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- Devin Chaloux October 2017
- Dimitar Ninov October 2017
- Marcel de Velde October 2017
- Nicolas Meeùs October 2017
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Dispelling Myths through a Little Tchaikovsky Piece
Dear Colleagues,
This morning I came across the piece "Winter Morning" from Tchaikovsky's Children's Album for Piano. I was pleasantly surprised with the freedom the author brushes away some postulates which are being imposed massively on those who major in music nowadays.
First, I will offer you a brief formal analysis of the piece. Then I will comment the theoretical myths that are being dispelled by Tchaikovsky's pen.
The form is simple ternary: ABA, with an eight-measure transition between A and B and an eight measure Coda. Part A (mm1-16) may be regarded as a compound modulating period which consists of two sentences of Schoenberg. All cadences here are imperfect, even the modulatory one. Part B (16-32) is in B minor. It may be analyzed as a compound sentence with an eight-measure presentation and an eight measure continuation which sounds like another compound presentation but the harmonic motion is more active and the cadential formulas are more articulated (ends with a plagal cadence: altered S - T). A sequential transition follows (mm.33-40) which modulates to the dominant area of D major. Reprise: part A (or A1), (mm. 41-57) - same compound modulating period. However, it ends with a PAC, the only one in the piece. Coda (mm.57-64), containing plagal gestures with a diatonic and altered S resolving into T, and ending with plagal cadence IV6-I.
Below are my comments on the myths that I call "false claims".
False Claim 1: "A triad in second inversion cannot substitute for a root position triad, because the fourth above a bass note makes the structure dissonant."
At the outset of the piece, Tchaikovsky resolves a series of altered dominant chords: first in T5, then in T6, and finally in T6/4. In measure 3 for example, one can hardly claim that the author resolves the dominant chord into a "dissonant sonority".
As for the level of acoustic perfection of a triad, I will add the following: 5/3 = perfect; 6 = imperfect but stable enough; 6/4 = more imperfect, unstable (but lacking a true dissonance), needs special conditions to sound like a substitute of a 5/3 chord. These special conditions are called passing, pedal and arpeggiated 6/4 chords which are generally weak metrically and have nothing to do with dissonance.
Besides, in three part close structures (encountered in choral music and piano accompaniments) the use of 6/4 chords as a substitutes for an original 5/3 takes even greater freedom.
False Claim 2: "Inverted dominants, subdominants and tonics do not produce a cadence and this is why this type of connection must be called "tonic prolongation".
Well...in the whole Tchaikovsky piece there is only one PAC in mm. 55-56...I do not think anyone would put forward the proposition that all those periods, sentences and modulations are executed miraculously over "a tonic prolongation". After all, when you change the key center in a modulating period, whose tonic do you "prolong" – the previous, or the new one?
False Claim 3: Plagal cadence does not exist. This type of connection must be called "tonic prolongation".
This funny concept is rejected even by some Schenkerian-influenced musicians, not to speak of the musical world as a whole. Certainly, Tchaikovsky uses a number of plagal resolutions in this piece, some of which rise to the level of cadence as they fall in the end of the period or the coda. A most interesting examples of plagal cadence is presented in mm. 28-29 and 31-32, where the composer resolves at a tritone an altered S chord into T. The chord is IV7#1 (an S with a raised root in minor mode, or your German in root position, if you will). Geographic terminology notwithstanding, one has to know if the diminished third/augmented sixth chord functions as an altered S or an altered D chord, according to the way it resolves.
Another interesting example of plagal resolution is the resolution of an altered SII2 into T (m.60), some would call this a French chord, followed by a plagal cadence IV6 –I, which marks the end of the Coda.
False Claim 4: "Avoid resolving a IV6 chord into the tonic".
That really sounds nonsensical, for in his piano album and elsewhere, Tchaikovsky displays a certain number of IV6-I connections, some of which rise up to a cadence (mm. 61-62 of the piece).
False Claim 5: The cadential six-four is nothing more than a V chord with two accented non-chord tones.
Generally, this concept is easily dismissed by all kinds of empirical evidence in the musical literature which include but are not limited to:
– embellishment of the cadential six-chord via non-chord tones (ironically, some of them are dominant members but sound like dissonant suspensions!);
– resolution into the cadential six-four of altered S chords in the same way they resolve into the tonic;
– free arpeggiation and rearrangement of the cadential six-four which may occupy one or more measures (see concerto cadenzas);
– free motion of the so-called "dissonant fourth" which occasionally moves up (see Marpurg cadence) or even leaps when going to the dominant;
– while a true Dominant with suspensions will produce an authentic resolution even if the suspended tones are not resolved prior to the resolution into the tonic, the Cad.6/4 is incapable of that, and this is why there is no piece of music in the literature which uses a "cadence" involving only Cad.6/4 – T.
