Tuesday, August 28, 2007

In defense of harmony

In my last post I promised to defend the chaste honor of harmony, which has Marc Geelhoed intrigued. The dastardly besmircher of harmony is Mathemusicality's James Cook, who criticizes an old analysis I did of Chopin's Op. 28 No. 4. I don't have a problem with the voice-leading analysis James uses to start his post, said voice-leading graphs being very important tools in music analysis. However, James has some very odd ideas about harmony, namely that it doesn't exist. He is attempting to move us back to pre-Rameau (1723) days where chords don't exist, everything is counterpoint alone. I was tempted to address his critique line by line, but I think I would end up repeating myself a lot, so I'm making a larger view.
Update: Spurred on by James, I have made a line-by-line critique here. And welcome to NewMusicBox readers.

Harmony does exist. Chords do exist. There are recognizable qualities of triads, seventh chords and extensions that engender clear tonal functions in any culturally invested listener.* A Major-minor seventh chord is rightly nicknamed the dominant seventh chord because its very sonority creates a sensation of dominant function, creating a desire to resolve to the triad a fifth lower, that mythical tonic chord. Likewise a fully diminished seventh chord will automatically be heard as a leading-tone chord, whether or not the listener is consciously aware of the categorization. If you play this fully diminished seventh chord and walk away, any listeners (including yourself) will sing, hum, play or think a resolution tone a half step higher than one of the notes in the seventh chord (it could be any of the four, if the chord was devoid of any other context). Thus far my examples, gleaned from years of teaching and party tricks, have been solitary chords, lacking any larger context. As soon as two or more chords are played together, they start creating perceptibly stronger harmonic relationships. And if there is a good melody along with it, there is no stopping the tonal functions from being present.

Heinrich Schenker's greatest realization was that the rules of counterpoint – set by 16th century compositional practice – had been altered by the evolution of tonality. Rules of voice leading had to take into account the scale degrees being used, something unheard of in modal counterpoint (except at cadences).

So, this is my first attempt at championing sweet Harmony's cause, undoubtedly hampered by my rusty blogging chops and the Leinenkugel Berry Weiss I just drank. I hope others will take up the cause celebre, or at least say that they believe in chords. I mean, c'mon, they're chords.

*By this I mean a listener who has either grown up in or been educated in Western music culture. These days this covers average people from nearly all industrial nations.


Daniel Wolf said...

Scott --

After reading some of Cook's thread I was struggling to make an argument of the sort, and now you've beaten me to the punch and saved me the work.

I happen to be a fairly weak harmonic composer/listener, but I have encountered too many musicians for whom harmonic thinking is apparently first nature. Some musicians, and some very good ones, do hear and think principly in terms of chord types, harmonic rhythm, etc.. (Recently a visiting friend, who has had a real career as a rock musician, was playing "Litte Red Corvette" for my son, a Corvette fan. At first, I didn't recognize it because the voice leading was off from the original, but for my friend the correct chord sequence was sufficient, regarless of the voice leading, and also gave him a bit more freedom to create varations within his own cover version.) Perhaps there is some physiological basis here, akin (if not rooted in) to the difference between AP and RP listeners.

One more thing: I think Cook seriously understates the degree to which a voice leading theory is a prescriptive aesthetic theory. Without recognizing this, the variety of possible musics generated within the theory is narrowed significantly, restricting innovation and locking the musician into a particular set of values. I'm unconvinced that this is a normative way of doing music.

ComposerBastard said...

Oh God ... here we go again...another wave of argument centered around the delusional promise of the microscopia of western musical materials.

Firstly, I question why this following supposition is moved to a footnote and so lightly stressed since it is clearly where all your other arguments are based?

By this I mean a listener who has either grown up in or been educated in Western music culture. These days this covers average people from nearly all industrial nations.

So, if I may expand on this as a start. The premise here is that culturally, by listening to western music over and over again, we have built in certain cognitive schemas for interpreting that music in new pieces that do come up. Ok, this is fine and in a few seconds I will return to this statement. Where your next argument breaks down for me are in the projected conclusions and examples you give which you conducted in uncontrolled experiments "gleaned from years of teaching and party tricks" which more often than not introduces a personal educational bias by the experimenter into the mix. Lets face a counterargument...you have been trained into thinking this V7 or V-I is true by your formal education and you are looking for it - consciously or uncounsciouly. Is this good double blind science or a good cause-effect argument between culture and listening? Can we trust the scientist here? I might argue that your education is working against you.

