Piano World Home Page Forums Our Most Popular Forums Composer's Lounge Walter Piston- Harmony: What the heck has happened???

- that two parts can only move in relation to each other in the following ways:

1) in unison
2) in contrary motion
3) in parallel motion
4) in oblique motion (one rises a step, the other by more than one step, and/or vice versa

These were the first rules of voice leading, and they were referred to as voice leading precisely because only the vox humanis (human voice) was allowed in church.

These four rules are rules that may as well be written in stone simply because they are what they are. They were not invented by anyone. They were a simple recognition of the four ways one voice can move in relation to another.

From there, from two-part polyphony, a third voice was added, creating punctum contra punctum, which eventually was shortened to its modern form counterpoint.

The rules prior to three-part compositions first involved the manner in which two voices could move against each other. When a third part was introduced, things suddenly got a lot more complicated.

In order to hear all the three parts clearly, new rules were hit upon through endless trial and error, based, not upon any type of convention, as no convention yet existed, but instead was based upon what works and what does not work.

For example, in order to hear all three parts clearly, it soon became apparent that this was best fascilitated by having the parts move at different note divisions from one another- hence the rule in counterpoint that one part moves, the other doesn't.

Anyway, I could go on for pages and pages here. But the point is, there's far more at work here than mere convention.

Sorry- I said something misleading there- punctum contra punctum or point counter point (later became counterpoint) began with two-part writing, not three.

There were conventions that have their origins in the crackpot religious thinking of the day. The tritone was said to be "the devil's interval", so-called "perfect" intervals were a result of Just Intonation, so at the time there were perfect 3rds and 6ths (which were done in by Equal Temperament). Octaves, 3rds and 6ths were given preference as they were considered more "sonorous" than 4ths and 5ths, "dissonant" intervals such as 2nds and 7ths were avoided altogether (at first), and so on.

However, these conventions were really based upon everyday perception, which at the time was attributed to ideas based upon religious anthropomorphism. This does not mean that those perceptions were false or incorrect: it means that, at the time, everything was deemed to have a religious connotation. Whatever name you give a perception, the perception itself remains, even if and when ideas about that percption change. In other words, dragonflies are just dragonflies, for example. Humans in the Middle Ages had all sorts of silly ideas about them, calling them "the Devil's darning needles" and so on, but the insect itself is the same as it ever was.

gsmonks:

Just butting here to say that I love reading your posts. They are so interesting to read and chocked full of good information.

If you ever write a book I want a copy.

I want to go back to this:


I don't want to put either ahead of either. There are compositions by Bach that that are little more than broken chords (typical in some preludes), and those might be analyzed effectively as "harmony". On the other hand, approaching a fugue with this thinking would be insane.

The overall principle for me is that ALL analysis is about using "tools" to get something accomplished, and the number one mistake is using the wrong tool for the wrong job.

In other words, using chord symbols (letters or Roman Numerals) to analyze a Bach fugue is about like trying to use a hammer to put in screws.

The thing is, Gary, that Bach himself conceived fugue both linearly and vertically. Bach was a master of both fugue and harmony, the latter of which is best illustrated in the form of his chorals, which for students of harmony and music history can be obtained in a single edition for the purpose of study.

While it is true that Bach (and other composers of his day who wrote fugue) conceived Inventions improvisatorily, during the process of notation the finished work was tweaked for harmonic structural integrity, much the way a structural engineer goes over the blueprints of a bridge in order to suss out flaws which may lead to the collapse of the finished product. The tools of harmonic analysis are of course the very symbols you've mentioned, and without them no harmonic analysis would be possible, ergo the vertical structure of the music, without it, would be utter chaos, and anything but pleasing to the ear.

I am considering writing an annotated book of harmony and its history, Studio Joe, which would necessarily include counterpoint, so that it would be a harmony/counterpoint hybrid of sorts, and would probably include composition techniques. But I don't know that there would be any demand for it as the information already exists out there, albeit in dribs and drabs throughout any number of texts.

I have never written a fugue, so I am limited to admiring the magic. However, I have recently spent countless hours examining four part writing and put myself through the challenge of starting with a few interesting chorale melodies, exactly what Bach used, and making a go at finishing them before looking at what Bach did.

My own experience was somewhat schizoid, though I think in a very positive way. I felt myself flipping back and forth from vertical to horizontal. In some cases I knew exactly where I wanted a cadence, which gave me the bassline automatically, then sort of fooled around with the inner voices until I succesfully avoided parallels. From this I began to see why parallels occur and started to sense horizontal patterns that avoid them.

In other places I heard bass and soprano, as a skeleton, and the inner voices more or less took care of themselves. However, there were other places in which I had in mind interesting movement in individual voices, and the others would shift or morph in a very intuitive manner. My feeling of some kind of harmony was always there, but it would sometimes dominate, sometimes fall into second place.