What is Tchaikovsky's answer to that? In m. 54 he elegantly introduces an embellished Cad.6/4 by suspending the second scale degree over it. Please, notice that the possible artificial label 5-4 suspension (as formally referred to the bass) is actually a disguised 9-8 suspension over the tonic root. Ironically, the suspended tone is the fifth of the dominant but it sounds like a dissonant suspension over the tonic structure of Cad.6/4. Thus the segment within mm. 53-55 introduces a series of chords embellished by a suspension: an embellished S, an embellished Cad.6/4, and an embellished D. Logical, isn't it?
Hence, is the cadential chord a true tonic? No. Is it a true dominant? No. What is it, then? Popular music very practically gives the answer to that – they label it as I/V (or T/D) – a tonic over a dominant bass. A tonic six-four which, falling on a metrically stronger position, losses half of its tonic function and acquires a dominant momentum in the bass, creating a conflict between T and D. Therefore, I think that the simplistic presentation of this unique chord as a "dominant with two non-chord tones" reveals lack of awareness of all the matters discussed above and most of all – a disregard to all the examples in the music literature wherein the structural equality between Cad. 6/4 and T is explored musically. For your reference, I have published a whole article on the cadential six-four (Functional Nature of Cadential Six-Four, Musicological Annual, LII/1, 2016) .
Before concluding, I would like to bring to your attention the fact that Tchaikovsky's free use of all harmonic positions of the so-called "augmented sixth chords" and their resolution directly into the tonic in root position bears the features of a late Romantic style, combined with the emancipation of the plagal cadence, pertinent to the Russian music of the late 19th century.
What is my point with this letter and deliberations? To promote the awareness of the fact that today's music theory studies in the "serious departments" across the country (and to a certain extent abroad) suffer certain lack of practicality which makes them quite detached from the real music practice. What is the remedy? Simple analysis of real music, the use of popular music and jazz as new perspectives of looking at harmonic functionality, and the removal of mythology. In our judgment and analysis it is good to keep in mind that, it is the entire routine language of composers which counts and creates a style, not only the "very typical situations" to which we should stick, ignoring or denying everything else.
I will appreciate all kinds of comments on that matter.
Thank you for your attention,
Dimitar Ninov
Dr. Dimitar Ninov
Texas State University
San Marcos, Texas
SMT Discuss Manager: smtdiscuss@societymusictheory.org
Comments
Hi Dimitar,
You write: "What is my point with this letter and deliberations? To promote the awareness of the fact that today's music theory studies in the 'serious departments' across the country (and to a certain extent abroad) suffer certain lack of practicality which makes them quite detached from real musical practice."
Time and time again, you have made this claim, but fail to identify specific schools, scholars, or artifacts in general that support your straw man arguments that you drag out once every few months. I suppose as someone who has had the privilege of being educated at what some would call "serious departments," I fundamentally have to reject your argument on the numerous fallacies that you build it upon.
Who wrote these myths? Who teaches music theory and doesn't connect it to musical practice? If music theory has somehow been disconnected from musical practice in "serious departments," then why are they (again...who is they) writing our theory books?
I feel like you continually bring this up because "they" teach "very typical situations" and that is your ultimate issue...it does not actually describe practice. Again, I do not think anyone here would argue with that point. There is practicality in teaching "very typical situations" because when you have 60 weeks (if you're so lucky) to cover music theory from beginning to end in an undergraduate curriculum, there is not the time to dive into every single stylism that exists. But to suggest that "serious departments" either a) don't recognize that or b) recognize it and don't care is ludicrous.
Music theory is imperfect. And art is imperfect. Art analysis brings beauty to the imperfections - and in that, analysis brings beauty to the imperfections in music theory. It is because of our understanding of "very typical situations" that we can talk about this neat little piece from Tchaikovsky. That doesn't invalidate what we do or how we do it. To the contrary, I think with the robust publications and presentations on a diverse repertoire demonstrates how much music theory has grown and improved even in the last 10 years.
I think the fundamental problem with this "conversation" is that you set them up by immediately disregarding the actual state of music theory that most of us in this community have learned, taught, and refined. Continually propping your arguments on logical fallacies that most of us reject is not productive to discussion in this vibrant scholarly community.
Best,
Devin Chaloux
Devin Chaloux
Indiana University
Dimitar,
Whenever any of us (including Schenker) publishes anything, i.e. makes it public, we open our statements to public criticism. There is no reason not to "openly announce the names", as you say. On the contrary, names (and references) are necessary to conduct a successful scientific discussion.
You denounce five claims, of which I cannot find any trace (at least in the terms in which you formulate them) in any of the books that I read, nor in any of the teachings that I received. We cannot discuss this further without knowing where you read these claims. They are:
1. "A triad in second inversion cannot substitute for a root position triad, because the fourth above a bass note makes the structure dissonant." [By the way, what do you mean by "substitute for a root position triad", in what sense to you understand "substitute"?]