Certainly, I don't hear *only* one V7-I movement. I here a lot more progressional movements to many other kinds of sonorities of equal importance to me - most of which don't sound functional to me nor sound as if they are related to 7-35 in any way. In fact I despise V7. I avoid music that has it - cant stand it. Please don't reify me into the utilitarian world of traditional theoretical harmony or I will call the Human Rights Watch.

Ok, so back to your original footnote which is more aligned with cognitive schemas. You say...

And if there is a good melody along with it, there is no stopping the tonal functions from being present.

...or an infinite number of other non tonal or unrelated sonorous real world mashups that could highlight the melos creating new ways of interpretation in totally new schemas just as understandable. In other words, there are infinite number of ways our brains can create templates for understanding music and sound. It just happens that one way has taken precedence historically in western culture by the sheer number of examples.

This to me is more an argument along the lines of natural selection or evolution than it does to anything along the lines of natural formitive musical and physical law. And evolution, if you know anything about it, is more a matter for random number theory and chaos theory than it is for concluding some superiority for a single organic species. Yes western harmony exists, but so do many other harmonic systems that can be invented or found of equal weight. Just because it has survived doenst give it value. It merely survived. Big F deal.

I might argue that tonality is based on the fact that the western major scale is the only set that has an uneven number of intervals in its interval vector, and that the placement between the two minor seconds intervals in the major scale are maximalized in distance. By highlighting the movement of the pc's 5->4 and B->0 you are reinforcing the unique distance in the set and that unique interval count by other pc's. Traditionlly V-I movement reinforces those minor seconds.

Thats one more scientific path of argument than the one you give.

However, as I know more about how the brain actually processes music and sound I realize that none of these arguments or theoretical technocratics- yours or my pc one above as being only two - makes much sense in the larger view of neural anatomy or what a composer can do with it, or how we can listen to traditional music and understand and discuss it. We need a more general psychological nomenclature...

Scott Spiegelberg said...

Daniel, that's a good point about the aesthetic postulates that form the backbone of parsimonious voice leading (which is the new-and-improved version of Westergaardian theory).

ComposerBastard, I make no claims that the concept of harmony is universal, in fact my footnote shows that it is culturally-based. The footnote is not stating a supposition, it is setting the boundaries for my claims. I completely agree with your statement: " by listening to western music over and over again, we have built in certain cognitive schemas for interpreting that music in new pieces that do come up." James Cook is effectively claiming that harmony is not part of Western cognitive schemata, while I disagree.

As for rigorous experimentation, I do not have to make these tests because they have already been done. Look at the studies of Ani Patel, Stefan Koelsch, and Isabelle Peretz, among many others. There have been fMRI studies, ERP studies, eye movement studies among children, and many others that confirm the encoding of harmonic schemata. My justification was meant to be flippant, not scientific accuracy.

There are many progressions from V7. Deceptive resolutions (V7-vi) are called that because they go against the dominant expectation, but they are not radically surprising. Treating a V7 as an enharmonic Ger+6 is also a culturally established and schema-encoded progression, but not at the same cognitive strength as V-I. Your statement, "I hear a lot more progressional movements [...] most of which don't sound functional to me..." is very revealing. It says that you do hear some functional progressions, that there is in fact a difference between tonally functional progressions and other sorts. You weight all these progressions equally within your aesthetics (ignoring the subsequent contradiction), but aesthetics and cognitive expectation are two different things.

I agree completely that Western culture includes more musical systems than just tonality. The expectations engendered within a Stockhausen piece are much different than that of Stravinsky, or Mozart, or Phillip Glass. And I completely support your decision, or that of anyone else, to eschew tonal harmony on aesthetic terms. My defense of "Harmony's honor" was solely intended to argue that tonal harmony does indeed exist, contrary to James Cook's Westergaardian claims.

I like the diatonic set theory argument you bring in, along with the ties to what Butler and Brown called the "Rare Interval" cognitive theory of tonality. But I disagree with the need for a more general psychological nomenclature. If there is one thing that cognitive scientists have going, it is technical jargon. The difficulty arises in matching musicological terms with psychological terms, but those psychological terms do exist.

Thanks for the involved comment!

ComposerBastard said...

ok, don't worry...so this will be my final response since I tend to go crazy with blog polemics.

James Cook is effectively claiming that harmony is not part of Western cognitive schemata, while I disagree.

I'm not sure he is saying that so much as he is saying there is a "better" way of creating a theoretical basis for representing it than roman numerals and figured bass functionality etc.

It says that you do hear some functional progressions, that there is in fact a difference between tonally functional progressions and other sorts.

Only because I have been corrupted by too many harmony classes. I can "imagine" non diatonic functions in sound or other sets. I can equally "unimagine" traditional functionality in the diatonic spectrum.