Most interesting was that at times opening up range between voices (such as tenor and alto) to a distance almost condemned by books gave me the most freedom for adding more ornate lines, mainly climbing or falling in interesting parallel or contrary motion. And Bach did that a lot.

Finally, there are times when "no-no" parallels or things like augmented 2nds can be defty avoided by allowing the tenor to ascend above the alto, and the individual lines may take on special interest that way. Again, Bach did that a lot.

I think what is most important is to keep in mind "general, practical rules" BUT, at the same time, pay careful attention to how fine composers "thumb their noses" at them, either deliberately, or because they developed such a fine instinct that their ears always guided them to the best solutions.

One final thought: we are always in danger of assuming that when two people do something that is equally effective and very similar in results, their ways of getting there were the same or similar. Ultimately the creative process remains a mystery.

That makes perfect sense. I hesitate to say this, since where I am in all this is rather elementary compared to where you no doubt are, but my personal experience seems to be in line with what you just said. While exploring SATB writing, falling back on certain rules helped me find parallels that my ear was missing. I found I had to check the four voices against each other, and I assume that over time Bach developed such an instinct about this that he simply did not have to do that. Regardless, each time I discovered weaknesses that could be identified by "checking for structural integrity", the solutions to eliminating weaknesses also lead me to more interesting and more musical ideas. It was not just a matter of avoiding "no-nos". It was the additional creative ideas that occurred to me through the process of checking.

An important thing you should know, Gary, when it comes to "breaking the rules", is that all composers are both experimenters and autodidacts (self-teachers), the former because you test ideas on your own sense of hearing, the latter because intuitively going beyond the "rules" means teaching yourself to alter your own view of the underlying mechanics of music.

Your mention of playing with voicing is a perfect example of this, because you've reached the point where you're beginning to realise the part that acoustics plays in the perception of Harmony.

Let me give you some examples:

Composers like Bartok, Rachmaninoff and Ravel (listen for the piccolo doubling in Bolero, for instance) sometimes employed the use of organ stop technique to the voicings of their orchestrations. In case you've never had the opportunity to fool around with a big pipe organ, many of the stops produce false harmonics at intervals such as P5th's and Major 7ths. By "false harmonics" I mean that pulling a stop brings extra pipes on line in order to augment the sound. You can only hear these intervals by playing a single note and really listening for them, but the manner in which they enrich the sound is amazing.

Now, remember that Bach was a well-known organist in his day. He was well-aware of the role played by both harmonics and false harmonics. Did this influence his voicings and the way he "broke the rules"? You bet it did! And hundreds of years later, composers like Rachmaninoff were still following this precedent. The opening of his Prelude in C# minor employs the use of parallel harmonies, not after the fashion of organs and false harmonics this time, but after the fashion of church bells, which strongly produce harmonics of a similar nature. Give a big church bell (of high quality- not some cast-iron dog) a good whack, and you'll hear all kinds of odd harmonics, in some cases which almost overpower the standing tone.

Complete agreement there...

I'm sure that's true. Of primary importance to me is that what I have learned in the last year reaches out in strange ways and gives me a different view of music that I felt I completely understood.

No, my opportunities for playing a fine organ were very close to zero. However, I have heard these harmonics in performances, and they can be heard even on recordings. I have not noticed major 7ths. Because of my background in brass, I am familiar with the harmonic series as we use it on such instruments, since we actually PLAY the harmonics, and which harmonics we choose has an incredibly strong effect on tone color. For instance, in one of Vaughan Williams symphonies a solo trumpet plays a bugle-call, and one of the notes is very "out of tune". In fact, it is perfectly IN tune, but to the natural harmonic series, since the "sour" note is somewhere around 30 cents flat to the tempered scale. The effect is eerie, very effective. In order to get to the major 7th on brass, you would have to play in the third octave and play a normally never used harmonic. It might be useable on a valveless French horn with the use of the hand.

I'm quite familiar with what you are talking about re large bells. In regards to "breaking rules", I only know that I can't think of anything Bach wrote that sounds in any way "wrong" to me, and to the extent I am able to analyze what he wrote, it always seems 100% logical. There is a lot I do not know (actually I only know a little), but I do know that he seemed to be very careful, for instance, in avoiding augmented 2nds in voices, chorale writing, but thought nothing of including one in a theme for something fugue-like.

It sounds to me like you have the potential to become a good arranger, if not a composer. Having your ear deep in the sound is just as important as having it in the mechanics of harmony and counterpoint. More so, in my opinion.

You have a background in brass? We have that in common. Lots of more modern composers use the brasses and winds to "colour" their arrangements. This is due in part to the nature of orchestration/arranging. Lots of doubling at the unison with only a hint needed from other instruments to colour the sound. The ratios are often mind-boggling. The sound-source from a piccolo or trumpet is an area from 12.00 mm to 18.30 mm (1.2 to 1.83 cm) across, yet it can dominate an entire concert hall.