2. "Inverted dominants, subdominants and tonics do not produce a cadence and this is why this type of connection must be called "tonic prolongation". [I fail to see why being a "tonic prolongation" would be contradictory to "producing a cadence". I thought to understand that Schenker's initial tonic prolongation, the Ursatz, was nothing but a perfect cadence.]
3. "Plagal cadence does not exist. This type of connection must be called 'tonic prolongation'." [Same question: if you want to speak of "tonic prolongation" (there is no obligation to do so), should not all cadences ultimately be considered tonic prolongations?]
4. "Avoid resolving a IV6 chord into the tonic".
5. "The cadential six-four is nothing more than a V chord with two accented non-chord tones."
Here, you provide a number probably of your own claims against the initial one, but once again, do you have references for any of these?:
– "embellishment of the cadential six-chord via non-chord tones": do you believe an embellishment tone cannot further be embellished?
– "resolution into the cadential six-four of altered S chords in the same way they resolve into the tonic": why would a S–T resolution exclude a S–D one?
– "free arpeggiation and rearrangement of the cadential six-four which may occupy one or more measures (see concerto cadenzas)": is there any prohibition of long embellishments? Is it not so that non-chord tones often are stressed (e.g. appoggiaturas)?
– "free motion of the so-called "dissonant fourth" which occasionally moves up (see Marpurg cadence) or even leaps when going to the dominant": aren't these cases of resolution with voice exchange or register transfer?
– "while a true Dominant with suspensions will produce an authentic resolution even if the suspended tones are not resolved prior to the resolution into the tonic, the Cad.6/4 is incapable of that": how do you make the difference between "a true Dominant with suspensions" and a "Cad.6/4"?
I think we really need answers to these questions, if we want to have a serious discussion.
Best,
Nicolas
Dimitar,
I just want to reiterate the two major points in my post since your reply fails to address them.
First, in order for those who you are criticizing to engage in this discussion, you need to be specific in who and what sources you are deriving these myths from. At face value, you have set up straw men arguments that are not based in reality.
Second, you continuously disparage talent musicians and scholars by claiming that they have no touch to real musical practice. Every day I interact with the community, I am impressed at the level of musicality of our community. Making broad claims that the community as a whole is full of people who "artificial theorists who are masters of nothing" is not only incorrect but irresponsible.
We can't engage in meaningful discussion of these works if a) the arguments are philosophically unsound (i.e. full of logical fallacies) and b) you fail to empathize with the scholarly community as a whole. Until you address these, there's not much discussion to be had here.
Devin Chaloux
Indiana University
Thank you. You are actually facilitating my task. All of these false claims (except the appeal not to resolve IV6 into the tonic) are found in Schenkerian and post-Schenkerian theory. Thus Schenkerians:
- do not recognize the existence of triads in second inversion; they think of them as dissonant sonorities produced by a bass tone and two non-chord tones above it;
- do not recognize the cadential capabilities of a harmonic closure involving inverted dominants, subdominants, and tonics (yes, they think that a tonic prolongation and cadence are two different things, but I do not think so; in some cases a tonic prolongation does not obliterate the cadence, as you have realized that yourself);
- do not recognize the existence of the S function; Schenkerians call it either a "pre-dominant" or "a tonic prolongation". The former is nonsensical, and the latter may be a Plagal connection, a Plagal cadence, or an embellishment of the tonic via IV6/4, all depending on the particular context;
- think of the cadential 6/4 as a true V with 2 non chord tones, but I think of this as a false claim. References? 1. Show me a piece of music which ends with K6/4 - Tonic. (if you think K6/4 is a true dominant, then it must be able to produce an authentic resolution into T. Notice that any true D chord with suspension(s) can do that immediately with no additional moderator between itself and the tonic)
2. Many additional references - send me your email and I will attach to it my published article on the K6/4 where plenty of musical examples from the literature dispel the "true V chord" myth.
"Do not resolve IV6 into T". See Concise Introduction of Tonal Harmony by Burstein and Straus (Norton, 2016). They call this resolution "poor" and advise their students to avoid it (p. 168). Tchaikovsky and many others do not think so...they have not read this book :)
Finally, I pasted below a list from article "The defects of a Reigning Theory (delivered in Moscow, 2015) which contains suggested shortcomings of Schenkerian and post-Schenkerian doctrines:
A list of suggested major defects of Schenkerian theory:
1. Repudiation of the subdominant function and the plagal cadence.
2. Imposition of an exaggerated notion of functional prolongation, which leads to analytical methods ignoring stepwise cadences and implied cadences over a pedal point.
3. Repudiation of ascending melodic lines and the leading tone as structurally important factors in the background analysis.
4. Interpretation of typical six-four chords as dissonant sonorities.
5. Neglect of rhythm and phrase structure as important factors in tonal analysis.
I hope that helps at this stage. As you can see, I do not forge information and can quickly refer you to the false claims I listed in my first letter. Best regards!-DN
Dear Dimitar,
In answer to my request for references to the «claims» that you denounce, you propose to send me further texts where you denounce them. This is not what I was hoping for. (One of) my mail address(es) is given in my https://discuss.societymusictheory.org/profile/148/Nicolas page. Use it if you want, but I think that once you raised your point publicly here, the discussion should remain public.