From a creatitvity standpoint, the choices depends on what I am wishing to do as a composer at the time which may be more related to form and structural needs, or even voice leading or any other infinite attributes other than harmony which is last on the list and can be more easily manipulated to serve. And though I might think those choices are caused by my aethetical view of the works needs, they can be easily unconsciouly chosen due to other personal factors that have nothing to do with music - such as Paris Hilton or George Bush. The mind is a clever beast.

I maintain that the choice of the current figured bass Tonal Harmony and how it is taught is more aligned with natural selection and evolution, in that it s a reflection of historical changes in the environment than aligned with physical or cognitive law. What would music theory have been like if there was no Baroque or should I say protestant movement? We might have had more permutations of species counterpoint in school? - e.g. veritical = protestant and horizontal = catholic?. Or what would happen if the Ottoman empire had won out Europe? Im of course a bit crazy...but the most valuable classes I ever took were in counterpoint and I always felt they were undervalued in the education system base curriculum only because I learned something incredibly practical about harmony in it that wasn't necessarily "functional" as a nexus.

I disagree that cogsci descriptive nomenclature cannot serve us in music. I believe we might "simplify" that nomenclature with our own alias terms or create a subset of those findings that are practical for us to apply.

ok im done...

Scott Spiegelberg said...

CB (if I may), don't apologize for engaging in this great conversation.

I'm not sure he [James Cook] is saying that so much as he is saying there is a "better" way of creating a theoretical basis for representing it than roman numerals and figured bass functionality etc.

He says it in the comments to his post criticizing my Chopin analysis: "What I said was that I don't believe in harmony or chord progressions."

As for the cultural vs. cognition debate, I believe that our perception filters are altered by our culture as much as by evolution. Some schema we are born with, others we learn through engagement with the sights, sounds, smells, tastes, and touches of our surroundings. Your point about the historical basis for our current theoretical models is spot on, but I disagree that harmony is less important than counterpoint overall. I think they are equally important subjects, thus why we include counterpoint in our four semesters of theory and offer additional counterpoint classes when possible.

If we simplify psychological terms for musical usage, we are changing the meanings, thus we might as well stay with our own terms. As I said, there is much effort among theorists and scientists to map the terms from both sides, to the edification of all.

Peter (the other) said...

I have always felt that Susanne Langer's remark about music conveying the morphology of emotion was mostly understandable in terms of harmony. Now, I don't think in classical western cannon, more in western folk. To me the true music of the west was going on being sung by the people while the court and church composers spun out their fripperies for a few centuries. So to me the harmonic change that reflects the change of emotion is about the change from one chord to one other, not whole, complex sequences. Life is experienced from one chord to another. I love to play the game with friends, a grab bag of chords in a hat, pick any two, play one slowly after the other. What does their relationship feel like?

In these simpler, folk models, one finds much more music that is more easily relatable to many more cultures. Some people still argue with Paul Eckman's work of universal facial expression, and I imagine musical universality will be argued long past my caring, but it does seem to me that the deeper one goes, the more universal music is. The cultural differences may be the superficial. Some of Mark Tramo's work I have seen somewhere in the last year pointed towards this. He was measuring the actual signal on the audio nerve coming from the ear drum. I seem to remember that he found that a) a minor chord sets up a small riot on the nerve, thus aligning it with chords we might rightly consider dissonant, and b) that major chords presented a very smooth signal. Right away I imagine a chorus of angry ethnomusos "what about these guys wah!wah!wah! and those guys wah!wah!wah! and the Indonesian major mode funeral music wah!wah!wah!", all of which denies the human capacity, nay genius, for perversion ;-) ! But listen to Ravi Shanker's score for Pather Panchali(1955), and tell me he doesn't use the same harmonic morpholgy as a western composer might, for the same emotional situation. The verticle interrelationships of fundementals and overtones are an important and perhaps inate quality of music.

(please excuse me, that I don't think or write in academese)(I can only plead content over form 8-0)

james cook said...


Okay, now it's my turn to correct a theoretical mischaracterization.

Studies of "parsimonious voice leading" are most certainly not "the new and improved version of Westergaardian theory". Far from it. In fact, given the context in which "parsimonious voice leading" is usually discussed (that is, neo-Riemannian theory and related areas) it would be more accurate to describe it as the latest offshoot of harmonic theory.

There really hasn't ever been, I'm sad to say, a new and improved version of Westergaardian theory (which is about how to understand complex musical surfaces as elaborations of simpler structures, and not merely how to connect pc-sets to each other). This is unfortunate for a number of reasons, one of which is that the book (ITT) isn't perfect. Even Westergaard would do some things differently were he to rewrite the book, according to what he has said.

