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Old Feb 6 2008, 12:54 AM

echurchill's Avatar

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Finally, the surely much awaited lesson has arrived; this week and the last I have been auditioning at various colleges. Sorry for the delay, but I do plan to keep up a one-lesson-per-week average if I can!



CHROMATIC HARMONY



Harmonic Function
(I am posting some review in case you aren't used to looking at harmony this generally. If you understand all of this just ignore it . Tomorrow I will describe the voice leading of specific chromatic harmonies... I didn't get there tonight.)


From what I see in your short melody and its accompaniment, you have a fairly good "textbook" knowledge of chords, that is, you can use common chords like I, V, IV, ii, etc... to effectively harmonize a melody. Not to say that your technique is dry or primitive; after all I did ask for a very simple melody.

And I do not doubt that your understanding of harmony is even deeper than that. I do however want to briefly describe a more general way of viewing harmony that both you and I should be aiming for. Let us begin with with a simple chord, C Major. Let us say this is our tonic chord.

We follow it with a secondary dominant, V/V (D Major).

Then we finally reach V, a simple G Major chord.

So what comes next? Does the ear expect the tonic chord? Actually, you have probably noticed that our I V/V V progression in C Major is also a IV V I progression in G Major. Unless that final G Major chord has a 7th, our ears will be perfectly content to accept it as final.

Thus it makes no difference how we label a G Major chord: it could be V in C Major or c minor, I in G Major, IV in D Major, VII in a minor, VI in b minor, III in e minor, a Neapolitan in f# minor........ the possibilities are endless. And no matter how you choose to label it on paper, you ear may be hearing it as all of those to some very minute degree. It is important to realize that tonality isn't automatically set to D Major when we add two sharps to a key signature; instead the chords we pick will either confirm or reject the tonality. Thus in our D Major, a progression like vi ii vi I will not sound very final and may suggest i iv i III in b minor; a progression like I IV V, we both know, will certainly suggest D Major even if the V never resolves.

Basically what I mean is that any chord lies not in the key you want it in but in the key it wants itself in.


The degree to which a particular key is suggested can be very variable. There is no need to make a clear division between "tonicisations" and "modulations" because there is a gray area between them.


How do we describe the "function" of a chord? Different authors subscribe to different theories and argue over them; the truth, on the other hand, I think lies somewhere between all of them. Thus I think it is useful to keep all of them in mind simultaneously, as they all come into play:

1. The Circle of Fifths. I think you have Kostka and Payne's Tonal Harmony. They justify progressions as being based off of the circle of fifths:
iii - vi - ii - V - I,
where IV performs much the same function as ii and vii* as V:
iii - vi - [IV ii] - [vii* V] - I

2. Strong versus Weak Progressions. Since Rameau theorists have classified progressions into strong progressions (up or down a fifth, up a second, down a third) which more clearly suggests sequences like
I vi IV ii V I
I iii IV V I
Weak progressions to be avoided are up a third and down a second, ruling out tonally weak progressions like ii - IV or V - IV. (Notice that I can move anywhere, permitting I - iii and I - vii*)

3. Tonic, Dominant and Subdominant Functions. The progression I IV V is very strong and uses every note of the scale: a convenient summary of the entire tonal mechanism! Some authors consider all progressions to be modified I IV V progressions, where the function of IV is fulfilled by IV, ii, and maybe vi; the function of V can be replaced with V or vii*. iii does not clearly fulfill any of these.


All of these viewpoints reveal the inner workings of tonality, but none of them are definite. The circle of fifths must be altered considerably before it fits most music, and it fails to explain plagal cadences and progressions that seem to flow backwards. Many beautiful passages particularly in French, Spanish and Italian music move backward along the circle: I V ii vi V/vi. The weak vs. strong theory fails to allow such beautiful modal passages like one in the Lachrymae Pavan, i III v VII... Tonality is a fluid concept and can be manipulated artfully once we begin to see past "rules" and "progressions."
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Old Feb 6 2008, 10:58 AM

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I've read this through, and understood it all, am now going to sit at my piano for a bit, and try playing some progressions while thinking in different ways, as my normal way of thinking is based on strong versus weak progressions, as you put it, so I shall have a try at playing progressions based on the other schools of thought you mentioned, to get myself used to working with them.