You now propose a list of "suggested major defects of Schenkerian theory". Let me tell you, Dimitar, that I have spent many many hours since many years reading and rereading Schenker both in German and in English translations, and reading many (serious) Schenkerians, and never found even only an allusion to any of these statements that you present as "major defects". Once again, we cannot discuss this further if you don't give references, to specific pages either by Schenker himself or by his followers. For the time being, I have no clear idea of what you are speaking.
Can you provide if only one Schenkerian quotation "repudiating the subdominant function", mentioning "functional prolongation" (a concept utterly foreign to Schenker), "repudiating ascending lines as structurally important", "interpreting typical [?] six-four chords as dissonant", or "neglecting rhythm and phrase structure"?
It would seem that your knowledge of Schenker is based on a second-hand reading of Oster's translation of Free Composition. Are you aware that Schenker published about 4000 pages of theory, of which the less than 200 pages of Free Composition form but a very little part?
Best,
Nicolas
Dimitar,
Am I understanding that you are conflating Schenkerian theory with music theory studies in the "serious departments" across the country? Sure - Schenkerian theory is one of the modes of thought which is taught at these schools, but it is not the only one. Schenkerian analysis is a tool, a means to an end, that helps some theorists talk about real practical musical moments. It's not some empty exercise in drawing lines on a staff paper. It is a kind of performance.
Secondly, I have to agree with Nicolas's rebuttal and emphasize his point that Schenker wrote so much over his lengthy career. To distill his ideas down to axioms tangetially supported by Free Composition (and the translation of it) is misrepresenting his contributions to the field.
Thirdly, have you noticed how Schenkerian theory is less prevalent on conference programs and article publications? I think there are many excellent additional methods of analysis that have been developed and refined over the last 15+ years.
Fourthly, I bring up these quotes and phrases that you use in your posts because I don't think you understand how the community at large interprets them. What is your point in including that Schoenberg quote if you don't agree with it? There's no suggestion for the opposite and your generally combative approach to the music theory community definitely invites a more antagonistic approach when there is little to suggest otherwise.
Lastly, this quote is so problematic: "I imply that there is an army of impostors out there, who rely on their diplomas from a "prestigious institution" to find a good position, but they are complete diletants anyway." This serves no purpose than instigating conflict for no good reason. You use this as justification for students who have difficulty harmonizing a melody. (By the way, I had many many students in my time that were very good at doing this...so I generally disagree with your comment). However, student learning outcomes are a separate issue here to the one that you bring up. There is plenty to talk about regarding student learning outcomes, but blaming Schenkerian theory (which is essentially what you are doing) and then the music theory community at large is not a very productive way of a) addressing a complex problem, b) assessing the causes behind student learning outcomes, and c) initiating appropriate change to improve student learning outcomes.
Again, I find your original argument troubling and your responses have only made them more problematic.
Devin Chaloux
Indiana University
Dimitar, you write: "Come on, you do not need me to provide you with a quote from Schenker saying there is not S function in music..." But on the contrary! I need it, because I cannot find any myself. Let me first stress, with Devin Chaloux, that modern theory teaching must not be judged only on the basis of a caricatural American Schenkerism. Schenker is a historical figure of a century ago and must be viewed in his historical context. But he has been an important figure and he should not be rejected on the basis of the same caricatural Schenkerism.
You must be aware that the very concept of harmonic function was created by Riemann only in 1893. Even Schoenberg does not make use of it in his Theory of Harmony – the translation by Roy Carter may give a false impression in this respect, for instance when he translates (p. 15) that in modulation as in the cadence, "the architectonic, the structural functions of harmony, of chord connection, are indeed most intensively expressed," while Schoenberg had written das Architektonische, Konstruktive der Harmonisierens, des Akkordverbindens etc. (p. 9 of the 7th Viennese edition).
Considering that you would not do it yourself, I began a search in Schenker's published writings. My search can be trusted to the extent that OCR can be trusted (I have all these books in electronic form). I checked the following works (from the original editions in German), with the following results:
• Der Geist der musikalischen Technik (1895). Mentions neither harmonic function, nor subdominant, nor dominant, nor tonic.
• Harmonielehre (1806). Does not mention harmonic functions as such, but mentions once the Dominantencharakter (p. 269, translated by E. Mann Borghese, p. 205, as "the dominant V"). He uses the word subdominant (Unterdominante) eight times, the figure IV (as figure for a chord) more than 210 times (i.e. in average close to once every two pages). §122 is devoted to the plagal cadence.
