Talk:Augmented sixth chord/Archive 1

x6 = -7 ?

Whaaaaat? There is no Augmented Sixth, just minor sixth and major sixth

Maybe you mean minor seventh? —The preceding unsigned comment was added by Shagmaestro (talk • contribs) 19:43, 21 June 2004 (UTC)

There is an augmented sixth. For example, B flat to G flat is a minor sixth; B flat to G natural is a major sixth; and B flat to G sharp is an augmented sixth. You can enharmonically respell that last one as B flat to A flat, and then its a minor seventh, but if you spell it as a G sharp, it's an augmented sixth. --Camembert (20:18, 21 June 2004)

Request to Rainwarrior, or Camembert, or whoever's minding the shop:

Since you asked for suggestions, would you mind explaining the above distinction in the article, even if only in passing? Shagmeistro's opening unsigned comment is a fair one that any educated reader might have. No sense burying the answer here on the Discussion page. There's an analogous situation in the article about diminished sevenths (i.e., why the artifice of a o7 when there's already a perfectly good +6?). Kkken 10:18, 27 August 2006 (UTC) (just passing by, looking for information about a chord)

I think it's time I got aorund to working on this page. I'll start working on it today. - Rainwarrior 20:04, 27 August 2006 (UTC)

There, how's that? I've rewritten the whole article, basically, and added an example picture. I tried to incorporate everything that was already in the article before, as well. - Rainwarrior 22:13, 27 August 2006 (UTC)

Seems fine to me. The picture certainly gets one's attention. I gave the rewrite a quick proofread as you invited me to on my Talk page, and nothing jumped out at me. It was an easy read. But I'm not a subject matter expert (couldn't tell a modulation from a transition) so I have to trust all the tech info. :-)

Kkken 07:34, 28 August 2006 (UTC)

The reason for the spelling probably has more to do with the use of meantone temperaments where the augmented sixth and minor seventh are actually NOT enharmonic. See Septimal meantone temperament for more explanation. 69.7.77.20 (talk) 21:05, 29 May 2008 (UTC)

Complaint

This article is awful. How do you seriously expect music students to learn about music theory when you employ such convoluted and unnecessarily complicated language. Make it simple and use plainer language so that people who don't already understand the material can appreciate it and therefore learn!! —The preceding unsigned comment was added by 88.109.1.174 (talk • contribs) 20:40, 31 July 2006 (UTC)

While I agree with you that the article is in bad shape; why don't you make some suggestions, or better yet, rewrite the article, instead of just complaining? Comments like the one you have just made do not help. While I have not yet made any contributions to this page, it has been on my list of things to work on... as such, a comment like this shows up on my watch list and is really just an annoyance. I'd be glad to discuss any suggestions you have about the page, but don't just come here and say "this is terrible". That's just a waste of time to read. - Rainwarrior 22:49, 31 July 2006 (UTC)

I did have a stab at editing some of the article, in order to remove some of the unhelpful language. However, I don't feel sufficiently adept with the material to confidently rephrase things such as "applied-functions within subordinate prolongations found in lower Schichten, such as #IV7/IIb". I feel this makes my point better. I hope now attention has been drawn to the fact (stated quite clearly above), that the poor choice language is what I object to, not the content. I think this is a valid point, in order to point out to persons thinking of writing articles that maximum effort should be made to render things clear and comprehensible. Is that a waste of time? —The preceding unsigned comment was added by 88.111.178.137 (talk • contribs) 22:57, 31 July 2006 (UTC)

It's not a waste of time at all when you make suggestions, or even ask questions. That sentence is a good thing to point out. The word "schichten" is not even an English word and should be replaced with "parts", for starters. "Subordinate" I guess refers to the fact that the "#IV7" is an Aug6 prolongation of the chord "IIb", which isn't one of the primary chords of tonality. The whole sentence should probably actually be stricken.

I'm sorry to have complained back at you. It's just that, yeah I was already watching this page because I know it needs cleanup. I'll get to it sooner or later, but the main thing I was trying to say is that: if you've got questions, please ask them; if you've got suggestions, please make them. - Rainwarrior 23:09, 31 July 2006 (UTC)

