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Thread: Baroque "chord progressions"

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by EdwardBast View Post

    Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.
    Eww, music shouldn't be mixed with mathematics.
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    Quote Originally Posted by EdwardBast View Post
    For years, actually. I'm a theorist, among other things.

    Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.
    I'm afraid I don't.
    The only statistical reference I have is for the cadences, which you can find in Malcolm Boyd, Chorale Harmonization and Instrumental Counterpoint, Kahn & Averill (London), 1999. If you want, please send me a privare message and I can scan and send you the small analytical table of the cadences (for personal study purposes, of course).

    Otherwise, for an excellent study of Bach's chorale practice I use William Lovelock's The Harmonization of Bach's Chorales. I believe it is no longer in print.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by TalkingHead View Post
    I'm afraid I don't.
    The only statistical reference I have is for the cadences, which you can find in Malcolm Boyd, Chorale Harmonization and Instrumental Counterpoint, Kahn & Averill (London), 1999. If you want, please send me a privare message and I can scan and send you the small analytical table of the cadences (for personal study purposes, of course).

    Otherwise, for an excellent study of Bach's chorale practice I use William Lovelock's The Harmonization of Bach's Chorales. I believe it is no longer in print.
    Thanks for those citations. I'll query on SMT and AMS discussion forums because I think that's where I heard this kind of data quoted.

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    Quote Originally Posted by millionrainbows View Post
    Is this a test?

    A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).

    Maybe in earlier times, it is treated differently...

    In some convoluted sense, it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense. Is this what is being gotten at, as some sort of test? Is this one of the academic hurdles one is expected to deal with?

    WIK: Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note (not a root function). They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).

    Because that would be "harmonic thinking." Right? Is this the trick?
    Functional theory is based on the structure of diatonic scale in just intonation by Hugo Riemann (and this is just a small part of his theories).
    Don't search for functions in older theories. You won't find them anywhere before his time (1849–1919); he introduced mathematical word "function" in musical context. This (German) theory is not popular at all in Britain and US, aside from simplified analysis using roman numerals (it's overcomplicated and the notation is horrible - see the book below; it's also unsuitable for non-classical music, just like any other "classical" theory). Schoenberg/Schenker's (Austrian) school is what is popular there.
    You will find plenty of nonsense in both theories, imo.

    https://archive.org/details/cu31924022305357/page/n3

    It is funny how long it took for people to recognise various chord and scale "inversions" as permutations of the same abstract object. The same is valid for scales - there were even in the beginning of 20th century scale "cheat-sheets" that were listing the same scale in a different mode.

    Edit: Interesting video on history of Roman numerals:
    Last edited by BabyGiraffe; Mar-28-2019 at 20:33.

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    Senior Member isorhythm's Avatar
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    Quote Originally Posted by Woodduck View Post
    You've piqued my interest. You can't back out now.
    Well, one reason I haven't done it is that I'm not sure I have either the requisite knowledge of Wagner's music or the command of music theory to really support my case.

    But the short version is that I think the claim of the "Wagner leads to atonality" people is being misunderstood: no one's actually saying that tonality isn't central to Wagner's music (as counterpoint is central to Bach's, even in the prelude that's just a sequence of of arpeggiated chords). The claim is that Wagner pushed the role of unstated tonics to the point where other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar, and that suggested new directions to composers that ultimately led to atonality.

    I was reminded of this recently when you quoted this book: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers."

    I think the reason it was largely unexplored by later composers is that if you push it much further, the unconscious psychological process breaks down and most listeners cease perceiving the sequences of unstated tonics. Anyway that's how it is for me when I try to listen to Berg's piano sonata or Schoenberg's chamber symphony, and it seems very natural that those composers ended up going the way they did.
    Last edited by isorhythm; Mar-28-2019 at 22:32.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by TalkingHead View Post
    Sure.
    For use of IV7:
    a) Jesu, joy of man's desiring;
    b) Nun ruhen alle Wälder;
    c) Ich dank' dir, lieber Herre.
    I examined all chorales under these titles in Riemenscheider and didn't find examples of the use of a IV7 chord. The closest was Nun ruhen alle Wälder (no. 117), which has what looks like a IV7 on the first beat of the final bar. But on the last beat of the preceding bar we have a IV6, which makes the C on the next beat a passing tone.