• Kontrapunkt I (1910). Harmonic functions and the terms Tonic, Dominant and Subdominant are seldom used, as is normal in a treatise of counterpoint, but when they are the quotations are of importance. Schenker writes (in Rothgeb and Thym's translation, p. xxviii):
(my underlinings). This was before Schenker turned anti-French (after 1918), but it may have been intended to minimize Riemann's merit. And later, p. 23:
This obviously is directed against Riemann and in favor of Simon Sechter's Stufentheorie, assuming distinct harmonic functions for each of the seven degrees of the scale. The text continues with further similar criticism.
• Beethovens Neunte Sinfonie (1912). The "function of the harmony" (Funktion der Harmonie) is mentioned once (Universal Edition, p. 60), apparently refering to the function of a diminished 5th as dominant. The term Dominante occurs 43 times, Unterdominante 15 times.
• Kontrapunkt II (1922). No mention whatsoever of Funktion in any meaning. No term denoting the subdominant. Dominante and Tonika are used a dozen times, mainly to denote the 5th and the 1st note of the scale (Dominantenton, Tonikaton).
• Der Tonwille (1921-1924). No mention of harmonic functions. In vol. 8-9, about variation XXIII of Brahms' Variations op. 24, William Renwick's translation (p. 97) reads "the final note of the third-progression, a2 (standing for a1), completes the neighbor-note chord a1–c2–eb2–gb2, whose function—VIIb7 V—is actually in opposition to that of the divider at the lower fifth", but Schenker's term translated as "function" is Wirkung (German, p. 27). Later (p. 105), Renwick mentions a bass note "functioning as a dominant", but Schenker had written (p. 34) im Sinne der Dominante. On p. 109, Renwick writes of "functional strength", where Schenker had written (p. 40) Stufenwärme, Stufenglanz. The subdominant is mentioned twice in volume 1, twice in volume 2, three times in volume 4, and twice in volume 5, but never in volumes 6-10. The divider at the lower fifth is discussed in volume 5 and further mentioned in all the subsequent volumes.
• Das Meisterwerk in der Musik (1925-1930). In vol. II, p. 21, Schenker introduces his famous "swan slur" (the term is not his; the shape was inspired by Lorenz, Das Geheimnis der Form, vol. I, p. 16), stressing a T S D T succession. The examples given include I–(IV)–V–I, I–(II)–V–I, I–(VI–II)–V–I and I–(III–VI–II)–V–I, where the degrees between parentheses realize what Riemann would have called the subdominant function. Otherwise, Ian Bent translates as "harmonic functions" what was harmonische Verhältnisse in Schenker (vol. I, p. 134). The term Unterdominante appears only twice, first (vol. II, p. 76) in a quotation from Riemann, and again (vol. III, p. 82) describing a "fugal answer in the subdominant". In the English translation, in all three volumes, Schenker's expression IV. Stufe is five times translated as "subdominant".
• Der freie Satz (1935 edition): No mention of harmonic functions. Dominante occurs 9 times, Unterdominante only once – in a footnote of § 204, quoting a paper on Brahms in "a Viennese journal" which Schenker derides; the footnote disappears in the 1954 edition and is not in Oster's translation. Schenker refers twice (§§ 91 and 111) to the I–IV–I progression as the plagale Satz, translated by Oster the first time as "plagal bass motion" and the second time as "plagal setting".
What can be deduced from all this is that Schenker was not much interested in harmonic functions in general. He preferred to think in terms of Stufe, degrees, in conformity with the Viennese tradition, and preferred to denote the subdominant degree and the subdominant chord by their Roman numeral. On the other hand, the swan slur (and its implicit aknowledgement of the T–S–D–T functional cycle) remained a constant feature of his graphs until the end.
Considering your statement about "Schenker saying there is not S function in music", I must admit that perhaps my research was not accurate enough, and I would be extremely grateful if you could give me the reference of any of his statements to this effect.
Dear Nicolas,
Thank you for the exhaistive information and research. I do not argue with your points. I am just bringing up some outright discrepancies and what I think of as "nonsensical" claims concerning functional harmony as we know it today (the T-S-D-T cycle being an example of typical progression).You know that classical and jazz analysis relies explicitely on this cycle when it comes to tonal music within the so-called "common practice period" and beyond.
As for the cadential six-four chord, things are pretty simple: whoever claims that this chord is a true dominant, must prove to us that it is capable of producring and authentic resolution into the tonic and show examples of that. Yes, it is that simple.
Best regards,
DN
Dear Nicolas,
Sorry for the delay in this matter - please find below my comments to each of your remarks attached to the my "false claims":
1. "A triad in second inversion cannot substitute for a root position triad, because the fourth above a bass note makes the structure dissonant." [By the way, what do you mean by "substitute for a root position triad", in what sense to you understand "substitute"?] Ninov: Please, ask American theoreticians, they come up with this strange phrase, meaning that a six-four chord cannot express the harmonic function of the root position triad whose inversion it is. I do not agree with this; sometimes it can, other times it cannot - it depends on context.