There is some interesting stuff in W.A. Mathieu's book "Harmonic Experience" about augmented sixth chords. He claims that the name is essentially wrong and misleading, resulting in all kinds of confusing and misleading explanations of what these chords are, harmonically. Adding to the confusion is that the chords are "conceived of being an (altered) triad with an Ab root" (in the key of C), resulting in the notation bVI#6, or, spoken, "flat six sharp six chord". And that the German version's Eb note (key of C) is often misspelled D#, adding more confusion. His take on the augmented sixth chords is based on a mixing of overtonal and reciprocal energy -- the (key of C) Ab being submediant to the tonic and the F# being the tonic's dominant-dominant-mediant (C-G-D-F#). The chords are thought to have an Ab root, but the French version especially makes as much sense as having a D root. Then there is stuff about how the augmented sixth chords and the dominant seventh chords are "diaschismic pairs" -- different in terms of overtone/reciprocal energy, but enharmonically equivalent in equal temperament. Personally, I'd long been confused by the augmented sixth chords until I read his take on it. Every other music theory text I've seen does a terrible job of explaining them. Has anyone heard of Mathieu's explanation? If I find the time I can try to add it. Pfly 03:50, 13 March 2007 (UTC)

E minor

Hey, I just happened to work out the German augmented sixth used in the graphic at the top for myself, and it seems that it's basically an Fmaj Augmented sixth, but built from the tone A (i.e. the F is an inverted minor sixth) - so this ought to resolve to either E minor or E major, depending on the key of A - and beneath the graphic it says it is in A minor, but it resolves to E major - isn't this an error?? 71.58.57.23 02:04, 17 March 2007 (UTC)

The dominant (V) in the key of A minor is an E major chord (all dominants are major). You can check almost any piece of classical music written in a minor key to verify this. - Rainwarrior 03:39, 17 March 2007 (UTC)

I'll verify that too. However, I do notice one more specific problem in that graphic, which you may or may not deem irrelevant--the Ger6 chord resolving directly to the dominant is typically considered bad voice-leading because of the parallel fifths (in this case, if I remember correctly, they're shown in the bass and tenor). The typical way of avoiding this is the 6/4 dissonance over the dominant, but I don't know if this is relevant enough to the topic at hand to warrant changing the graphic. Just thought I'd point it out. maestro 09:03, 18 March 2007 (UTC)

The German Sixth section of the article makes a comment about the example picture and parallel fifths. I thought adding a suspension to the picture would make it less clear as to which chord was which. Do you think it needs to be changed, or alternatively do we need more description in the article about it? - Rainwarrior 23:38, 18 March 2007 (UTC)

No, actually the description in the article is sufficient, I just didn't see it before. Sorry! maestro 22:25, 21 March 2007 (UTC)

Dominant 6/4

Uh oh, someone's finally gone and done it. And now we have to get into the dominant 6/4 discussion. The new, Schenkerian approach, which is starting to become widely accepted (the Royal Conservatory of Music's Toronto centre has started to recommend it to other Canadian branches) is that the dominant chord with the familiar 6/4 accented dissonances be called V 6/4, because roman numeral analysis should reflect function and not merely the notes. Calling it I 6/4 tells you nothing about the function of the chord (unless you're someone who was brought up with the unnecessarily roundabout explanation that I 6/4 counts as a dominant chord). maestro 13:02, 2 May 2007 (UTC)

I agree with this. When listed out of context "V 6/4" should be taken to mean the dominant chord in this particular inversion. "I 6/4" is something else except in the context: "I 6/4 - 5/3", in which case the 6/4 is not the chord's inversion, but rather a figured dissonance of the root position I that follows. Calling V 6/4 a I 6/4 is like calling I 6/3 a III 6/3. Roman numerals shouldn't refer to bass, but rather to function. - Rainwarrior 15:33, 2 May 2007 (UTC)

I agree too that this six-four chord has nothing to do with I – it is obviously a V with two suspunded tones. I think it should be referred to as the Cadential six-four (or 6/4) (that's the way it is being referred to in "Harmony and Voice Leading"), since the name V6/4 on its own is really confusing. The name V6/4 is usually used when writing harmonic degrees under the music (as I did in the M. Haydn example) when it is resolved to V3/5 in root position, and then it's clear that the sixth is resolved to the fifth, and the fourth to a third, and it does not appear to be an inversion of V. FraKctured 20:37, 8 May 2007 (UTC)

Unfortunately the article is now all mixed up and inconsistent, even if it wasn't before. Look at this already obscure and unhelpful sentence, from the section preceding the one in question:

French sixths can also resolve to the tonic, though usually such "resolutions" are the result of chromatic neighbor inflections or passing chords (usually from V 4/3 to I).

Here "V 4/3" might be taken as a second inversion of V⁷ chord. And that's how it would be taken by most readers moderately familiar with standard notations. But it seems that what is intended is something like "V 4 - 3", if we were to adapt slightly Rainwarrior's notation in his "I 6/4 - 5/3" (above). To put it briefly, if "6/4" has its "6" and "4" simultaneous, so should "4/3" have its "4" and "3" simultaneous.

