Yes, exactly!

Two blog posts — one recent, the other less so — that have me jumping up and down in excited agreement:

  • You’re Calling *Who* a Cult Leader? — in which Eliezer Yudkowsky (one of my favorite bloggers) points out that that it’s okay to be really enthusiastic about something:

    Behold the following, which is my true opinion:

    “Gödel, Escher, Bach” by Douglas R. Hofstadter is the most awesome book that I have ever read. If there is one book that emphasizes the tragedy of Death, it is this book, because it’s terrible that so many people have died without reading it.

    I know people who would never say anything like that, or even think it: admiring anything that much would mean they’d joined a cult (note: Hofstadter does not have a cult)[…]

    But I’m having trouble understanding this phenomenon, because I myself feel no barrier against admiring Gödel, Escher, Bach that highly.

    He continues:

    You know, there might be some other things that I admire highly besides Gödel, Escher, Bach, and I might or might not disagree with some things Douglas Hofstadter once said, but I’m not even going to list them, because GEB doesn’t need that kind of moderation. It is okay for GEB to be awesome. In this world there are people who have created awesome things and it is okay to admire them highly! Let this Earth have at least a little of its pride!

    Yes! As I have noted before, there is an inhibition in our culture against expressing strong feelings. Away with this!

    I’m embarrassed to admit that I still haven’t read GEB, even though everybody raves about it and it’s got both a mathematician and a composer in the title. Well, it’s now (higher) on my to-do list. But anyone who has ever visited this blog will know that I harbor a similar level of enthusiasm for Westergaard’s ITT. And that does not make me some kind of crazed fanatic.

  • What’s in a number? — in which a member of the Texas Tech music theory faculty correctly explains the meaning of figured-bass symbols (link added by me):

    I often tell my students that figured bass evolved as a shorthand notation for species counterpoint.That is, figured bass actually suggests lines, not chords. Consider the example below:


    If you look at those examples without worrying about vertical sonorities, the figured bass makes quite a lot of sense. Once you begin trying to assign Roman numerals, the task becomes a bit muddier. In the first example, we can easily understand the E-F motion in the soprano as some kind of neighbor motion or perhaps as the beginning of a passing motion. I prefer that interpretation to one which says the first chord is a root-position tonic and the second chord is a first-inversion submediant.

    And rightfully so. In fact even to speak of this measure as being composed of two “chords” is a misleading distortion. If there are two entities into which this measure is divisible, they are a second-species line on the one hand, and a complex of three first-species lines on the other. (As a minor quibble, I will point out that “worrying about vertical sonorities”, which species counterpoint does just fine, is not to be confused with “assigning Roman numerals”, the discredited province of harmonic theory.)

    In short: figured bass tells us diatonic intervals above the bass and nothing else. If notes are to be altered, the accidentals will appear in the figured bass. Figured bass is simply a shorthand for linear motion.

    So true! Whether or not it is technically accurate that figured bass evolved in connection with species counterpoint per se, this is much closer to the truth than to suppose, as many still do, that it indicates some sort of preexisting awareness of Rameauvian “harmonic” concepts on the part of Baroque-era musicians. (Of course anyone who thinks that hasn’t read Schenker, but that’s for another time…)

(Not too long ago it finally occurred to me why this confusion exists. The reason for it is that people mistake figured basses, which are a form of musical notation, for some sort of analysis of the music. When you look in a treatise and see a figured bass at the top of a page, say, followed by a realization below, perhaps it’s natural to suppose that the figured bass on top is in some sense a “more primitive” structure, from which the realization is derived. But this is a misunderstanding. Figured bass was a performance practice; it was not the purposes of such treatises to engage in music theory as we know it, of the sort practiced by Westergaard — the subject had not yet come into existence as an explicit discipline. So one is by no means obliged to think of a passage in terms of some underlying figured bass. Quite the contrary, in fact: the figured bass is but a shorthand for the realization, and thus if anything the latter “explains” the former, rather than the other way around.)