2. "Inverted dominants, subdominants and tonics do not produce a cadence and this is why this type of connection must be called "tonic prolongation". [I fail to see why being a "tonic prolongation" would be contradictory to "producing a cadence". I thought to understand that Schenker's initial tonic prolongation, the Ursatz, was nothing but a perfect cadence.] Ninov: Americans think that tonic prolongation obliterates the sense of cadence, if you do not believe, ask my friend William Caplin and all other American Schenkerians.
3. "Plagal cadence does not exist. This type of connection must be called 'tonic prolongation'." [Same question: if you want to speak of "tonic prolongation" (there is no obligation to do so), should not all cadences ultimately be considered tonic prolongations?] Ninov: Not necessarily, cadence means "an ending". If everything is tonic prolongation, then there is no beginning and no ending, just one tonic...a generalization which will render harmonic analysis superfluous.
4. "Avoid resolving a IV6 chord into the tonic". See Poundie Burstain "Concise Introduction to Tonal Harmony", p.168.
5. "The cadential six-four is nothing more than a V chord with two accented non-chord tones."
Here, you provide a number probably of your own claims against the initial one, but once again, do you have references for any of these?:
– "embellishment of the cadential six-chord via non-chord tones": do you believe an embellishment tone cannot further be embellished? Ninov: Cadential Six-Four is not a tone but a chord, and when you hear a dissonant suspension colliding with this chord and then resolving within it, you know that this event occurs within a chord structure which physically coincides with the tonic triad.
– "resolution into the cadential six-four of altered S chords in the same way they resolve into the tonic": why would a S–T resolution exclude a S–D one? S-D is not a resolution, but a succession, connection, progression with an open end. S-T and D-T are resolutions.
– "free arpeggiation and rearrangement of the cadential six-four which may occupy one or more measures (see concerto cadenzas)": is there any prohibition of long embellishments? Is it not so that non-chord tones often are stressed (e.g. appoggiaturas)? Ninov: When a K6/4 is arpeggiated, I do not hear embellishments in the form of non-chord tones sounding over a dominant function, but a tonic triad arpeggiated over a dominant bass. If you do not believe me, see the melodic content which usually occurs over any cadential six-four, and you will realize that it outlines the tonic contour. Of course, in longer extensions of K6/4 during concerto cadenzas you may insert any chord or outline that you wish, all the more the sound of the cadential stops for a minute or more and when the cadenza is over, the dominant takes the upper hand.
– "free motion of the so-called "dissonant fourth" which occasionally moves up (see Marpurg cadence) or even leaps when going to the dominant": aren't these cases of resolution with voice exchange or register transfer? Ninov: It is not only a voice-exchange within the cadential but also a motion from K6/4 to dominant. Mozart occasionally makes the fourth over the dominant bass in K6/4 (the tonic note) to leap up a fourth up and provide the seventh of the coming dominant chord (the fourth scale degree). The Marpurg cadence is very frequent in classical music. It melodic contour is this: a descending sol-mi-do over K6/4, followed by "re" over the dominant. In view of this beautiful cadential gesture, a colleague (whose name I will not say here) said during a presentation in Belgium (2014): this cadence has a problem, because the dissonant fourth does not resolve". Now we learned from this colleague that Mozart, Haydn and Beethoven all had big problems, applying this cadence without knowing that the poor "dissonant fourth" must reolves down a step. Ridiculous, no?
– "while a true Dominant with suspensions will produce an authentic resolution even if the suspended tones are not resolved prior to the resolution into the tonic, the Cad.6/4 is incapable of that": how do you make the difference between "a true Dominant with suspensions" and a "Cad.6/4"? Ninov: The beginning of the above sentence tells you that - a true dominant produces an authentic resolution, while K6/4 does not. A dominant with one suspended tone may be V7sus4. A dominant with two suspensions may be V7 (sus6, sus 4). That is one thing. However, A "dominant triad with two suspensions" (such as 6 and 4) physically coincides with the tonic triad and fails to behave like a true dominant chord when followed by the tonic itself. That is the litmus. In fact, the K6/4 - T connection sounds like a combination between an arpeggiated tonic six-four which occurs on a strong beat and a tonic in root position. Such things do occur in music, and I call them "fusion between K6/4 and an arpeggiated T6/4). Also, very interesting cases of fusion between K6/4 and a passing T6/4 may be observed in music practice; for example, a chord is introduced dramatically as cadential six-four, but after that it is followed by a subdominant chord and it becomes clear that this is simply an accented passing T6/4 (a rare event, given the fact that arpeggiated and passing 6/4 are weal metrically. See Mozart A La Turka, the reprise of the first section. Also Fur Elise, the middle section modulating from F to C.
A bit late, but let me add my 2 cents to this.
The cadential 6/4.
Agreed we do not hear the fourth and sixth above the bass as suspensions. I do not see how the sixth could be a true suspension anyhow as it's not prepared. The fourth could've been a suspension, and is if we play a fifth or minor seventh instead of a major sixth above the bass, but this isn't the case for the cadential 6/4 and I do not think it makes sense here to hear it as the dominant with an added sixth.