In this article, and in the Wikipedia music theory articles in general, clear conventions need to be settled on and respected. They should also be lucidly explained somewhere, and there should be links to that location from all articles using these conventions. Where there are divergences in common usages, they should be carefully noted. Meanwhile, this article fails to communicate its meaning.

– Noetica^♬♩ Talk 23:22, 8 May 2007 (UTC)

I agree with Noetica here... although I haven't recently checked the Fr6 part of the article, in standard (computer) notation, the forward slash is used to indicate simultaneities and the hyphen/dash to indicate motion. If indeed the article intends to convey a dominant chord with motion on top of it the proper notation should be V4-3, or better yet V(4-3). maestro 13:24, 9 May 2007 (UTC)

Actually, looking at the example more closely (I was just responding to the talk post, I hadn't looked into the article), I think it is rightly the I 6/4 by the reasons I outlined, or more accurately V with a 6/4 suspension. It might seem nice to add little tidbits of information like how things commonly resolve, but I would agree that here it is rather muddled. The pictured M. Haydn work has a very nice example of how the German sixth can proceed through that suspension to V without parallel fifths, but simply trying to list the chord names and inversions is probably not descriptive enough to someone who isn't already familiar with it. A more simple picture might be a good way to help explain this properly (I don't have any notating software installed on this computer or I'd make one now; maybe in the future though). - Rainwarrior 05:23, 9 May 2007 (UTC)

What I think we really need is to call it either cadential or dominant 6/4 and create an article on it. It's going to come up in all sorts of music theory articles and it's worth a detailed discussion that can't happen in every article.

FWIW -- I don't know many music theorists under the age of 40 who really care about the whole issue any more. Last year at MIT we used a text (Clenningden and Marvin) which called it V64, next year we're using Benjamin et al. where it is I64; this particular point was not ever raised as a concern by the theory faculty. I certainly teach both (or all) interpretations to my students and expect them to read analyses which use either.

As far as notation of the figures, could we use the superscript and subscript on V⁶₄ or is there any other way? We might need to upload graphical versions of each of these terms. --Myke Cuthbert 19:50, 14 May 2007 (UTC)

Try using LaTeX: <math>\mathrm{V}^6_4\,\!</math> == $\mathrm {V} _{4}^{6}\,\!$. The \,\! is important so that everyone sees the image, and not the HTML representation (which is this: V₄⁶). Gracenotes^T § 22:59, 14 May 2007 (UTC)

The problem with simply notating the chord as V⁶₄ is that it is the exact same notation as a second inversion dominant triad. This article is, obviously, pointless if it is not intended for readers who do not know the typical resolutions of a German augmented sixth chord to begin with, so specification is obviously necessary, but the current edit seems a tad verbose. Perhaps we could notate the chord as a V8/6/4? That notation specifically denotes a cadential 6/4 chord, and it could simply link to the cadential 6/4 chord page. --SockEat 22:51, 14 May 2007 (UTC)

I like this format for the chords:

I $_{4}^{6}$ – V $_{3}^{5}$

This is very similar to user Gracenotes' suggestion. There are technical questions that Gracenotes or someone else may be able to help with, like how to include such additions as ° and ^♭ in the superscript and subscript elements. But along with deciding on and implementing such things, we ought to deal with some other matters:

• More general conventions for naming and labelling chords. First let me say that I like Myke's remarks about making an article about the whole I $_{4}^{6}$ versus V $_{4}^{6}$ thing. This issue is indeed worth special treatment for its own sake. At MIT there are, I'm sure, innumerable opportunities to clarify the issue; but here our readers can only look things up and hope for the best. Let's help them with an article. And then, of course, easy reference can be made to it in any other music article. Also, a comprehensive article devoted to the naming and conventions for chords more generally, covering and comparing the various protocols, would be a great asset. I don't think any existing article does this properly.

• The theory of these augmented sixths needs to be sorted out in discussion here. I'm sure that we jointly have the talent to manage that well.

• The terminology and technique of exposition needs to be discussed. We don't have links for some terms, so if they are to be used here they need to be introduced properly here. An example, from a paragraph I recently deleted: chromatic inflection. Looks simple, yes? But it will confuse and dismay some readers, and in fact it does have more than one meaning. I intend to add something explaining these meanings at Diatonic and chromatic, when I next wax enthusiastic about that article. Meanwhile, let's watch our language!