11 Responses to Yes, exactly!

  1. Brian says:

    You are certainly right that figured bass indicates voice leading. I don’t that many music theorists think otherwise. It also indicates what the chord is; that’s why Schenker liked thoroughbass theorists like C.P.E. Bach so much.

    Incidentally,your comments in this post and in others seem to indicate that Rameau was thinking only about harmony. That is simply false.

    Rameau did recognize that inverted chords are essentially equivalent to those in root position. But, he was very concerned with voice leading. That’s why he he analyzes all non-tonic chords as sevenths. For him, the seventh (and the leading tone) are dissonances that propel music forward, and he is very concerned with resolving these dissonances correctly.

    His theories were misrepresented by those that translated his work in the latter part of the century, D’Alembert and especially Marpurg were the chief offenders. Marpurg, for one, was a very vertically-oriented thinker. Unfortunately, misunderstandings that were perpetuated by Marpurg still persist among a small minority today.

    Thomas Christensen has written a great deal about Rameau and he shows, quite convincingly, that many of Rameau’s theories were anticipated in early thoroughbass treatises. Joel Lester takes a similar stance. And, I’m pretty they have both read Schenker.

  2. James Cook says:

    I have edited the post to avoid the historical questions about Rameau’s own ideas. I’m willing to accept what you say about Marpburg being a bigger culprit; and certainly I’m aware there is a lot more in Rameau besides the fundamental bass. But unless I’m mistaken, the latter remains his chief contribution; and, nationalist slurs and possible historical errors aside, I think Schenker’s music-theoretical critique of the approach to music theory that is Rameau’s legacy is basically right on target.

    Christensen and Lester are more sophisticated than most of the people I find myself arguing against in this context, and I don’t want to be seen as disputing the results of their historical scholarship. The main point I want to make is that the figured-bass tradition, especially as exemplified in C.P.E. Bach’s Essay (hence the reference to Schenker), does not militate against the approach to tonal theory that I take — even on historical grounds.

    • Mini says:

      James… please read ‘Compositional Theory in the Eighteenth Century’ by Joel Lester. The author insists that Beethoven’s studies clearly show he followed fundamental bass principles, as did Mozart (to a significant extent) mainly through Kirnberger’s writings (as evident in Mozart’s lessons for his pupils).

      He also claims that Albrechsberger’s writings are unlikely to be all ‘by him’ at all, and that the whole Rameau vs Bach is largely based on an oversimplified revision of history.

      I don’t know if Lester was bias towards harmony, or if it’s a genuinely unbiased survey and conclusion. Up to now it seems quite an easy read, so I’d love to hear your thoughts.


  3. miquel says:

    do you know the website ?
    It has a very interesting chapter about harmony. Its main thesis: tonal tertian chords are always tetrads (sevenths or sixths). Triads are just fragments of tetrads. An innovatove view over harmony (reductive als ever, sorry James).
    Please give me your opinion about musicnovatory.


  4. James Cook says:

    Please give me your opinion about musicnovatory.

    Looks like crackpottery to me.

  5. Mishka says:

    “You are certainly right that figured bass indicates voice leading. I don’t that many music theorists think otherwise. It also indicates what the chord is; that’s why Schenker liked thoroughbass theorists like C.P.E. Bach so much.”

    Schenker from what I have read positively loathes Rameau who “turned away from the very essence of music itself” (masterworks in music.)

    It’s pretty clear what Rameau is on about, it’s not an argument about definition.
    Every figured bass teachers I have ever had have taught it from within the functional harmonic model. I am really struggling to liberate myself from this particular teaching mantra drummed into me from the age of 6 which I now know is just a theory derived from the idea that “Rameau did recognize that inverted chords are essentially equivalent to those in root position.” Many of our erroneous conceptions about figured bass seem to come from F.T Arnold. I agree with Buelow when he states in his book on figured bass master Heinichen ” Arnold applies terminology… which is actually anti Baroque in conception..centering around the concept of chord inversion championed by Rameau,….composers organised chords on the actual bass, not a basse fondamental.”

    There is a similar approach in Partimenti, this is a great resource, generally not a V I in sight.