I eagerly await the next lesson
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Old Feb 15 2008, 10:38 AM

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These lessons WILL move forwards! Unfortunately I have been busy with auditions, but they're all over for now.

So I guess you have had a lot, or perhaps too much, time to think over the mysterious inner workings of our tonal system .



I have two short topics concerning the last lesson to briefly discuss, followed by an in-depth study of the uses of secondary dominants.

REGRESSION VS PROGRESSION

The first is an example of the backwards circle-of-fifths sequence. It can be very beautiful because of its movement away from the tonic rather than towards it. The attachment "Zipoli Example" shows a pair of particularly beautiful examples from an organ canzona by Domenico Zipoli. (The repeat bars separate examples; they are not real repeats.) I mention this because it relates back to yet another way of classifying progressions and perhaps the most general: regressive versus progressive. A traditional circle of fifths sequence, such as

vi ii V I

moves towards the tonic and thus regresses in tension, beginning far from the tonic and then resolving back to it. On the other hand,

I V ii vi

moves away from the tonic and thus progresses (the terminology sounds a bit backwards). Tension and excitement increase as we move further and further away from the tonic (especially with the irregular resolution of V). Yet, when this progression continues, we usually see

I V ii vi V/vi

since a new goal has to be set, another key. So in practice, this backwards sequence is often modulates to the relative minor of a major key.

MODALITY VS TONALITY

A while ago I commented on your little aria and said I still objected to an iii V (actually iii I64) progression. It is clear to both of us that that progression is weak and does not follow the circle of fifths, and that the iii chord cannot successfully fulfill any tonal function (except for perhaps EXTREMELY WEAKLY IV, as you have used it here). But of course I mentioned that such weak progressions form many of the most beautiful passages in Renaissance music. What is going on with your example?

The real question begins during the slow rejection of modality that occurred towards the end of the 16th century. Before then all harmonies were determined by voice-leading; really almost any harmony could follow another harmony; in a sense, there were no harmonies, only consonant combinations of notes flowing in counterpoint. The one exception was the dominant chord, clearly viewed as a true harmony, with a tonal implication and function. Especially in minor the dominant chord required chromaticism; thus from V arose the tonal and chromatic systems of the next two centuries.

My basic point is that iii V would sound beautiful in a modal context. But the voice carrying B in the iii is hardly a soaring melody in your exercise. So since the accompaniment is not meant to be melodic, it is wiser and more appropriate to choose, for example, I6 V (especially since that would prepare the I64, something you do not seem to be doing). Now in a modal context, a progression like ii IV vi I iii happens to be among the most beautiful in all music in a piece like Dowland's Lachrymae, especially because its beautiful imitations transcend later tonal theory.

Don't think that I actually bothered this much about the tiny chord; I just used it to explain something much larger.



SECONDARY DOMINANTS

Please open the attachment "Chromatic II."

You see that in measure 2 I have a V/ii chord. What effect does it have on the feel of the piece at that point?

A secondary dominant is a very brief tonicisation, a modulation of about two chords, so to speak. And you should think of it that way, a temporary venture into another tonality lasting a few seconds, more as an ornament to the main tonality than anything powerful itself.

In this case, the V/ii resolves just as a dominant chord should, in this case to ii. The effect is a brief touch of the minor mode feel in an otherwise major phrase.

Now open up the attachment "Secondary Dominants."

In fact, many times the most beautiful secondary dominants imply a new mode briefly: in Major, V/vi and V/ii (and possibly V/iii) and in minor V/VI and V/III (and perhaps V/VII, though almost a modulation).

Also keep in mind exactly how chromatic a secondary dominant chord is. V/V in major is very common. In minor however, two notes have to be sharpened in V/V, so it must be used with care to avoid sounding harsh (the same applies to V/iii in Major, which is very hard to convincingly use (example 1)).



