# Functional Chord Substitution or How Wagner did it !



## ed buller (Dec 21, 2020)

Very interesting analysis from my current fav book author : 

https://global.oup.com/academic/product/desire-in-chromatic-harmony-9780190923426?cc=gb&lang=en&#






Desire in Chromatic Harmony



interestingly all the substitute chords are part of the octatonic collections, also a minor third apart.The same patterns keep appearing in tonal music

best

e


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## FelixDeepTerror (Dec 22, 2020)

Amazing stuff!


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## youngpokie (Dec 22, 2020)

This is really nice, I've been trying to describe the TSDT with chord substitutions along these lines in several threads but he just captures it so well and so clearly, it's amazing.

There are two things in his "introduction" that are missing and under-developed, in my opinion:

- the prolongation. He gives an example of F major to d minor as a way to extend the S function, but he skips many other techniques (e.g. using augmented chords as stepping stones from T to S, for instance)
- the reverse progression (T-D-S-T), especially from Romantic (and a lot of Russian) music

Of course, the reason might be because he's doing an analysis of a specific piece. But his introduction itself (with expanded chapter on cadence) could be an entire course on creating progressions.

Thanks for this find, I will look into his book...


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## ism (Dec 22, 2020)

Another great reference Ed.

Read the first few pages in the amazon preview, and quite fascinated by the Lacanian take (how many comopers are going to have the patience for obscurity of Lacan though I wonder).

Would love to hear you thoughts on the book, both at the philosophical, and practical, compositional level.

Do you think, for instance, that it would be worth sitting down with that video, really working though the chat he draws to internalize it, and also the Tristan example with his theory of substitution as a practical approach to building composition technique?

ie. could this be popularizes for the average composer? Because it *feels* like there's something quite insightful and practical here that might be distilled to a coal face composition tutorial from the high music theory and psychoanalytical philosophy.

One doesn't need to be rewriting Tristan und Isolde to want to maybe a bit more yearning to one's improvised chord progressions.


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## ed buller (Dec 22, 2020)

The book is deep...but very manageable. I like the concept very much as it seems so practical. I think there are many instances where simple chord substitution ( for that is really what's this is about ) can yield enormous results. If I understand the premise correctly each of the three functional areas of harmony have 4 options ( simply put ) all bizarley a minor third apart. This is a variation on Lendvai's AXIS theory (https://en.wikipedia.org/wiki/Axis_system#:~:text=In music, the axis system,relationship between tones and chords.)...But for me a little more profound. Although like Lendvai he avoids describing the chords quality.



As to the WAGNER video yes !..totally worth slogging through it. I had to pause it a lot but again you can see how using the Tonal function as a driving force behind the chord choices all make sense. Yes the voice leading, suspensions and appoggiaturas are really the beauty of the piece but the frameworks is still basic prolongation with sensible choices. Rather than rely on endless diminished sevenths and enharmonic spellings he makes it look rather straightword. Although it did take old Dicky a couple of years to write it.

As to internalising it and adding it to your toolbox...most definitely....however the yearming is really the result of constantly delaying the resulion ( No Perfect cadences ) and the liberal use of appoggiaturas on weak beats and suspensions. But just using the alternative chords in each tonal area and learning how to move from one to the other is very useful. Again in the tristan he shows you how it's done.....................................

and anything that helps me write music Like tristan is fine with me !

best

e


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## styledelk (Dec 22, 2020)

I watched like half of this before bed last night and it may be the greatest A HAH! music theory moment I've had.


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## ism (Dec 22, 2020)

Thanks Ed, I think I might have a serious go at working through the 1st video.

And the third video on entropy, watching it as a physicist who's long had a sense the music and quantum field theory have something to teach each other, is very suggestive also.

Huron's book on counterpoint has a similarly inflected insight, in he distinguises (I think it's) part writing and voice leading in terms of what would make sense in reverse. If a voice leading works as well backwards as it does forwards, the it isn't invoking this kind of resolution. Which - if you'll forgive a bit of handwaving - I think should therefore be easily framed in terms of a dynamics of entropy, and the notion of 'reversibility' (which is a key concept of QFT). 