    In none of the versions of Ich dank' dir, lieber Herre in Riemenschneider did I find a IV7 chord, although there were a couple with the 7th as a passing tone.

    Do you have anything more specific for these references — like which of the multiple settings you meant?
    Last edited by EdwardBast; Mar-29-2019 at 00:39.

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    Quote Originally Posted by isorhythm View Post
    Well, one reason I haven't done it is that I'm not sure I have either the requisite knowledge of Wagner's music or the command of music theory to really support my case.

    But the short version is that I think the claim of the "Wagner leads to atonality" people is being misunderstood: no one's actually saying that tonality isn't central to Wagner's music (as counterpoint is central to Bach's, even in the prelude that's just a sequence of of arpeggiated chords). The claim is that Wagner pushed the role of unstated tonics to the point where other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar, and that suggested new directions to composers that ultimately led to atonality.

    I was reminded of this recently when you quoted this book: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers."

    I think the reason it was largely unexplored by later composers is that if you push it much further, the unconscious psychological process breaks down and most listeners cease perceiving the sequences of unstated tonics. Anyway that's how it is for me when I try to listen to Berg's piano sonata or Schoenberg's chamber symphony, and it seems very natural that those composers ended up going the way they did.
    Your explanation for the theories of the "Wagner leads to atonality people" is very conciliatory! Actually, I don't think all those people have the same theory about how an expanded tonality "evolves" into atonality. There was Schoenberg's concept of "the emancipation of the dissonance,"which postulated that, over time, people learn to regard harmonies previously considered dissonant as consonant, and that logic therefore dictates that we go all the way and remove the tonal functions that provide the criteria for what's consonant and what isn't. Then there's the notion that because Romantic composers were making harmony more and more chromatic and using more chords that couldn't be "explained" by reference to theoretical systems then current, the obscuring of tonal centers which resulted would inevitably lead to a "breakdown of tonality" and its total abandonment as a constructive principle in music.

    Wagner would have spat out his coffee at such notions. No composer in history was more attentive to tonal relationships than he was, or exercised more far-reaching and iron-handed control over them. He was, however, well aware of what a Pandora's box of potential abuses his enriched tonal vocabulary would open up for aspiring composers tempted by what he described as "effects without causes." Young composers, he said, would come to him with compositions filled with novel and complicated harmonies, hoping to be praised for their expressiveness and creativity, and he would be quick to set them straight.

    Wagner's music does indeed force us to think of musical form - and this includes harmony - in ways that Bach's or Mozart's does not. But it no more implies, or suggests as desirable, the negation of the very principle of tonality than theirs does. I would dispute your suggestion that in his music "other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar." Wagner's radical movement away from a "top-down" approach to harmonic structuring - in which the stations of tonal movement, the "functional" pillars of tonal harmony, are explicitly stated as the audible scaffolding of a basically abstract form - to a "bottom-up" approach - in which tonal structuring is guided by a sense of dramatic/expressive narrative inherent in the tonal language - is not a movement away from tonality but an extrapolation of a potential which had been present in it from the start and was in fact adumbrated many times in the work of earlier composers. What Wagner saw was the extent of that potential to create large-scale dramatic works in which the expressive language of tonal harmony could guide the creation of coherent musical statements without signaling its "mechanics" to the conscious mind of the listener.