Exercises

In my next lesson I will discuss specific ways to voice lead secondary dominants, but before then I would like to see how you handle them so far. So choose a mode, either major or minor, and write ten little four-part-harmony chorale phrases, two to five bars long each, each one using a different secondary dominant (e.g. in Major, V/iii, V/vi, V/ii, V/IV and V/V, in minor, V/VII, V/III, V/VI, V/V, and V/iv). The dominants can have sevenths of course. Each phrase should be its own little unit, moving through a variety of different chords and finally resolving at a cadence. The secondary dominant should not sound terribly awkward, just colorful (be especially careful with V/iii in major and V/V in minor). The bass and soprano lines should be satisfying.

Now choose three of those little phrases to ornament each in two different ways, perhaps with counterpoint, perhaps with a florid soprano or bass, perhaps with arpeggiation, etc... I want to see how creatively you manage your texture in actual music! You can, of course, take out inner voices to lighten the texture, or add full chords where appropriate. Show me some sarabande rhythms!

Just to be clear, I am asking for sixteen little exercises. It may sound like a lot, but it isn't really that much once you start. I understand it might take a while, or that you might not finish them all, but most importantly have fun and explore. Carefully notice the sound of each dominant. Remember, I will be doing all of these too; I could use the practice .
Attached Files
File Type: mus Zipoli Example.MUS (30.5 KB, 19 views)
File Type: mus Chromatic II.MUS (29.7 KB, 19 views)
File Type: mus Secondary Dominants.MUS (29.4 KB, 17 views)

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Old Feb 15 2008, 11:54 AM

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As I think about that last long exercise, keep in mind it can be a work in progress, as the knowledge in our next lesson will definitely help you.

I also have Sarabande listening homework! These two Sarabandes are among the most beautiful I have heard, as well as being excellent performances. Please listen to them carefully; enjoy but also notice the chromatic harmony:

1. Track 13 of Janine Johnson: J.S. Bach Works For Harpsichord

This is by Bach and has its fair share of secondary dominants and secondary leading tones.

2. Track 6 of Trevor Pinnock: Rameau - Les Cyclopes

A very difficult but exquisite piece by Rameau filled with exotic harmonies and ornaments in the French style.



Feel free to ask any questions or request particular topics as our lessons continue! I would appreciate, in addition to homework, just comments on your general opinion of the concepts I am teaching.
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Old Feb 15 2008, 1:02 PM

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I've started work on the long exercise, and am enjoying myself

One question I have is regarding the second example in the secondary dominants file, the second and third beats of the first bar and the first beat of the second, I don't quite understand that... it seems to sound quite crude compared to the rest or the example, and what is the chord Bb D# F# doing there?

As for your examples, they seem to be linking to the player as opposed to the exact work you wanted me to listen to, could you specify which piece of music I should look for in each please?
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Old Feb 15 2008, 4:09 PM

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Here are my first 5 phrases using V of ii, iii, IV, V and vi in C major.

I thought I'd 'hand in' these first, make sure I'm not barking up the wrong tree before ploughing on with the rest of the exercises. The only one I'm not sure about at all is V of iii, I think that one was a bit dodgy

These are surprisingly fun, composing phrases 'to order', makes you think about the melody a bit more, making sure you'll be able to fit the chromatic chord in there.
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Old Feb 16 2008, 12:49 AM

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Quote:
Originally Posted by Mark View Post
One question I have is regarding the second example in the secondary dominants file, the second and third beats of the first bar and the first beat of the second, I don't quite understand that... it seems to sound quite crude compared to the rest or the example, and what is the chord Bb D# F# doing there?
It is very interesting that you don't like the III+6 (the D F# Bb chord)... yes, an augmented chord in first inversion performing the function we normally associate with i64! Let me just say that it is not everyone's cup of tea. It just so happens that my favorite composer used it a lot; I picked up that habit from him. Try to hear it a few more times and see if you can pick up the feel for its sound... it almost belongs in the twentieth century, which makes it even more bizarre in the middle of modal Renaissance music. I will discuss its uses in detail tomorrow, along with examples from the great masters.