The large narrative is that the human mind (in it's perceptive capacity, of musical perception and cognition is just one example of human non-cartesian perceptive capacity) doesn't calculate in the way that our conventional (lambda calculus) mathematics of computation implies. But in the dynamics flows of possibility and context.


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## ism (Dec 22, 2020)

styledelk said:


> I watched like half of this before bed last night and it may be the greatest A HAH! music theory moment I've had.


Which part?


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## styledelk (Dec 22, 2020)

ism said:


> Which part?







The way he described this flux capacitor of progressions here kind of tied together the years of music theory I’ve cobbled together from starting over at the beginning a few dozen times. The example progressions he played I could immediately tie to oodles of romantic and modern romantic music I adore that I (admittedly) haven’t taken the time to analyze.
At least for me, now that I’m engaged in a formal music education, it was a moment that my brain just went OH THAT’S WHAT’S GOING ON, HOW STUPID AND RIGID I’VE BEEN. 

Humbled and brain whirring with re-thinking my basicness.


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## ism (Dec 22, 2020)

Nothing like a good theory of everything that just hits you in the face.


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## fantasy sound (Dec 22, 2020)

youngpokie said:


> This is really nice, I've been trying to describe the TSDT with chord substitutions along these lines in several threads but he just captures it so well and so clearly, it's amazing.
> 
> There are two things in his "introduction" that are missing and under-developed, in my opinion:
> 
> ...


I thought the same thing about the reverse progression. And there seems to be difficulty in analysing just a simple T-D(-T) progression in the diagram, let alone reversal T-D-S-T. To place the T-D motion in the diagram, you need to draw the line from right to left, or skip the S column then jump to the D, apparently.

And in that regard I found some of the chord symbols analysed in the video a bit questionable. For example, he is analysing the chord at T.25(around 15:30) as Dm AND G7, but that seems a bit odd to me. The upper g in the melody is clearly a suspended note of Dm, thus Dm sus4, not G7. I assume that he needed to interpret it as G7 at the same time in order to keep the T-S-D-T pattern as is. Otherwise, skipping from S to T(=E♭) must have been done.

That said, I'm really interested in the concept, and probably will buy the book later. I will be able to learn a lot from it.


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## cqd (Dec 22, 2020)

Yeah, this is great..Thanks..Might pick up that book at some stage..


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## styledelk (Dec 22, 2020)

Liszt and Wagner took turns sitting on this egg.


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## youngpokie (Dec 22, 2020)

fantasy sound said:


> And in that regard I found some of the chord symbols analysed in the video a bit questionable.



I haven't read the book yet and I'm really only focusing here on the introduction part of the video where he's describing the chord substitutions inside the T-S-D-T pattern - but I don't think his analysis is questionable. 

He simply has a specific goal - analysis of a Wagner piece and potentially an explanation that links together the chromatic and functional aspects of it. The guy is a professor, after all.

The thing to keep in mind is that he's literally rushing through the explanation of chord substitutions. It's way too fast for something that has a direct and immediate impact on improving harmonic skill and mastery and this should be the main takeaway from the video, not Wagner. 

My few quibbles: some of his explanations (for example adding Ab to the subdominant group because it's found in the Neapolitan 6th) are at first blush really overcomplicated.

The easier and simpler way to understand this is to take a basic subdominant chord and just go to town with it:
- substituting with chord from parallel key
- adding a new root tone min3 below (that's how F becomes d minor 7)
- adding a new tone maj3 above
- altering a tone within a chord (raising or lowering 2, 4 and 5th scale degrees depending on function)
- altering more than 1 tone within a chord (same)
- altering tones within a chord AND adding new tones like maj/min 3 above/below

In a way, it's a slightly different way of describing the same end result: in this concept, you have very few base chords and through simple manipulations/alterations of those few you obtain a huge amount of "new" chords that sound different but still perform the same role. Compare this with the other way of conceptualizing it - you look for new chords to add to the subdominant group by calculating intervals or by observing common use, which is what I think he does.

Also, at first I was puzzled by the inclusion of so many chords into the tonic group. But I guess it's because his theory is literally based on "going in circles (chromatically)" through these 3 functions - and from that standpoint it makes perfect sense to construct it the way he did.