    A real comprehension of what Wagner was doing in his music depends first and foremost on an intuitive sense of its organicity, its underlying logic, and that depends on our ability to abandon the Classical expectation that musical form, particularly form based on tonal structures, is created and perceived "from the top down." The musical conservatives of his day were opposed to his conception of musical form; I've known people, even musicians, who are not comfortable with it even today, and can't listen to a Wagner opera without feeling disoriented and irritated by the refusal of the music to congeal into neat structures. Wagner's mature works are an uncompromising expression of the Romantic conception of music as the language of the soul, a language which comes "from the bottom up," and Wagner uses drama as the scaffolding on which our conscious mind can fixate while the music goes to work on our unconscious.

    I've managed to get my hands on a copy of the book from which the excerpt you've quoted comes: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers." The book, "Musical Structures in Wagnerian Opera" by Marshall Tuttle, is a work of thorough scholarship and meticulous analysis, and it isn't an easy read (I'm skimming parts of it first time around). But it's definitely confirming and filling out my long-standing intuitions about Wagner's music and how it works. Among other things, it helps me understand why his scores are full of changes of key signature when it's often impossible to find more than a bar or two that actually seems to be in the specified key - and why, despite surface appearances, Wagner stated that one should never leave a key until one has said everything necessary within it.

    I understand Tuttle's suggestion that "the possibilities which [Wagner's techniques] opened may remain largely unexplored by later composers" to indicate, not that composers declined to push his techniques further lest they inevitably confound the listener's tonal expectations or be forced to leave tonality behind, but that they simply could not manipulate the surface vocabulary of his style with the intuitive control of the layers of tonal organization, mediated through motivic sequence and metamorphosis, which enabled him to generate a sense of narrative inevitability and expressive specificity on a grand scale. There's a great deal of post-Wagnerian music that sounds "Wagnerian" but, in any profound sense, isn't. Tuttle's observation also points out the fundamental fact that Wagner's music took the form it did under the impetus of the need for dramatic expression - "dramatic" in the specific sense. Tuttle's book shows in (sometimes ponderous) detail how dramatic ideas and musical structures are inseparable in the operas, to the extent that, more than with any other composer, understanding the latter is essential to understanding the former, and how the precise manipulation of tonal relationships provides a key to that understanding. Wagner was so convinced that music could be an articulate language, and so relentless and thorough in the use of hamony's tools to achieve that end, that he would eventually call his operas "deeds of music made visible."

    I would say that anyone who thinks that Wagner's music "leads to" atonality doesn't understand very much about it. Scholarly scuffles over how to name the Tristan chord are apt to be missing the forest for the trees.
    Last edited by Woodduck; Mar-29-2019 at 08:14.

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  13. #84
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    Once again, the defense of Wagner as the supreme tonalist must retreat back to a nebulous aesthetic, dramatic, and 'spiritual' position, because from a purely musical standpoint, there is nothing left to hide behind.

    In Wagner, the absence of functional harmony as a primary structural element, and the reemergence of purely melodic-rhythmic forces as major determinants of musical form, and the emphasis on expressive chromaticism as a logical, perhaps inevitable consequence of the weakening of tonal centers (as in Wagner’s Tristan und Isolde), had caused successive chords to relate more strongly to each other than to a common tonic firmly established by intermittent harmonic cadences.
    BTW, I hear Berg's op.1 Sonata as a prime example of this "circulating" travel around the chromatic scale, with no resolutions or cadences, as a prime example of the musical, technical aspects of this Wagnerian practice, which led to the abandonment of tonality (as we knew it).

    Eventually, the 12 equidistant semitones superseded the diatonic scale (necessary for functional harmony), to the extent that melodic-rhythmic tensions and resolutions took the place of the harmonic cadences and modulations that had determined the structure of Western music for centuries.

    Dramatic "Wagnerism" was a nebulous aesthetic more important to literature and philosophy. When the subject is music, the technical aspects are more important than dramatic, spiritual, or aesthetic notions.

    So, while Wagner may have influenced the young Schoenberg's early dramatic works, the 12-tone works owe little to Wagner in dramatic or aesthetic ways so much as a abstract, technical and musical ways.