Speaking of how easily a single trumpet is heard, one of the most interesting experiences I had was the first time I heard the Beethoven symphonies played on "period instruments". I know there is a huge debate about how "authentic" the instruments, tuning and interpretations are, but I remember being struck by how "untamed" the percussion is in the 6th Symphony, and when the horns have to be stopped with the hand in order to play certain notes, it is just a different world. In the recordings I heard, everything sounded more rugged. Less smooth but more character.

In contrast, the instrument I played, euphonium, does not project well at all, and of all the brass instruments I believe it is the most difficult to play quietly.

And with that I probably ended this discussion, since I am WAY off topic.

Not at all. I know exactly what you're talking about in terms of sound. It's raw, like a wooden chair made using a mallet and wood-carving set, with sweat and wood-shavings and chips flying, the smell of clean wood in the air, like a lumberyard.

You can certainly hear it in the percussion. Timpani were made of wood, with calf-skin heads, and when hit produced a robust, earthy, satisfying sound that is entirely absent in the modern version.

The old bassoons, like those you hear as an entire section in Berlioz' Symphonie Fantastique- such a big, robust, woody type of sound, full of character and drama.

The composers of that music were exploring a new-found freedom, largely because of the emergence of fully chromatic brass which, unlike trombones, could play with great speed in all registers. Walter Piston's later editions of Harmony are anathema to the freedom experienced in those days, simply because things were changing far faster than anyone could codify them. The same thing would happen again with a vengeance in the late 19th century, and the process would continue in fits and starts until between 1963 to 1965, when the wheels fell off the proverbial pony-cart.

I don't know much about Piston, in fact I don't know much about music theory other than the few years as a teenager when I was forced to learn it for those ABRSM exams.

I don't want to talk about how harmony is taught in a completely wrong way to younger students, but as a kid I didn't understand why on earth the progression I6/4-V-I is actually called that, or in easier piano pieces when the bass line goes DO-SO-DO-SO it's called I-I6/4-I-I6/4 (when it's not I-V-I-V of coruse). Because, I was taught that the I chord is supposed to end cadences and what nots.

These days, I look at it and I think this kind of nomenclature is utterly misleading. When it's I6/4-V I think it's exactly a double appogiatura. It's what you hear, it's what you expect, what else can one classify it?

Obviously I6/4 is used in many more ways than just I6/4-V. But it's pretty simple, really--notes and chords have different functions in different contexts, just like individual words have different meanings in different sentences. Moreover, music, just like language, evolved over time, and what's expected in one composer's time is not necessarily expected in another composer's time. Maybe it's just better nomenclature that's needed, or else make sure one does not lose track of the fact that music theory is supposed to only assist in the making of music, not making music itself.

Am I on track or am I completely off base here?

No, you're exactly right. The job of theory is mainly to give students of music something to "hang their hat on", something which provides a semblance of structure, that semblance of structure entailing a common language so that we can all do what we're doing right now- talking about music and having a common language which allows us to do that.

The reason I say semblance of structure is that there are endless possibilities when it comes to analysing music. Walter Piston developed his Theory of Secondary Dominants as a teaching tool in the beginning, and what we're talking about here is that he went too far, intending what began as a teaching tool to become an all-encompassing, codified, written-in-stone understanding of Western Music based solely upon one person's (his) methods.

The problem here is that Walter Piston, as a composer, was doubly off-base, not only because Harmony and our view of it changes over time, but because, as every composer knows, the advanced student of music eventually synthesises an internal understanding of Western Music, which in turn finds expression, through composers, in the form of entirely new interperetations of what Western Music is, what it's inherent possibilities are, the manner in which its underlying mechanics can be manipulated and developed, and the manner in which the relationship between Harmony and acoustics can be altered in order to produce an entirely new palate of colour.

Further, Harmony belongs to composers and potential composers, not analysts, and in the world of composition, less is more. Using terms like "double appoggiatura" is to clutter the tools of composition. For the composer, there is no "double appoggiatura". There is only a box of notes which may be assembled any old which-way to the composer's content. The composer may use a whole bunch of those notes to build chords, and then assemble those chords into a piece of music, the way one fits together a jigsaw puzzle, but although the composer (or anyone else who puts together a jigsaw puzzle) notices recurring patterns in the pieces, the composer knows that giving those patterns names is a fool's errand, because they're a secondary matter which is not directly related to the making of music.