    Robert Gjerdigens superbly excellent book “music in the gallant style” is one of the best books on improvisation I have ever read and has helped solve the dilemma, how do you teach theory correctly? I now teach harmony in two ways, the conventional, and the other practically and aurally, memory taking that place of paper, using a still germinal modern-day updated version of thoroughbass inspired practice in a group setting. I can use any music as examples, from Messiaen to Charlie Parker to Monteverdi without the theory falling apart, as the basis is melody, I don’t have to rig the argument with carefully chosen examples anymore. The practical results as demonstrated by students extemporisation composition and aural perception are actually startling. The other novel aspect of this approach is that harmony can finally be taught from a non keyboard perspective. The bad influence functionalism has had on piano writing is another matter, many piano masters including Glenn Gould and Godowsky Art Tatum saw the piano as intrinsically linear.

    Sloppy Functional Harmonic thinking has particularly run amok in much modern Jazz theory, where it has been taken to it’s logical extreme and everything is usually considered a transposition of a mode. There are interestingly a small minority fighting the linear contrapuntal corner, a camp that thankfully is gaining ground and more advocates.
    (Goal note method, Berg, and Hal Galper’s forward motion.)

    some Issues yet to be resolved…..

    Schachter/Salzer, in Counterpoint and composition stated a chord progression can be expressed harmonically (bass leaps) or contrapuntally, (bass moves by step) I am interested in this as it has a hollow ring to it.

    One other problem I find with a lot of the linear theory proponents is Fux. C.P E who is often quoted as critic of Rameau also wrote JS “omitted all the dry species given in Fux and others” and taught harmony not as theory but as “practice” working physically on a keyboard. I’m with C P E here but no longer see the keyboard as primary. In my opinion a fluent knowledge of species counterpoint unnecessary for understanding harmony or counterpoint (for want of better words), and is another example of victorian baggage that can safely be let go. Principles of course can be extrapolated, dissonant leaps and rules of motion etc, but the whole 5 step model has become a pointless dogma. Like Functionalism.

    It is interesting how composers like Schoenberg and Reger can step out the box yet write conventional theory texts. Regers book on modulation has the most ludicrously elaborate descriptions of chords, yet the solutions are essentially contrapuntal. You get far better results teaching modulation through two part melody rather than with ‘harmony’ or ‘pivot’ chords. It’s obvious that humans are naturally monodic creatures, so logically any theory of human music should start with monody.

    I admire the principle of the Texas music blog, but teaching Bach Choral harmonisation like that shows the result of living in a music college for too long. Do any teachers ever stop to ask themselves, how did Bach teach Bach choral harmonisation? Why then do we teach it differently? And just why are we using them as models? In fact, just what is the theory we are teaching actually about? And what’s it for? And don’t get me started on functionalism in ear training……


  6. Mishka says:

    Rameau did recognize that inverted chords are essentially equivalent to those in root position.

    Essentially? Just want to add this this idea must be the biggest incorrect tenets of functional harmony. If it were true were a cadential six four would not “work”. A second inversion is a completely different sonic entity than a root position triad.

    Escaping this particular ‘equivalence’ dogma is one of the most liberating yet difficult things I have ever attempted in trying to understand music.

  7. Brian says:

    Mishka, I’m not entirely sure what your getting at. I’ll mention just two things in relation to your comments.

    (1) Schenker certainly did not subscribe to Rameau’s principles. The point I was trying to make is that Rameau’s thoughts are driven by voice leading more than history has acknowledged. We can make some indirect connections between the two, however. Simon Sechter was a prominent music theorist and teacher in the middle of the 19th century. He taught Schubert and Bruckner, and Bruckner was Schenker’s teacher. Of all his predecessors, Schenker’s theory is most like Secther, who had a Stufentheorie that clearly predates Schenker’s. Furthermore, Sechter was a very conservative thinker who still thought of music in terms of the Rameau’s fundamental bass.