    The repeated retreat back to Wagner's nebulous aesthetics is a cop-out to the real musical issues.

    Instead of proclaiming that "anyone who thinks that Wagner's music leads to atonality doesn't understand very much about it," then why can't this be demonstrated? Because it can't.

    "Scholarly scuffles over how to name the Tristan chord are apt to be missing the forest for the trees" is true, if they are not "Wagnerites" who subscribe to these nebulous aesthetic notions you refer to.

    Apparently, to understand Wagner, one must have "
    an intuitive sense of its organicity."

    Try it, man, it's organic!

    I'm wondering if this statement:

    Among other things, it helps me understand why his scores are full of changes of key signature when it's often impossible to find more than a bar or two that actually seems to be in the specified key - and why, despite surface appearances, Wagner stated that one should never leave a key until one has said everything necessary within it."

    ...is actually a
    reference to Tuttle's claim that...

    "...
    Wagner liberated the higher-level organizers of tonal structure (e.g., orbits of keys—known as tonalities—rather than just keys) from diatonic/scalar structures. That is, a piece ostensibly in C major was no longer limited to modulations to D minor, E minor, F major, G major, A minor, etc., but now the superset of modulatory choices could be determined by motives. This is demonstrated brilliantly in the orchestral introduction to Act I, Scene v of Tristan und Isolde (analyzed in Chapter 3), where the modulations outline the Tristan chord itself. (I alluded to this sort of outlining in the discussion of Beethoven's Ninth)

    Tuttle also explains why previous analytical scholarship has not been able to identify this feature (in this case, it is because the tonics are earmarked by half cadences rather than full cadences, and a contrapuntally-biased theory like Schenkerian analysis can only account for what is literally in the score)."


    ...and that this way of thinking, outlined in Leland Smith's Handbook of Harmonic Analysis, can be explained geometrically, as I tried to tell earlier academics:

    From Leland Smith: An analytical methodology called linear harmonic analysis is introduced, wherein modulations are treated as recursively referencing higher levels of tonal organization. This is profoundly different from a contrapuntally-inspired analytical system like Schenkerian analysis in that is allows for the projection of elements which are not evident on the surface. Charts dubbed "Tonic Guide Tones" show the sequence of tonics of a wide variety of pieces, and impressive results obtain, e.g., in the analysis of the prelude to Tristan und Isolde (pp. 129-147), where it is demonstrated that the Tristan chord becomes elevated from a surface-level sonority to an arbiter of tonal organization for the entire prelude (as it transits the keys of a, c, and e♭, ending with the sailor entering in G minor).

    I understand Tuttle's suggestion that "the possibilities which [Wagner's techniques] opened may remain largely unexplored by later composers" to indicate, not that composers declined to push his techniques further lest they inevitably confound the listener's tonal expectations or be forced to leave tonality behind, but that they simply could not manipulate the surface vocabulary of his style with the intuitive control of the layers of tonal organization, mediated through motivic sequence and metamorphosis, which enabled him to generate a sense of narrative inevitability and expressive specificity on a grand scale.

    I think that this is now possible, using geometric analysis and thinking.

    As Dmitri Tymoczko concludes in A Geometry of Music, "Musicians who recoil from these (Second Viennese) post-Wagnerian extremes, but who did not want to write traditional music, would therefore need to go back to the drawing board, devising new approaches that could coexist more peacefully with tonality."

    Attention: Hey You! Back to the drawing board! And Dmitri Tymoczko's book is a helluva lot cheaper than the Tuttles or Leland Smith 300-600 dollar tomes.

    And, as the cherry on top, Dmitri Tymoczko is a guitar player! Haha haa!
    Last edited by millionrainbows; Mar-29-2019 at 18:26.

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    Quote Originally Posted by EdwardBast View Post
    For years, actually. I'm a theorist, among other things.

    Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.
    It was done by American theorist Allan McHose in The Contrapuntal Harmonic Technique of the Eighteenth Century (Appleton-Century Crofts, 1947). But not perfectly: "Whereas he uses the study of over two hundred Bach chorales to illustrate one point, he refers to a study of all 371 chorales for statistics to demonstrate suspensions, ..."(David M. Thompson, A History of Harmonic Theory in the United States, Kent State University Press, 1980). Likely there has been a more consistent study since then.

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    Senior Member isorhythm's Avatar
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    Woodduck,

    I think we're talking past each other a little bit. I'll happily admit that I don't know much about Wagner's music compared to you or EdwardBast or some other posters here. My point, however, is that it makes no sense to insist that Wagner's music doesn't imply or suggest moving away from tonality when, in actual fact, it did imply and suggest that to a number of very good composers. That's independent of Wagner's intentions and of how Wagner's music itself works. Art often suggests surprising new directions to others that the original artist didn't think of or even actively rejects.

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    Quote Originally Posted by BabyGiraffe View Post

    The best books on common practice are these that basically teach historical methods. These are very good, imo:

    "The Art of Accompaniment from a Thorough-Bass: As Practiced in the XVII and XVIII Centuries" (2 volumes) - Arnold (Bach, Vivaldi etc lovers may find this one interesting,)

    "Music in the Galant Style" - Gjerdingen (Mozart fans will love this)
    Good point. We have the whole area of historically informed practice now that requires skill and expertise in harmony according to the period involved. It helps in Baroque "Chord progressions"/Music Theory/TalkClassical to discuss different approaches in theory and practice, which are not completely separated.
    Last edited by Roger Knox; Mar-29-2019 at 15:53.

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    Default Walter Piston's Harmony (1941)

    "The appearance of Walter Piston's Harmony (1941) marks a return to the practical philosophy of theory. ... Piston states that his theory is 'the collected and systematized deductions gathered by observing the practice of composers over a long time, and it attempts to set forth what is or has been their common practice. It tells not how music will be written in the future, but how music has been in the past.' Throughout the work Piston systematically rejects opportunities to support his statements with acoustical arguments.'" (David M. Thompson. A History of Harmonic Theory in the United States. Kent State University. Press, 1980.)

    So, Walter Piston's (1894-1976) approach is empirical, his book full of examples by great composers. He uses (invents?) the phrase "common practice" for eighteenth & nineteenth century classical music. His studies composition (not harmony, which would have been redundant) in Paris with Nadia Boulanger. And no Riemann, Schoenberg, or Schenker. But to correct my earlier post, apart from the general point that Rameau influenced all subsequent harmonic theories, Piston's harmony isn't really French-derived. At the time it was an empirical reaction against some English theorists who pressed acoustic theory of harmony based on the higher overtones to excess.

    He is making a crucial distinction between harmony for education of all advanced classical music students, and harmony for composers and improvisers interested in recent and new practices.

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    Quote Originally Posted by BabyGiraffe View Post
    Functional theory is based on the structure of diatonic scale in just intonation by Hugo Riemann (and this is just a small part of his theories).
    Don't search for functions in older theories. You won't find them anywhere before his time (1849–1919); he introduced mathematical word "function" in musical context. This (German) theory is not popular at all in Britain and US, aside from simplified analysis using roman numerals (it's overcomplicated and the notation is horrible - see the book below; it's also unsuitable for non-classical music, just like any other "classical" theory).
    Since I know nothing of how music theory is taught in Europe your post is useful! All I learned about Riemann was the T, S, and D functions and how chords are included in each. But now there is much more interest in Riemann in the English-speaking world.

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    Quote Originally Posted by Roger Knox View Post
    Since I know nothing of how music theory is taught in Europe your post is useful! All I learned about Riemann was the T, S, and D functions and how chords are included in each. But now there is much more interest in Riemann in the English-speaking world.
    You would do well to heed his words. But on the other hand, he was talking to me.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

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    "I don't mind dying, as long as I can still breathe." ---Me

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