Here again, I think a much simpler way to understand most modulation (including to some pretty remote keys) is that it's easily done with by altering a chord and putting it into a cadential progression. 

And finally - he touches briefly on the idea of prolongation, that instead of thinking "one chord = one function" you can actually sit on the function over several chords. In the video he shows it with an arrow going down from F major to d minor. But he's so brief here, it's maddening...

This idea of taking your time and packing several chords inside the subdominant bucket before you finally move on, it opens a whole new way of thinking how to link the chords one to another inside the progression. And because here you link several subdominant chords, the chromatic semitones and chromatic harmony can become those chain links.

Still, his explanations are so clear and easy to grasp! And I love the diagram idea. Anyway, I downloaded the Kindle preview of the book to read. And this post has been waaaaay too long, lol.


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## mikeh-375 (Dec 22, 2020)

ism said:


> Thanks Ed, I think I might have a serious go at working through the 1st video.
> 
> And the third video on entropy, watching it as a physicist who's long had a sense the music and quantum field theory have something to teach each other, is very suggestive also.
> 
> ...



@ism , I'm not a physicist, but have a long standing interest in some of its disciplines. I too have felt a connection between QM and associated disciplines (albeit on a 'popular' level) and music, especially atonality. When writing in an extended chromaticism and with no external commitments other than one's aesthetics, technique and instinct, I sometimes intuit a sense of parallel, something analogous, something beyond the readily tangible.
I guess it's another manifestation of the music=nature duality.


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## mikeh-375 (Dec 23, 2020)

[email protected] Pool...you've got a glittering career as a lecturer awaiting if you aint one already. Would be interested to hear some of your work.


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## ed buller (Dec 23, 2020)

This can go further. "Harmonic Function In Chromatic Music" makes the case that individual chord tones have there own sense of drive and function. 



Chapter two details "the functional role of scale degrees" and splits triads into their component parts and weights accordingly the activity and choices of each

best

e


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## Fox (Dec 23, 2020)

Cool stuff! Thanks for posting. Wrapping my head around this now...


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## YaniDee (Dec 23, 2020)

For a slow, patient discussion (as opposed to the hyper-fast talking video above) on these topics, check out this video..


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## rhizomusicosmos (Dec 23, 2020)

Hmm, the psychodynamics of chromatic harmony . . . Does this mean that prior to the CPP Western music wasn't Oedipal? May have to read this book just to see how Lacan and Deleuze factor into it all, especially after reading Badiou and Žižek's _Five Lessons on Wagner._


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## cet34f (Dec 23, 2020)

fantasy sound said:


> I thought the same thing about the reverse progression. And there seems to be difficulty in analysing just a simple T-D(-T) progression in the diagram, let alone reversal T-D-S-T. To place the T-D motion in the diagram, you need to draw the line from right to left, or skip the S column then jump to the D, apparently.
> 
> And in that regard I found some of the chord symbols analysed in the video a bit questionable. For example, he is analysing the chord at T.25(around 15:30) as Dm AND G7, but that seems a bit odd to me. The upper g in the melody is clearly a suspended note of Dm, thus Dm sus4, not G7. I assume that he needed to interpret it as G7 at the same time in order to keep the T-S-D-T pattern as is. Otherwise, skipping from S to T(=E♭) must have been done.
> 
> That said, I'm really interested in the concept, and probably will buy the book later. I will be able to learn a lot from it.


I have the exact feeling as yours. I feel he is using this ambiguous Dm/G7 marking to avoid the fundamental problem of his approach with the minor second upward motion.

In the classical music, the minor second upward motion is usually a Neapolitan chord (T-S) or a deceptive cadence (D-T). T-S and D-T should be considered _moving forward one step _in his concept, but as you can see in the video, a "minor second upward motion" is considered _moving backward one step _in his system.

That being said, I still consider his approach valuable. If he expands his concept a bit more, this problem could be easily tackled. I am going to buy his book to see how he deal with the minor second upward problem, since the the short length of the video doesn't do justice to his approach.