As for the V/V chord in minor.... pretty much the truth is that it is really that harsh! Remember, ii* is diminished in minor; to make V/V in minor requires two accidentals, just like V/iii in Major. I will, however, post more examples from various composers. Its sound is instantly recognizable.

So yes, this "crude" sound is something I intentionally produced with these rather unprepared chromatic chords. Try to think of them as just another color, perhaps to bright to use very often, but useful in the right circumstances. Both can be found in Bach, though not too often. While the first example sounded like a chorale harmonization, no composer would have used the second in a chorale. I meant the second as more of a skeleton for faster music.

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Originally Posted by Mark View Post
As for your examples, they seem to be linking to the player as opposed to the exact work you wanted me to listen to, could you specify which piece of music I should look for in each please?
As for these, you can click and scroll down to the track numbers I posted next to the links.

1. Track 13 of Janine Johnson: J.S. Bach Works For Harpsichord

This is by Bach and has its fair share of secondary dominants and secondary leading tones.

2. Track 6 of Trevor Pinnock: Rameau - Les Cyclopes

A very difficult but exquisite piece by Rameau filled with exotic harmonies and ornaments in the French style.
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Old Feb 16 2008, 7:04 AM

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Ah, I obviously didn't notice the track numbers Sorry about that.

Having read your explanation of the second example, I now understand what you were doing, but I'm afraid it still jars my ears slightly, maybe it would sound more acceptable to my ear if there were less metrical accent? it seems that havig it on the first beat of the bar makes it really stick out, which I suppose is a good thing if you're a fan of it's effect. Ah well, maybe I'll start to appreciate it more when we go over that chord in detail and I can hear/see it in some different contexts.

Both pieces you recommended I have listened to several times, and in the case of the Bach one, listening with score in hand and doing a bit of analysis on the form. This is the first of Rameau's music I've actually heard, and I must say I rather enjoyed it, and have been checking out some of the other stuff on that album.

I've been reading over a few of your comments on modal harmony again, and found sheet music of Dowland's Lachrymae, which I have come across before, when looking for more Guitar repertoire, and I have played this before and enjoyed a great deal:

YouTube Video
I think it may be time to dig out the sheet music again and analyse it, as some of the progressions, as you say, don't sound remotely tonal, but are incredibly beautiful
(Original Source)
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Old Feb 16 2008, 10:21 AM

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I'm very glad you enjoyed the Rameau! It is awesome, among the most expressive and difficult music for harpsichord. I very much recommend on that album Track 10, the gavotte and doubles which I think is Rameau's best. Not too chromatic though, but the progression featured in the second half is exactly this backwards circle of fifths I mentioned.

As for Lachrymae.... it may be my favorite piece of music from all times. At around 2:10 of your video, begins a progression whose roots move up by third. A progressive motion rather than regressive: so very non-tonal. So hearing such a novel progression combined with careful imitation makes that passage my favorite in all music .
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Old Feb 16 2008, 3:22 PM

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I'm now digging into a lot more Dowland, finding a few more of his pieces that I've played in the past. 'Frog Galliard' in particular is a great piece, a video, if you're interested:

YouTube Video
I loved this piece when I first played it. Have just tried sight reading it through, but it looks like I'll need a few readings before I'm playing it properly again
(Original Source)


I listened to the Rameau Gavotte and Doubles, and very much enjoyed them, was it the first double that had the progression we're discussing?

You've really rekindled my interest in Baroque and Renaissance music, and for that I thank you, as for one it's made me pick up my guitar for the first time in some time

Would you be able to have a quick look at those first secondary dominant phrases please? I would like to make sure I'm not doing anything wrong before doing the other 8 exercises

Once again, thank you for doing these, I'm learning loads and really enjoying myself
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