways to modulate, some of which are very simple: In popular songs, especially the really schmaltzy ones and I've found this a lot in the sort of choral music you sing when you're in high school; there's that last repetition of the chorus a half or whole step higher--for excitement! That's a straight-up stop and start over in the new (rather distant) key, and it doesn't happen much in art music. Then you've got the modulation that hangs on a single common tone; the whole texture gets pared down to just the one note or notes that appear in both keys.
Which leads us to a method of modulation that's much more common in western art music, the use of pivot chords. Pivot chords are basically common tones in chord form. All the notes of the chord are diatonic for both keys. So they do exactly what the name implies. They pivot from one key to the other. You can see how this works when you look at the analysis of something that modulates by use of a pivot chord. There's an overlap in the analysis, where one chord has a different function (and a different roman numeral) within each key. Seamless transition from one to the other.
Now, the more closely related two keys are, the more often you'll see modulations between them, and the easier these modulations will be. So a major key and the key on its dominant, which are right next to each on the circle of fifths and have very similar key signatures are likely modulations. They have almost all the same notes in their scales. The likelihood of a useful pivot chord is much higher, And in fact, one that's used a lot in the major mode is vi in the tonic key, which is ii in the dominant. Just like with tonicization--because, really, modulations are just extended tonicizations--you can go around modulation to all kinds of keys. The less closely related they are, the more work you have to do, to have it make sense.
As with progressions between chords that stay within one key, modulations between two or more keys can happen either diatonically or chromatically. For example, German augmented sixth chords can be spelled enharmonically (thanks to the miracle of equal temperament) as a seventh chord. Combining several levels of chromaticism.
Chromaticism, tonicization, modulation: lengthening and coloristic processes that fall on a continuum from total diatonicism, staying completely in one key to progressions that travel over many other keys, close and foreign, before returning home to the big V-I. The term chromaticism refers to both the single non-diatonic notes and to the technique of using these notes in a piece. Just like the music it describes, it applies on many levels. Composers of the common-practice era used and developed chromaticism, starting from minute departures from diatonic limits and going to dense, frequent key changes roving all across the circle of fifths. Though the spectrum was not traversed wholly chronologically--there is plenty of chromaticism in Bach--eventually this led to such extreme departure from traditional harmony that the common-practice system was transcended altogether, taking flight as its evolution changed it into quite a different animal, what came to be known as atonality.
But that's another story.
Only I've never taught. I mean, I've done one-on-one stuff, peer tutoring and carillon instruction and small stuff like that, but not actual teaching, and certainly not actual teaching of music theory. Well, after much angsting, I have at least written a text for the video, though when and how I'm going to make it I still don't know. Anyway, I was hoping to test the actual recording out on people, but that's just not gonnna happen, so I thought I'd at least stick the text up here and see if anyone will read it and tell me what they think.
It's 1600 words, and it's going to have musical examples which I have to play on the keyboard, when the time comes, but for now it's just text:
Chromaticism, Tonicization and Modulation
Music has an hierarchical structure; it also has an iterative structure. What happens at a top level of organization often happens or could happen at each subsequent level, down to the level of greatest detail. We see the same processes in the overall formal content of a piece as we do in the relationships between individual notes, in each unit of musical time.
One instance of this phenomenon that you are all familiar with is the relationship between I and V. At the note level, we have the simple chord progression I-V-I, a progression which immediately establishes key in a very straightforward way. At a much wider level, we have, for example, the sonata form. There, the entire theme journeys from tonic to dominant, through a ladder of many other keys, and back again.
To travel to other keys is called modulation, and to do this requires a departure from the diatonic scale.
So you've got your scale, in a key that you've established. Seven notes, in a set pattern of whole and half steps. Nice, comforting, familiar. We all know it, feel pretty much at home there. But you noodle around, and it gets a little boring. You can do a lot with just the diatonic notes, but it's like spending your whole life playing in your own backyard. After a while you know every square inch of the yard a little too well. You want to open up that gate, walk down the path, and see what else is out there. Going into the world enriches your experience of home when you return.
Enter what we call the accidentals. The non-diatonic notes. Extra sharps, flats and naturals that aren't in the original scale, joining us mid-journey. They're not just there to trip up beginning piano students. Let's leave aside the various minor scales for the moment, which have their own reasons for some accidentals, and look at why we use them most of the time.
Equal temperament is a powerful thing. Equal temperament allows us to roam by leveling the playing field in key-relationships, like a very successful civil rights movement or road-paving project. (It does this by making the very smallest intervals in western tonal music--the interval of the second--the same.) It makes chromatic harmony possible.
Chromatic harmony is what this is all about. The next big step. All the juicy stuff.
The term 'chromatic' comes from chroma, color. And, especially at an early level, that's what it is. The most simple insertion of chromatic notes stems from voice-leading practice. A passing tone--what's a passing tone?--bridges the gap between two chord tones, facilitating the movement of the line, and a chromatic passing tone towards an especially strong, emphasized note, will greatly intensify that movement. In the grand scheme of things, though, the effect of this most basic instance of chromaticism is slight. It really does provide color more than function, almost like a decorative sconce with no weight-bearing properties.