    (2) Reameau analyzes “cadential 6/4 chords” as suspensions or as chords of supposition. His analysis depends on the preceding chord. When the tones of the 6/4 are prepared—when they follow a tonic chord for instance—Rameau analyzes the chord as a suspension. Otherwise, he thinks of the chords as having a supposed bass. Again, voice leading is very important. So, at least in relation to the 6/4 chord, Rameau does not seem to be propagating an “‘equivalence’ dogma” as you suggest.

    I don’t mean to be a Rameau apologist and actually feel sort of strange in the role, but I think it is important get the facts straight before criticizing anyone.

  8. Mishka says:

    I don’t mean to be a Rameau apologist and actually feel sort of strange in the role, but I think it is important get the facts straight before criticizing anyone.

    Agreed, and thanks for your reply. I suppose I was reacting (or over reacting!) to your statement

    “Rameau did recognize that inverted chords are essentially equivalent to those in root position.” I do not find this to be the case, the inner tension of a 6/4 chord is completely different from root position triad.

    I will admit to finding Rameau’s works quite hard going, often a real maze, so it is likely I am getting some of it wrong. I have ordered the Thomas Christensen book and will see if it makes things more clear. I do feel I understand the principles of functional harmony and I also understand how it can be re-considered from a more linear perspective. It is obvious that voice leading is part of Rameau’s ideas, my main point is that it was a bad idea to replace thoroughbass practice with the theory of fundamental bass even if it gets quicker results, and modern figured teaching generally bass does not make this distinction.

  9. viveutvivas says:

    I think you should post more!

  10. Anonim says:

    I’m only just beginning a study of composition and so I’m currently investigating the best methods. I’m very happy to have found out about this approach.

    The only things that confuse me are:

    1) Why did C.P.E Bach include the concept of inversions (apparently) from Rameau’s principles (see intro to his Keyboard Treatise)
    2) Why did Kirnberger (despite being of the J.S. Bach school) attempt to reconcile Rameau’s principles with figured bass if the latter are utter nonsense?
    3) In light of James Cook’s statement that “…people mistake figured basses, which are a form of musical notation, for some sort of analysis of the music…”, why then did the highly respected (by Haydn, Mozart, Beethoven) contrapuntalist Albrechsberger describe thoroughbass as exactly that. That is, as a kind of ‘skeleton’ of the music (see his collected writings on Thoroughbass and Counterpoint).
    4) There appear to be purely vertical operations when realizing a figured bass part, as students are advised to make the chords ‘fuller’ by spacing the harmony (and that can be found in Mozart’s lessons for Attwood).
    5) Some teachers of counterpoint encourage Figured Roman Numerals. That is, they get rid of the inversion symbols a, b and c, and just have figured bass against Roman numerals. Any thoughts on the usefulness of this?
    6) In music that was clearly composed via Rameau’s principles, is it not worth understanding it by the composer’s actual method?
    7) Apart from composers like Berlioz then, what about jazz, folk music, blues, pop etc, and any music that was clearly harmonized by stringing along chords on instruments? I mean, if there is a clear ‘harmonic rhythm’ (like in many jazz standards) doesn’t it make sense to remember and play the song by hearing that as a sequence of chords? Surely in jazz and blues, chord changes are used as structural markers (for sections, song phrases)?
    8) Similarly, where ‘ideal’ counterpoints are not realized, specified or figured, it is not clear to me how I would think about or remember some music without considering the position of chords in time. (For example, if I hear a ‘roughly’ harmonized folk or pop song on the radio or TV.)
    9) I’m currently training my ear in order to learn more about counterpoint, but as I encounter harmonized melodies, I struggle to hear the melody in relation to the tonic rather than another harmony (e.g. chord IV or V). So I tend to consider the melody in relation to the chord underneath it. Is this something that needs practice or am I misunderstanding the alt approach?
    10) (If not) wouldn’t a system that regards all notes in relation to the tonic not be better? Therefore, in C major, wouldn’t it be simpler to think of a harmony involving the notes G B D as 5 7 2?

    These are not objections in support of general bass or chord progressions, but rather just a few nagging factors that bother me before I decide the best way to teach myself… especially since teachers and most books clearly can’t be trusted not to be bias towards Rameau’s principles. Thanks in advance.

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