Wednesday, June 15, 2005

Analysis I: Menuet by J.S.Bach, No. 15 From Anna Magdelena

I've decided to wait to post my next Miscelaneous Musings about melodic trajectories until tomorrow, mostly because I got distracted with this piece last night, which is a Menuet by J.S. Bach that is No. 15 in the Anna Magdalena Notebook of 1725 (You'll have to do your own search for it as I found no good descriptions to link to. The Urtext is by Henle, but I have the Edition Peters version, which is complete and unabridged, and I like it a lot. I was not able to locate it so it may be out of print since mine is the printing of 1949). I have wanted to make a guitar transcription of this piece for quite a while, and I also wanted to do a detailed contrapuntal and harmonic analysis of it as well, so I decided to kill several birds with one stone last night when I discovered that it would work fabulously well on the guitar in B minor, and I am needing a small piece in that key for my set. Not only that, but it is the single most supreme example of some of the concepts I've been presenting here over the last month in actual musical practice.

The only way to describe this piece when it is considered in the larger context of Bach's corpus of work is to aptly call it strange, weird, or even bizarre. Whenever someone tells me that strict 1:1 ratio counterpoint should be taught as an all consonance environment, or that strict 1:1 counterpoint is just a theoretical exercise that has no application in musical reality, I wave this marvelous little trifle in their faces. On first listen, it is strikingly dissonant and the chromaticism is just plain unnerving, especially when you consider the source and that it is such a tiny little miniature intended as a practice piece. I can't help but think that if a student turned this in as an exercise for a counterpoint course, the instructor would laugh him out of the classroom. There is a picture in my mind of Bach waking up one morning to dash out a few pieces for his bride and geting this mischevious little grin on his face as he noodles this out, giggling as he goes. It's a fantastic conceit of my imagination, of course, but that's the way I envision it. The piece certainly makes me laugh, that's for sure, and knowing that Bach had a robust sense of humor, I'm virtually certain that this "monstrosity" is intended - at least in part - as a joke.

The following conventions are used in the analysis:

The contrapuntal (intervallic) analysis is on the top line.

The home key harmonic analysis is on the second line.

Regions other than the home key are on the third line if present.

The overall regions are indicated at the bottom.

Intervals are notated as P= Perfect, M= Major, m= minor, A= Augmented, and d= diminished.

The harmonies are in bold with the root progressions in between in plain text.

Subsequent inversions of the prevailing harmony are in brackets and in plain text.

The piece starts out very conservatively with an immitative figure at the octave below (If you disregard the opening B in the bass, which I will probably omit when I perform this), and the intimated root motions are simple and conservatively Progressive in nature. Then, into the fourth measure, Bach suddenly has a Tri-Tone as Progressive root motion which is into a "five of five", and it even has the "melodic" progression of a diminished third in the lead! This is quite disconcerting and humorous. I mean "laugh out loud" humorous. It's like the man went instantly insane or into "The Twilight Zone" or something. The effect is to produce the sound of a V(b5)/V, which is just plain goofy in this context.

Then the bass moves down by step to produce the effect of a Vb6/4/2 of V, which just increases the weirdness factor. When the expected V6 appears, does it's leading tone resolve up as expected? Of course not: It progresses down chromatically to become the minor seventh of a V4/2 of iv (Note that this is actually the regular crosswise transformation that you might expect in an all seventh chord diatonic Progressive root motion, but it's not what secondary dominants are expected to do). Then, the root progresses to the fourth degree as expected, but there is another secondary dominant on that degree: It's leading tone progresses down chromatically in sequence to the previous instance, and I'm expecting a little gray creature to say "Take me to your leader!" at any moment now. Note that all the root motions are simple Progressives though? Abnormalcy via normalcy. Very cool. And riotously funny. Bach uses the Tri-Tone as Progressive root motion in the same place in this phrase as well, with an augmented ninth sonority in the lead just for good measure. The two phrases are structurally balanced in a logical way, despite the fact that their overall character is so uncanny. The insult is then repeated, of course.

The second section starts out with a four measure prolongation of a V to i in the subdominant region. One thing to notice here is the minor seventh at the end of the second measure that is leapt into. In a pure and strict 1:1 ratio contrapuntal environment, this would be unacceptable. Period. However, since this is a harmonic contrapuntal environment, subsequent validations of a prevailing harmony allow for this sort of thing, especially on a weak beat, as we have here. After the resolution to the "tonic" on the subdominant degree, the bass moves down to intimate a V4/2 of V in the relative major region, despite the absense of any G-sharp in the phrase (At least that's the way I hear it - comma - man).

This same V to I sequence is then repeated a whole step lower in the relative major region with only a single minor variation: No seventh is lept into and the IV of the prevailing region is implied instead. These are probably the most "normal" phrases in the piece. Good thing too, because Bach is just about to top all the weirdness that has come before with the single most outrageously mad succession of 1:1 counterpoint I have ever heard from a tonal composer. Hold on to your butts.