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## fantasy sound (Dec 24, 2020)

cet34f said:


> I have the exact feeling as yours. I feel he is using this ambiguous Dm/G7 marking to avoid the fundamental problem of his approach with the minor second upward motion.
> 
> In the classical music, the minor second upward motion is usually a Neapolitan chord (T-S) or a deceptive cadence (D-T). T-S and D-T should be considered _moving forward one step _in his concept, but as you can see in the video, a "minor second upward motion" is considered _moving backward one step _in his system.
> 
> That being said, I still consider his approach valuable. If he expands his concept a bit more, this problem could be easily tackled. I am going to buy his book to see how he deal with the minor second upward problem, since the the short length of the video doesn't do justice to his approach.


Exactly. You explained that Dm/G7-E♭part much better than I did.

An upward major 2nd movement can be easily traced in his diagram, which I think is one of the best parts of it. On the other hand, an upward minor 2nd could be a bit problematic, as you already mentioned.

Anyways I ordered the book. Looking forward to it arriving!


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## ed buller (Dec 24, 2020)

cet34f said:


> I have the exact feeling as yours. I feel he is using this ambiguous Dm/G7 marking to avoid the fundamental problem of his approach with the minor second upward motion.
> 
> In the classical music, the minor second upward motion is usually a Neapolitan chord (T-S) or a deceptive cadence (D-T). T-S and D-T should be considered _moving forward one step _in his concept, but as you can see in the video, a "minor second upward motion" is considered _moving backward one step _in his system.
> 
> That being said, I still consider his approach valuable. If he expands his concept a bit more, this problem could be easily tackled. I am going to buy his book to see how he deal with the minor second upward problem, since the the short length of the video doesn't do justice to his approach.


i'm just wondering whether the Neapolitan as a sub dominant is thought of here as fad or flavouring rather than being rooted in more robust Harmonic theory ?....

best

e


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## cet34f (Dec 24, 2020)

ed buller said:


> i'm just wondering whether the Neapolitan as a sub dominant is thought of here as fad or flavouring rather than being rooted in more robust Harmonic theory ?....
> 
> best
> 
> e


Good question. For your reference, I used Igor V. Sposobin's harmony textbook when I first studied harmony.


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## youngpokie (Dec 24, 2020)

cet34f said:


> Good question. For your reference, I used Igor V. Sposobin's harmony textbook when I first studied harmony.


 Has it been translated into English? If you know...


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## cet34f (Dec 24, 2020)

youngpokie said:


> Has it been translated into English? If you know...


Not sure, but now you mentioned it, I've never seen one...


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## ed buller (Dec 24, 2020)

I picked up this earlier in the year:



Sorta fascinating . Mostly the work of Yavorsky , the creator of " the theory of modal rhythm"





Turaskin is worth reading too

best

e




MTO 18.4: Ewell, Rethinking Octatonicism








Proto-Harmony and the Problem of Tonal Centricity in Rachmaninoff’s All-Night Vigil – Intégral







www.esm.rochester.edu


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## youngpokie (Dec 24, 2020)

ed buller said:


> i'm just wondering whether the Neapolitan as a sub dominant is thought of here as fad or flavouring rather than being rooted in more robust Harmonic theory ?....
> 
> best
> 
> e



under this view of T-S-D model, I’m not seeing how any altered IV chord, including Neapolitan, can be understood as anything other than subdominant substitution.....

what am I missing?


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## ed buller (Dec 24, 2020)

youngpokie said:


> under this view of T-S-D model, I’m not seeing how any altered IV chord, including Neapolitan, can be understood as anything other than subdominant substitution.....
> 
> what am I missing?


I see here he is placing the minor 2 Accent going to a dominant . TBH I really have a hard time with the neapolitan. I get that many theorists regard it as an altered subdominant from the parallel minor. I just think that's a stretch . Sure that's how you make it but !...to me it seems that a chromatic inflection occurs in a voice (almost always from a melody standpoint) and a new chord results. To me it seems that it's a flat 2 maj chord..not a f minor chord with the fifth raised.....

Best

e


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## ism (Dec 24, 2020)

rhizomusicosmos said:


> Hmm, the psychodynamics of chromatic harmony . . . Does this mean that prior to the CPP Western music wasn't Oedipal? May have to read this book just to see how Lacan and Deleuze factor into it all, especially after reading Badiou and Žižek's _Five Lessons on Wagner._



How is "Five lessons on Wagner"? I'd been thinking of picking it up. 