On another point: CB's paraphrase of my position:

I'm not sure he is saying that so much as he is saying there is a "better" way of creating a theoretical basis for representing it than roman numerals and figured bass functionality etc.

is much more accurate than yours:

James Cook is effectively claiming that harmony is not part of Western cognitive schemata

I make no grandiose claims about the whole of "Western cognitive schemata" (whatever that could possibly mean). Clearly, ideas of "harmony" have been part of some people's "cognitive schemata", otherwise we wouldn't be having this discussion. The issue is whether or not these harmonic schemata are a good way to analyze music. My stance on that question should be very clear at this point.

Scott Spiegelberg said...

James, I admit that I only skimmed ITT back in grad school, so I accept that I'm mistaken in equating it with parsimonious voice leading. If I have time, I'll take a closer look at ITT. As for my paraphrase, I'm only going with what you said, that you don't believe in harmony or chord progressions. But I accept your clarification. If you want to learn more about schema, a good book is Music and Memory, by Bob Snyder.

Hucbald said...

There is nothing cultural or subjective about the naturalness of the V7-I cadence, or any secondary dominant progressing to a target with a root a perfect fifth below. If you believe that there is, you simply have no natural, intuitive musical sensitivity. Sorry.

The reason that it is a fact, and not my opinion, that dominant/tonic and secondary-dominant/target resolutions are natural is because the harmonic overtone series itself makes a dominant seventh sonority. Every sound you hear has a dominant associated with it, and you are conditioned from birth (Or earlier if there is such a thing as genetic memory) to recognize the inherent naturalness of the primordial resolution.

In the overtone chord (Dominant seventh) is a tritone - the only dissonant interval within the harmonic range of the series that does not invert to a melodic interval (The seventh inverts to a second, which is a melodic interval, not a harmonic one).

The two tones in this tritone are active: One has a leading tone desire, and the other has a leaning tone desire. Their context is defined by the passive tones, which are in a perfect fifth relationship with each other in root position. So, each tritone can belong to one of two overtone chords with their roots a tritone apart.

For example, the overtone chord built on the generator G is spelled G, B, D, and F: The active tritone is from B to F, and the passive perfect fifth that defines the B as a leading tone and the F as a leaning tone is from G to D.

That same tritone can belong to a D-flat overtone chord, however, if spelled D-flat, F, A-flat, C-flat. In this instance, the passive perfect fifth from D-flat to A-flat reverses the functions of the active tritone: The F is now the leading tone, and the C-flat (Formerly B-natural) is the leaning tone.

The resolutional desire built into the tritone of the overtone chord (Dominant seventh, per theorist-speak, remember) IS THE VERY BASIS OF MUSICAL MOTION.

The very reason that we have the secondary dominant galaxy of sonorities - secondary dominants, secondary diminished sevenths, secondary dominants with diminished fifths (So-called French chords) and secondary dominants with diminished fifths and minor ninths replacing the root (So-called German chords) is because composers intuited out the naturalness of the dominant resolution and enhanced it by replacing the passive tones with other active tones, THEREBY INCREASING THE NATURAL RESOLUTION EFFECT.

Of COURSE a dominant seventh does not HAVE to resolve to its target: The resolutional desire is just that: a desire, and not a mandate. It is exactly by going with or against the inherent resolutional desire of the overtone chord that harmonic effects are created, and in Blues modality the overtone chord functons as a tonic (In fact, Blues modality is perfectly connected with the implications of the harmonic overtone series, because I, IV and V are ALL overtone chords).

When you hear a progression like V7/iii - iii - V7/ii - ii - V7/I - I it sounds natural and inevitable, BECAUSE IT IS. Harmony is a product of nature, and not artifice.

Men with natural, intuitive musical sensitivity worked this out in Western musical history first because Western art music was the first music in history to be literate: It can be written down for posterity, and so followers can build upon the work of their predecessors.

I've spent over thirty years studying this and working it out: I've read just about everything from the work of Hucbald of Armand, Prosdocimus de Beldemandis, Boethius, Jacobus of Liege, Vicentino, Zarlino, Fux, Rameau, Marpurg, Albrectsberger, Martini, Riemann, Gedalge, Jeppesen, Kennan, Piston, Seigmeister, Schoenberg, Schillinger, and Taneiev. If you haven't studied all of that, do yourself a favor and keep quiet and learn.

Over the years I've heard and answered just about every argument anyway: This is the most common one.

"Twelve tone equal temperament negates the overtone series' implications because the series is not in tune with it." (Or vice versa).