What can I really say about measures 17 through 22? The intervallic and harmonic analyses tell the tale and sol, le, la, te, ti do and ti, do, re, me, mi, fa and even re, me, mi, fa, fi, sol are not all that unusual for melodic progressions of this era in and of themselves; but all together one after another in an episode of the strictest kind of 1:1 counterpoint written circa 1725?! Note that despite the seeming outlandishness of the progression the root motions are actually quite logical, and measures 17 and 18 are perfectly reflected in measures 21 and 22 as far as the root progression types are concerned. That's what makes this work, and why it's such a brilliant joke: Beneath the apparent lunacy on the surface is a very logical and in many ways quite conservative construction that is well thought out. That Bach ends this phrase with one of the most common i - iv - V - i cliches of his time just puts an excamation point at the end of this "unforgivable" episode of musical jocularity as far as I'm concerned. I absolutely adore this abjectly idiotic little thing (And I mean "abjectly" and "idiotic" in the kindest of all possible ways ;^D).


Blogger Scott Spiegelberg said...

Great post, except your use of bIII and bVI where a simple III and VI suffice. bIII implies a major key, and chromatic mediant relationships. But III is a nice, easy-like-Sunday-morning relative major relationship.

I'm also not sure if the diminished third is so surprising, especially as Bach is expected to tonicize the dominant at some point in any of his binary pieces.

2:00 PM  
Blogger Hucbald said...

It took me a second, but I finaly figured out what you mean. I simply describe the relationship completely, the flat indicating the major III region a minor third above the tonic versus a major third. IOW, I relate everything to a major key as the normative pattern. That has to do with my relating virtually every aspect of music to the overtone series.

Since I have had nothing to do with university theory teaching for almost ten years, my analysis has evolved to serve me and me only, and that's just the way I like to see it.

I may rethink that in light of the indication of chromatic alteration of the natural degree as you mention. Good point. I'll have to give it some thought. Thanks.

9:55 PM  
Blogger Scott Spiegelberg said...

Do you perceive the minor key as a distortion or alteration of the major key? You would certainly be in some good history-of-theory company, such as Rameau and Helmholtz.

10:08 PM  
Blogger Hucbald said...

Hi Scott,

I have heard many theoretical "explanations" for the minor key. The most compelling to me is the different ways that the perfect fifth can be divided. I believe that theory involves the arithmetic versus harmonic division of the perfect fifth to get the major third either on the top or the bottom of the fifth (If memory serves: I may have the terminology a bit wrong). Personally, I adhere to the sine versus cosine versions of the harmonic overtone series as the solution to this issue. In the cosine version of the series, the overtones are theoretically reinterpreted to become "undertones" (Which do not exist in nature, of course). In that scenario, the initial triad encountered is a minor one. This is essentially the same thing as the two ways of dividing the perfect fifth that I mentioned above. If you go to my Links, there is a link to Tonalsoft and also to the Chrysalis Foundation. Both of those sites have detailed pages that describe intonational and intervallic theory. I found the divisions of the fifth postulate at one of those sites.

11:38 AM  
Blogger Scott Spiegelberg said...

Yes, undertones were an attempt by Riemann to explain the generation of minor keys. My question to you is, why does an artificial construction like tonality need to be generated from physical principles? Around the world there are other scale and harmony systems, so there is no need to try to explain some universality, beyond the basic octave equivalence.

Once you have consigned yourself to tonality as a natural occurence, then you have to generate tonality from physical principles. And then you find that minor keys do not generate from the overtone series unless you use non-physical entities such as undertones or co-generating tonics (Rameau).

The problem is that in practice, minor keys are not treated as inferior to major keys by tonal composers, and indeed are not preferenced in perception/cognition studies either.

I've blathered enough in your comments, I clearly need to write a post about this in my own blog.

3:26 PM  
Blogger Hucbald said...

Thanks again for posting Scott,

I think the arithmetic versus geometric or harmonic division of the fifth is the most compelling arguement for the minor modality, but the undertone theory is no less remote logically. In fact, as I stated before, they amount to the same "difference", if you will. In any event, the minor modes seem natural enough, but they are obviously "less perfect" than the major modes are, no matter how you slice the rationalizations. That I prefer writing in the minor is no secret, as the less-than-perfectly stable nature of the minor allows for much more freedom, in a sense. But I always write two versions of everything: Major and minor, so I can borrow elements from each in the final piece, regardless of which mode I end up putting it in.

I guess I should interject that I agree to only two modes, major and minor, and consider Lydian, Phrygian, and related modal elements to be merely extensions of the flavor of these two.

And finally, WHY DIDN'T YOU TELL ME YOU HAD A BLOG?! I'll check it out right now. I'm a firm believer in supporting my fellow musical travelers on this quest that we love.


12:50 AM  

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