I began music theory with a background. That background is that for a lifetime I did not as much as know the names of notes, but did have solfege from a primary grade - the little singing exercises that give a first feel of diatonic structure. As a child I had a piano, some inherited books of sonatines, and using my ear with that solfege sense deciphered the first notes. The patterns in that genre of music are readily absorbed: not only Alberti bass, ABA, modulations, but also how themes were developed and reiterated with variation. Some of this learning is frozen in time, because music that I invented then and kept in memory contains those same patterns. I had no instrument for several decades afterward so it's like a time capsule.

I got lessons in an instrument a few years ago, and it turned out that I was anticipating the music as much as reading it because I sensed where it would go. When I finally started theory, that theory meshed with what I had already internalized (the fact that lesson pieces are often Common Practice) helps. That meant that this artificiality of theory was not first for me - the realness that I had used for decades was first, and theory helped explain it and give it a better shape. You have the idea that there is more to it, and this gives the outlines.

In both lesson pieces to play, and music theory, I have personally encountered a curious phenomenon. Sometimes the music is dummied down for the student (or the theory contains only some components). It no longer meshes with what is sensed, and in me it creates a feeling of distress or confusion. The first time it happened I didn't know what was going on. It has to do with reaching toward the invisible structures that ought to be there ... but aren't because of the dummying down ... and then having to work blindly. It's a conflict between where you sense it should go, and what has been done to it. The dummied down version is no longer whole. I have had that feeling a couple of times with harmony theory, and if I chase it down, often there is something else which was left out "in order to not confuse". OR there is a feeling that the music explanation was made to fit with the theory. Which is what you are saying.

I'm glad you brought this up because it is a perfect parallel example of what has become broken in Harmony. Solfege teaches students to be sensitive to music in real time, something that disciplines like Harmony have always lacked. Solfege is therefore excellent when it comes to sussing out musical inaccuracies and fallacies.

The "dumbing down" you're referring to has become a glaring problem in the way our young people are educated, and concerns far more than just music. You also find it in the sciences, in mathematics, in what passes for "grammar" these days, to put a name to just a few disciplines.

There didn't used to be this "pass the explanation off till later" disease that has infected modern schooling. Once it had crept in, this mental laziness became worse, to the point that often the explanation simply was never forthcoming, that the "passing off" ended up being done past the point of graduation.

Parents in my childhood used to read their children Shakespeare, and would stop to explain the difficult passages and answer questions, for example. As a result, as a young adult I found Sesame Street insulting and appalling. And that was four decades ago!

I could write a book about education, but will desist.

I downloaded the book by Goetschius on musical form. A couple of things struck me:
- He starts with a general idea of form being a mix of predictability and variety, and consisting of the elements of rhythm (time), vertical (harmonic) and horizontal (melodic). This kind of broad picture is missing from all my modern books. Up to where I am so far, he always keeps this in the background.
- He stays with all three elements: vertical, horizontal, time.
- Students are asked to explore a multitude of excerpts for whatever concept he has introduced. However, he says that we will not be able to find everything because our ears are still developing, and to not sweat it - hear what you can hear, and don't worry about what you cannot yet hear.
- There is a sense that music is subtle, composers work in a subtle manner, and not everything can be defined or should be defined.

All of this seems in contrast to other more modern books. How does Goetschius fit with Piston time-wise or otherwise?

I have to comment.

I totally agree. I would say that all analysis is an ATTEMPT to explain why things work (or are effective) that already work perfectly. Furthermore, the problem is that analysis always plays "catch-up". Whatever it is that we call "harmony" already exists before people begin to attempt to describe what it is, or existed before people tried to explain it in the first place.


It is interesting that you used the term "jigsaw puzzle". I frequently make the point that when 100 people assemble the same complicated puzzle, we only know that the result is the same. From the result we have absolutely no idea of the individual strategies that people use to put that puzzle together.

There are relatively rare instances in which I would see the "double-appoggiatura" idea as valid, although I would still not use the term myself. However, the I64 chord would have to move VERY quickly to the V(7) chord so that the voices move in the rhythm we would expect with an appoggiatura. Even then I feel uncomfortable. In Mozart's sonatas there are numerous instances in which the appoggiatura notation is used to both show appoggiatura-like melodic movement AND to discourage players of the time from further embellishing his melodies with extra ornamental notes.

I still think that the whole issue of anlaysis comes down to descriptivism vs. prescriptivism. Prescriptivists attempt to make rules, laws, and formulas that attempt to prescribe what is right and wrong, hence the name. One of the most famous examples of a fine composer butting heads with such people is Debussy. Such hard-headed, limited thinking is certainly not limited to harmonic analysis (or theory in general). We all know that Chopin's way of teaching technique was all but damned by most teachers, who basically told their students: "Don't study with that young Polish guy. His technical ideas will ruin you."

Descriptivists, on the other hand, are only interested in what was done, what is being done now, and where all of this might lead to. They basically say, here is the music, here is what composers A through Z from different time periods *did* or *do*, now you form your own conclusions.