Ironic: The series implies a series of falling perfect fifths from overtone chord to overtone chord. If you go through twelve resolutional cycles, you loop back tho the beginning with one slight problem: twelve 3:2 perfect fifths create the well-known Pythagorean comma comparted to seven 2:1 octaves.

Since the series implies twelve possible overtone chords, and twenty-four possible tonics (Twelve major/twelve minor), in order for them all to sound the same in relation to each other, EQUAL TEMPERAMENT IS THE ONLY SOLUTION. In other words, the overtone series itself, through all that it implies, makes its own inescapable case for twelve tone equal temperament.

But, not only that: For a tuning system to negate the implications of the series, it would have to be so out of tune that the intervals were not recognizable in comparison to those in the series. This is never the case: Regardless of if you use TTET, 5-limit Just, 7-limit Just, or one of the Well Tempered systems, an octave is still an octave, a fifth is still a fifth, a thrid is still a third, and so on; they are perfectly recognizable as series-related intervals, even if they are "out of tune" with it. Just systems, in fact, have intervals that are MUCH more out of tune than anything in TTET, SO THEY ARE NOT WHAT THE SERIES IMPLIES IS CORRECT.

I've written a book on this subject, the first version of which is in the sidebar of my blog (Musical Relativity Theory), for those with an ear to hear and a mind to understand. It's not for lazy shortcut seekers, however. In it, I demonstrate, with musical proofs, how all five elements of pure music - harmony, counterpoint, melody, rhythm, and form - are ALL manifestations of what the harmonic overtone series implies.

ComposerBastard said...

Ok, Scott, we have the formal reply...the floor is yours here.

Scott Spiegelberg said...

Hucbald, first of all, let's not denigrate anyone's musicality. It won't help any discussion.

Second, how do you account for the intonation problem of the seventh in your overtone chord? If you are basing an overtone series on a G fundamental, the F will be 31 cents flat, almost exactly half way between F and E. Brass players know this problem with the 7th partial intimately, and avoid it like the plague. Thus your Fa that is crucial for the tritone is really flat.

Third, what about minor keys? There is no way to generate the minor tonic from an overtone series, whether you use the fundamental as dominant Sol or as tonic Do. Helmholtz wrestled with this and concluded that minor keys were deviations of major. Riemann invented "undertones" and Rameau tried co-generation (essentially two overtone series for one tonality). All of these have extremely problematic aesthetic or physical issues.

Fourth, let's assume every sounded pitch has a dominant seventh sonority associated with it, ignoring any issues of intonation or variability of partial amplitude by timbre. Now let's picture playing a simple C-E-G triad. By your reckoning, there are three dominant seventh chords activated: G-B-D-F, B-D#-F#-A, and D-F#-A-C. After all each of the three pitches generates partials of its own overtone series. What prioritizes the G-B-D-F sonority as wanting to resolve to C-E-G?

Fifth, I don't understand how your argument about the overtone series makes the "inescapable case for twelve tone equal temperament." You make many assumptions within this argument: that we want all chords to sound the same in relation to each other, that the twelfth P5 finishes the series because it is close enough to an octave, and that all intervals are recognizable as "series-related" even when out of tune. How do you justify these assumptions? There are many aesthetic stances that prefer the different tonic sonorities of well-tempered systems. Why are they incorrect? How far can you distort an interval before it is no longer recognizable? etc, etc.

Fifth, you might consider not SHOUTING when making your arguments. That tends to make people stop listening.

ComposerBastard said...

thank you for your very well directed reply scott. I was going to mentioned a lot of this equal temperment stuff, but was waiting for a more eloquent and structured retort...

ThumMeister said...

Much of this debate assumes that the harmonic series is the source of all musical structure and form.

Yet other cultures, which use other tunings, tend to use instruments which produce spectra which produce dissonance minima at the same points at which their tunings have steps, as is the case with Just Intonation and the Harmonic Series. This suggests that there' a more general rule here - something having to do with sound spectra and tunings.

Interestingly, all of the tunings used by the West, and many used by non-Western cultures, fall along the tuning continuum of the syntonic temperament, which includes 12-et, the meantones, Pythagorean tunings, and some interesting non-Western tunings.

Even more interestingly, there exist two-dimensional note-layouts that are "tuning invariant" (see Computer Music Journal, Winter 2007). On a tuning invariant note-layout, a given sequence or combination of notes has the same geometric pattern in any tuning of a given temperament (defined by a comma sequence).

If the human brain contained a hard-wired tuning invariant note-layout, culture-dependent musical schema could be inculcated in individuals atop such a hard-wired infrastructure without loss of generality.

That would be an interesting generalization, would it not?