I think I'd argue that the tripartite structure of the Oedipal represents a larger structural truth that might - conceivably - give hint's of an underlying mathematical (or at least mathematically expressively) scientific truths, perhaps at the level of fundamental mathematics of logic. So the structure of the "Oedipal" in Freud, which it may capture a truth of some underlying tripartheid structure if the human psyche, it's obviously clothed in a very of-it's-time (ie deeply western, patriarchy) reading idiosyncratic to the ambient ideology in which Freud was working. 

So pre CPP, one might still have this structure of the human psyche captured via the "Oedipal" morphology, but simply expressed within the different ideology of the day. I imagine that there's an argument (that presume someone will have made somewhere) that prior to the CPP, and the rise of reductive bottom-line reductivism endemic to enlightenment era science, economic, rigidity of social relations etc, the need for a constant drive to a "bottom line" in the form of a particularly satisfying resolution maybe wasn't the same kind of resolution pre CPP audiences needed. So that during the CPP, the "Mr. Literal Pants" logic of clear and unambiguous resolution dominated. Which ultimately opening up an angst to escape this logic of a single world, into logics of multiple worlds. (In that, especially after WWI, you can see discontent with overly neat and tidy logic driving the modernists (like the impressionists), sometimes explicitly expresses as it's inability to accurately represent dimensions of human experience). 


This parallel's the late 20th/ early 21st scientific understanding of logic. Recent results in quantum computing, for instance, propose a tri-partheid structure of topoi, each being a logic of world understood within the modern topos theoretic concept of logic, with the interactions (and mutual embeddings) of each logic within the others begin where things really get interesting. I would speculate that there's some shared notion of underlying structural truth with Lacan's tripartheid, interlocking regimes of the human psyche in the metaphor of the Boromean knot for the entanglement of the Real, Imaginary and Symbolic, each with their own "logic" (though of course Lacan simply lack the scientific knowledge to do anything other that speculate pseudoscientifically, if suggestively). 



There's possibly a deeper connection to Badiou here, via his Logics of Worlds, where he proposes topos theory itself as the "calculus of phenomenology". Unfortunately he's writing this before any of the really spectacular recent results that some of these same idea to reformulate quantum theory in topos-theoretic language, so I'm not saying any of this is rigorous, just deeply suggestive). 


But tying it back to this thread, this notion (in the interaction of multiple "logics of (multiple) wolrds") is suggested in other approaches to formalizing music theory. Mazolla's "The Topos of Music", most obviously. 

But I also recently read a paper (can't remember the author, but I have is somewhere if anyone's interested) that demonstrates that the relations between scales (modelled in overtones) can form a Temperely-Lieb algebra - which formally, forms an internal (modal) logic of a (the truth object of) a topos. ie scales for their own "logic of worlds". (this is a mathematical paper, based on properties of affine algebra, not a piece of musicology. So the musical justification proposed is suggestive, but not terribly rigorous musicology).


Intuitively, it all makes a certain sense - ie. music (at least within a particular set of traditions) is about establishing a certain "logic" of a world (ie T => S => D => T)... and then satisfying (via resolution) or breaking (ie via modulation, chromaticism or whatever) that logic and a motion between the logics of multiple worlds. Which the particular 19th century ethos of Freud's take on the Oedipal as a universal structure is, kind of stupid (and infuriatingly sexist, etc). Lacan is a bit better. And modern psychoanalysis of intersubjective (ie Jessica Benjamin) is a lot less stupid. With perhaps the dominant forming the "intersubjective third" to break the dialectic of the (tonic) self and (subdominant) other. 


From a very different angle, Tyzcmozko's "A Geometry of Music" uses the formalism of Orbinfolds (he doesn't use the term in his book, but it's in his academic papers), so there should be a connection to topos theory (which makes me wish I knew more Orbinfold theory). Tyzcmozko's approach is a very rigorous musicology, not just in the mathematics, but in it's empirical approach to musicology. But because he's at Princeton, he's of course require to harbour a visceral hostility to the likes of continentals like Mazola (who in fairness, reciprocates this hostility with equal passion). Which would presumably extend to a hostility to a continental like Badion. Tyzcmozko even takes the occasional pot shot at category theory itself. Which is a pity, since there's at least a sense in which what's unfolding here is the possibly of building \ bridges between the reductivism of (analytical) classical ("Mr. Literal Pants") logic, and the (continental) obscurity of traditional subjectivism. 