I think it makes most sense to see it as the tonic chord with the bass being heard as an anticipation of the dominant. This interpretation makes sense in all the examples you've given in this thread I belief.
As for dispelling myths.
I think a problem of current theory is that it is not critical enough of itself. Students are usually not made aware of it's severe limitations. They start studying music theory with the expectation that it explains how music works in a concise scientific manner.
Music theory as it currently stands is more like a collection of historical naming practices and competing theories of how we perceive chords and melodies, all mostly based on historical practices, and put together in an inconsistent manner.
Let's take a few very fundamental concepts as example.
Enharmonic equivalence. Is it a real thing or not? Much theory is inconsistent in this. I belief strongly that it is not a real thing. Even when we tune certain enharmonically different intervals the same, we never hear them as the same interval musically / functionally. Yet some theory speaks of it as if it is a real thing, or speaks of a composers choice / preference in enharmonic writing / "enharmonic niceties" etc. And I'm not that well aware of how many schools teach the subject but I've met many musicians who've finished a conservatory study believing that enharmonic writing is just a spelling thing done for score readability for musicians and it has no real functional meaning! Crazy.
In any case, once we see that there is no real enharmonic equivalence as far as our musical interpretation is concerned, we should admit to students that our perception of music is not well enough understood / our music theory not enough developed to teach them correct enharmonic spelling in all situations.
And another example. The concept of the "root" of chords. It is handled very inconsistently and it is surely full of errors. Most common theory of root is that it is the basis of tertian stacking. Yet this is handled very inconsistently in much theory, also with regard to naming chords (think German sixth chord or other augmented sixth chords for instance, which would have a diminished third etc above the root in a tertian root system not an augmented sixth). And in certain situations, especially with chromatic chords, the "functional" root movement resulting from this system makes not musical sense whatsoever. Yet we cannot and do not tell students when this happends, or what are exactly the limitations of this system.
But we should be telling students that current theory is a combination of things which have great musical logic and power, and things which are a complete mess. And that we can't tell them exactly which is which. This would save a lot of disappointment and confusion and loss of interest in theory.
Though probably a large part of the problem of telling this is that many teachers / theorists are themselves not very aware of the limitations of current theory..
Dear Marcel,
Thank you - I could not agree more with most of your comments, especially about the cadential six-four! In my article published in 2016 (Functional Nature of K6/4) I write exactly what you are saying about the perfect fourth - it is perceived as a dissonance when it appears as a non-chord tone accompanied by a true dissonance (seventh, second, tritone) which is present (in a multiple part texture) or implied (in a two-part texture). Also, there I maintain the idea that the cadential six-four is a tonic over a dominant bass - a tonic 6/4 which, falling on a stronger metric position, looses a part of its tonic function and gains dominant momentum in the bass. Yes, this concept explains all the possible appearances of the K6/4, including all sorts of embellishments which show how its structural equality with the tonic triad is explored musically. If you send me your email to my address dn16@txstate.edu, I would be happy to send my work to you.
As for enharmonic equivalence, I also agree; for example, a diminished seventh in context is quite different in character from a major sixth; a diminished third is quite different from a major second, etc. One of the beauties of the well-tempered system, however, is the miracle of turning a purely diatonic chord into a true chromatic one, changing the directions of its tendency tones to resolve (i.e. a minor seventh is a diatonic interval which resolves inward, while an augmented sixth is a chromatic interval which resolves outward)
For me, the so-called "augmented sixth chords" are not augmented chords at all (with some exceptions in more rare chords), and they are nothing more than altered S or D chords, depending on the way they resolve. While many chords have been derived in music via linear motion, once assessed aesthetically and functionally, they begin their own life of characteristic sonorities with a particular role (function). Yes, these are diminished third chords which, in their most typical harmonic position, display the interval of the augmented sixth. Many schools of thought do not use Geographic names to explain these chords, jazz musicians do not use nicknames either.
Thus the quality of the so-called German chord is a doubly diminished triad with a diminished seventh, and the so-called French is a major-diminished triad with a minor seventh. While most of the time these chords are used with the augmented sixth interval dramatically displayed, in a variety of cases they are used in root position or other positions and then students got confused and cannot find the aug 6th because it is not there...This is only one aspect of the inadequate teaching through Geographic names and "ready-to-go bass positions"... shall we name some other chords "Japanese aug 6th, Russian aug 6th, etc.?" (ha-ha).
Paradoxically, a true augmented triad with a minor seventh may be converted into and resolve as a chord with a diminished third/augmented sixth - I am talking about, say, G7#5 which may be interpreted as E#-G-H-D#. The diatonic basis of this chord is found on the fourth scale degree of harmonic major, for example in H major (I am using the German letter H instead of B which is the American Si), the minor S chord is E-G-H-D# (a minor triad with a major seventh. When you raise its root, here is your diminished third chord (doubly diminished triad with a major seventh) which is enharmonically equal to G7#5.