Take chromaticism a little further, and you have another level of organization exhibiting the same sort of process. Let's look at whole chords now. Even here, the load-bearing duties of the chromaticism can be light. Who can tell me what a secondary dominant is?
The circle of fifths: Start in D major, the fifth of that is A; the fifth of A is E; the fifth of E is B. And so on. If you're in the key of A major, and you see an E chord, generally followed by a B chord, that E is a secondary or an applied dominant, a dominant on top of a dominant. It's a momentary hop into another key, the key of E major, or the fifth, achieved by using its fifth to temporarily tonicize E, turning it into I. It doesn't last very long, but while it's there it lends flavor to a harmonic progression; sometimes it's for interest, sometimes it's for emphasis, sometimes it complements some motion in the voice leading.
You'll recognize tonicizations because of their brevity. They only last for a few chords. Pretty soon, you're back in the original key again, and you might not really feel as though you have gone to another key at all. Tonicizations also tend to happen in the middle of phrases, at moments of less rhythmic importance in order to support that fleetingness. And, as a teacher of mine once said, you can go around tonicizing all kinds of chords. Secondary dominants are a primary type of tonicization, but they're not the only kind. There are also, for instance, the various kinds of sixth chords, really juicy. Their function, as is the function of basically all harmonic progressions, when you come down to it, is prolongation of V/delay of I.
Okay, so we have passing melodic chromaticism, and brief harmonic chromaticism. That's two levels; what's next? Another level. What if the chromaticism wasn't so brief? What if the change in key is much more definite? What do we call it when we move into another key for a while?
Modulation can happen on a wide range of scale, of scope. It's really a continuum from the three-chord tonicization and back again, to the whole-section modulations that structure entire movements and pieces. Coming back to sonata form, modulations happen for the second statement of the expositional theme (generally in the dominant) and throughout the development, which is really all modulation, before returning to the tonic. It's basically like a novel in music. The main character, who is hopefully pretty dynamic, experiences his whole plot, be it a romance, an action-adventure, a coming-of-age story, whatever, and through his experiences is changed, even though he's still recognizably the same person. He's enriched and colored by having gone through his journey, just as our experience of the theme is enriched by having gone through all the modulation, the chromaticism! Juicy. Some people would say it's like life. I'll let you decide that for yourself.
So how do modulations work? They're a little bit different from what we call tonicizations, though, again, it's a continuum from one to the other. Modulations usually happen at rhythmically significant places and last for at least an entire phrase, making them much more noticeable, more definitely going somewhere. There are several actual ways to modulate, some of which are very simple: In popular songs, especially the really schmaltzy ones and I've found this a lot in the sort of choral music you sing when you're in high school; there's that last repetition of the chorus a half or whole step higher--for excitement! That's a straight-up stop and start over in the new (rather distant) key, and it doesn't happen much in art music. Then you've got the modulation that hangs on a single common tone; the whole texture gets pared down to just the one note or notes that appear in both keys.
Which leads us to a method of modulation that's much more common in western art music, the use of pivot chords. Pivot chords are basically common tones in chord form. All the notes of the chord are diatonic for both keys. So they do exactly what the name implies. They pivot from one key to the other. You can see how this works when you look at the analysis of something that modulates by use of a pivot chord. There's an overlap in the analysis, where one chord has a different function (and a different roman numeral) within each key. Seamless transition from one to the other.
Now, the more closely related two keys are, the more often you'll see modulations between them, and the easier these modulations will be. So a major key and the key on its dominant, which are right next to each on the circle of fifths and have very similar key signatures are likely modulations. They have almost all the same notes in their scales. The likelihood of a useful pivot chord is much higher, And in fact, one that's used a lot in the major mode is vi in the tonic key, which is ii in the dominant. Just like with tonicization--because, really, modulations are just extended tonicizations--you can go around modulation to all kinds of keys. The less closely related they are, the more work you have to do, to have it make sense.
As with progressions between chords that stay within one key, modulations between two or more keys can happen either diatonically or chromatically. For example, German augmented sixth chords can be spelled enharmonically (thanks to the miracle of equal temperament) as a seventh chord. Combining several levels of chromaticism.
Chromaticism, tonicization, modulation: lengthening and coloristic processes that fall on a continuum from total diatonicism, staying completely in one key to progressions that travel over many other keys, close and foreign, before returning home to the big V-I. The term chromaticism refers to both the single non-diatonic notes and to the technique of using these notes in a piece. Just like the music it describes, it applies on many levels. Composers of the common-practice era used and developed chromaticism, starting from minute departures from diatonic limits and going to dense, frequent key changes roving all across the circle of fifths. Though the spectrum was not traversed wholly chronologically--there is plenty of chromaticism in Bach--eventually this led to such extreme departure from traditional harmony that the common-practice system was transcended altogether, taking flight as its evolution changed it into quite a different animal, what came to be known as atonality.
But that's another story.