So I'm deeply curious how Lacanian notions ( "logic of the signifier" etc) might out to be useful to a working composer.


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## youngpokie (Dec 24, 2020)

I don't have a lot of time today but managed to watch the video again.

1. The way he's moving along the grid (T-S-D-T).

In my view, the grid should be completely flexible and can also be constructed as S-D-T, or T-S-T-S or T-D-T-D-T. The simple reason for this is because the nuclear unit of the model is a single-step 5th motion (either D-T or T-S). So, the grid should follow the harmonic/cadential design the composers chooses.

Right now, his layout seems to be precluding any skips, any Plagal moves, etc - which is of course crazy. But perhaps he's showing only one direction both in his circle diagram and later in the grid is because the entire video is about proving his 2 thesis on Wagner: that a minor is the home key and that the entire piece is moving in a single repeated pattern (rather than a combination of patterns).

2. The D minor - G7 chord.

I agree that this is a tricky moment in the entire video (and in full honesty I wasn’t really paying attention the first time around as I was so preoccupied by the introduction). First of all - is it a D minor - G7 - Eb progression or is it a leading tone B to D minor to Eb progression? They both work melodically and harmonically. I guess this is the point @fantasy sound was making earlier...

I would construct the circle differently - putting a single tonic in the center and having 2 rays out for subdominant and dominant chords and substitutions. His "tonic" substitutions would be distributed between dominant and subdominant.

This means my analysis would have to look at modulations inside each cadence because my tonic chords would change. And since he's not looking at that angle maybe that's why he's a little trapped with Dm-G7-Eb.


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## ed buller (Dec 27, 2020)

Gene Pool said:


> Neapolitans were mentioned earlier and I'm bored the day after Christmas, so this falls under the heading of _how I see it_—given that we're in largely subjective terrain.
> 
> It’s a mistake to pigeonhole chord functionality, whether it be a Neapolitan or anything else. While it's true that in practice they are typically considered to have a chromatic subdominant usage, there’s certainly a lot more to functionality than shoehorning everything into these broad umbrella categories.
> 
> ...


completely agree

e


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## rhizomusicosmos (Dec 29, 2020)

ism said:


> How is "Five lessons on Wagner"? I'd been thinking of picking it up.


Throughout the book both Badiou and Žižek are attempting to redeem "Wagner" from critics such as Nietsche and Adorno by analysing what the operas apparently do, in an ideological sense, opposed to what Wagner intends them to do.

There's frustratingly little discussion of the music in Wagner's operas, however. Badiou and Žižek are clearly focused on the dramatic elements even though Žižek states that the music must be "taken seriously" as an embodiment of the _Ring's_ philosophy. 

Žižek does attempt to try and redeem Wager's leitmotifs from Adorno's accusation of cinematic "kitsch", though he seems to concur that the technique was fetishized (to its detriment) later by golden-age Hollywood composers. He instead holds up Mozart as shining examplar of musical irony (_The Magic Flute_ and _La clemenza di Tito_) and opposes Beethoven (at his worst, e.g. the Violin Concerto and _Leonore _Overture No.3) as an example of musical kitsch. See pages 188 to 190 for Žižek's thoughts on this and the cinematic in Wager.

Badiou and Žižek also seem to disagree as to what is the most significant point in Wagner's works. For Badiou, it appears to be in _Parsifal _which ushers in the possibility of a secular ceremony to replace the Christian Mass, as per Mallarmé. It is only the possibility because ultimately it fails to achieve this.

For Žižek, it is the end of the Ring cycle where Brunnhilde's final act of destruction and sacrifice represents the triumph of _agape _over _eros _and a breaking of the sexual deadlock of the Oedipal matrix. All the other operas fail to break this deadlock.

The question I ask, however, is why are two revolutionary Marxists attempting to defend Wagner's works ideologically? From Badiou's preface, it seems that he made a passionate connection to Wagner's *music *at a young age through the influence of his mother. The psychodynamics of this passionate engagement remains unaddressed by either philosopher in the book.


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