Best regards! - DN
Dear Dimitar,
Ah yes, reading back to your conclusions on the cadential 6/4 I see now that we are indeed saying exactly the same thing. Except I've been calling it an anticipation. I think it's an error in current theory to only see anticipations as un-accented. (anybody know why this is so?) As far as I'm concerned an anticipation can be accented as well.
As for "changing" a chord from a diatonic one to a chromatic one in a well-tempered system. I do not think this is a feature exclusive of a tempered system. The thing is, even if we tune something "untempered" (which I belief to be "extended" Pythagorean but many others belief to be a form of 5-limit rational intonation or something else), then the context a chord progression gives is almost always still stronger than any cues from tuning differences. As a strong example, if we were to tune in an untempered system for instance an I-V-I progression with diminished fourths instead of major thirds (complete nonsense of course), then we will still hear it as an I-V-I with major thirds, only with the major thirds slightly out of tune. Similarly, in your example of a "changing" chord in an equal (or unequal) tempered system, this would still work in an untempered system as even when we tune a chromatic chord in a place where we first expect a diatonic one, we will still be lead to the same place, only to realize / hear internally it is a chromatic one when it resolves as such. I've been working with untempered systems for over 12 years now and can tell you that this really is the case in practice, no matter the accuracy of tuning and clarity of timbre etc.
As for a minor seventh resolving inward and an augmented sixth resolving outward. This is a tendency yes, but not an unbreakable rule. I didn't mention it before but one of the "myths" that is the topic of this thread is in my opinion that of a near unbreakable status of leading tones. We can however also resolve by a chromatic half step in certain situations.
I'm glad to see that you see the German sixth chord as a double-diminished triad with added diminished 7th. It is consistent to at least name things that way. I didn't know they also teach it like this in America. But I personally disagree that this describes the root position of this chord. I agree with the musical logic of scale degrees of course, and I agree with the musical logic of building chords out of thirds including diminished and augmented thirds (in a perhaps slightly modified view from usual). But I do not subscribe to a general rule that the root is always the base note of a stack of thirds. And I don't think this is the case for the German sixth chord and that it is a subdominant chord even though the subdominant major seventh chord shares all scale degrees with the German sixth chord and therefore has certain musical similarities. I'll point out one difference. A major seventh chord we interpret as such in its own right, same for a dominant 7th chord, but the German sixth chord we can only interpret as such out of context. Play it all by itself, no matter in which inversion / root, and we will hear it as a dom 7th chord (no matter the tuning either). But I'll leave it at that or I may start describing what I think is a more logical system of root which is a long story and mostly off-topic. I'll add that I think a true root always has a perfect fifth implied above it (I think the root is infact the interval of a perfect fifth, not a single note) and that I think there are only the subdominant, tonic, dominant and relative major or minor subdominant, tonic, dominant root positions, no alteration possible of the root.
Anyhow, in the current system, which most students are led to belief is a coherent explanation of how music "works" we get the following. Chords are in the basis built out of stacks of thirds. But sometimes we get intervals "added" to this. The root is the base note of this stack of thirds (and you have to use your musical insight / experience to pick out the added notes which don't confirm to this). The basis is the diatonic system, but you can alter scale degrees if this altered scale degree leads to another note by leading tone (no real mention if it can be altered if it moves by whole tone though some musical examples are usually given which do just that). Then hiden away some examples are given of the "Enlgish / Swiss / Alsatian sixth chord" and "Australian sixth chord" which conform perfectly to the given "rules" of leading tone chromaticism, but have the rediculous interval of the double-augmented fourth, and the footnote that these are anomalies or something like that and have alternative interpretations as in more realistic interpretations where the resolution is by augmented prime instead of a leading tone. And then the other exceptions where resolution is by chromatic step and sometimes strange "rules" / exceptions given for them. And this is before we get to jazz etc. Perhaps the well read student of many years can somewhere find that the natural tones of the diatonic scale can't be replaced by enharmonic equivalent intervals without modulating, but most won't be taught this and are swimming in an endless sea of possible intervals and altered chords which they feel unsure about, usually resulting in no confidence to explore much outside their comfort zone as they'll mess up (and they do as far as spelling goes). Coupled with the many unmusical results one gets by composing randomly following these theories. And then many students think it's their own fault it doesn't make sense to them yet.. I mean I can write a big book full of the inconsistencies and errors of current theory. I really think it is like I said. A collection of mostly unscientific theory based mostly on past compositions, some parts of which have great musical logic and power, and some parts which are a complete mess. And that we can't tell them exactly which is which. I think knowing this beforehand would help them better learn from it and better develope their own musical understanding at the same time.
Sorry for the long post.
And I'm sending you an email now for your article. Very interested in reading it, thank you!
Kind regards, Marcel