As I have said before, elsewhere, we have a chance to excel with the music theory articles, but at the moment they are undisciplined and chaotic. I for one will be happy to collaborate in fixing all this – if a group of us will work in a sustained way and with commitment, contributing where we are experts and deferring to others where we are not.

– Noetica^♬♩ Talk 04:53, 15 May 2007 (UTC)

This is the great quick work toward a consensus on a controversial subject that makes me proud to work with people here. I think the last I $_{4}^{6}$ or V $_{4}^{6}$ looks really good (thanks to GraceNotes for the initial suggestions! I think we should use the important flag only when the HTML representation looks nothing like what we imply). Might I suggest that, given that there's no consensus in the music theory world, there won't be a consensus here ever on which is correct, and that we agree to treat the term like we do British vs. American English: one or the other term is used throughout a page, chosen by the first substantial contributor to a page, and that later editors employ the existing usage. (oh my, I just realized that we also have to deal with British chord labellings, which are another valid system). Are there Wikiprojects which we should run this by (I know Composers and Classical Music; is there a WikiProject Music Theory?)

SockEat -- two arguments might be made against calling the chord V8/6/4: the first is that I don't know of another source which has this usage, so we'd be creating a new term which might not be known elsewhere. Also, there are a number of cadential second inversion chords which don't have the bass doubled at the octave, so V8/6/4 could be called erroneous. --Myke Cuthbert 02:50, 16 May 2007 (UTC)

I've started work on a page which I propose to put at "Cadential second-inversion chord." If no one objects, I'd like to work on getting a working first version by the weekend. I just find it can be easier to start a big page if one editor commits to getting it beyond stub status as a start. I've put my proposed outline at User:Mscuthbert/sandbox. Best -- Myke Cuthbert 03:06, 16 May 2007 (UTC)

All good, Myke. Some thoughts:

• Since we need standard usages across several articles (for style of representation, and also for the matter of V versus I), I don't think it is workable simply to allow the "first substantial contributor" a right of choice, in this case. The style thing is more easily decided. As for V versus I, it is much harder. My own suspicion is that the cadential six-four is marked as I $_{4}^{6}$ far more often than as V $_{4}^{6}$; but I would defer to a well-established consensus, provided only that all other chords were labelled in a way that fits the chosen practice, and that the intent could always be understood readily, without constant recourse to notes.

• I think both issues need discussion at a place that reflects their generality, which is not here. Options include: Wikipedia:Manual_of_Style_(music), Chord (music), and Wikipedia:WikiProject_Music_terminology.

• It's great that you've started work on a cadential six-four article. I'll be happy to help. Two things:

1. While redirects can cover a multitude of sins, the naming of the article needs considerable care, which means that the next point needs close attention also:
2. I would urge that the article deal with all kinds of second inversions, not just cadential – and if just cadential, than also the plagal form, or plagal extension, IV $_{4}^{6}$ – I $_{3}^{5}$ (or should that be I $_{4}^{6}$ – I $_{3}^{5}$!?). Sometimes a $_{4}^{6}$ chord may be approached as if it were to be treated as cadential, but then it is left in such way that it needs analysis as a passing $_{4}^{6}$, or as something else again. (And vice versa, in fact.) The boundary is not so clear (one reason for favouring the tonic-root analysis of the cadential six-four, in my opinion).

– Noetica^♬♩ Talk 05:55, 16 May 2007 (UTC)

One has to differentiate chords from harmonic degrees. The Cadential $_{4}^{6}$ is a chord, not a degree. It should neither be designated as I $_{4}^{6}$ nor V $_{4}^{6}$, since these only need to symbolize harmonic degrees, and not chords created by voice leading and contrapuntal extensions of degrees. Hence, when analyzing a piece, and wanting to describe the melodic movement when such a chord precedes V one should use V $_{4}^{6}$ – $_{3}^{5}$, that way it is clear that the 6 of the chord resolved to the 5, and the 4 to the 3.

Understanding the history of this $_{4}^{6}$ chord will enable us to refer to it properly. This chord originates in the world of 16th century counterpoint, where every cadence always has the leading-tone suspended (1 of the mode) and then resolved (♯7 of the mode). This is exactly the same motion, only including a suspension of not only 1 but of 3 as well. But even in common practice compositions it is quite common to find a suspension of 1 (and not of 3), which will be described as V $_{4}^{5}$ – $_{3}^{5}$. How can you describe this kind of motion, which has almost the same effect, by simply using harmonic degrees such as I or V?

These chords is by no means I and have no function of I, it is V with two suspended tones. It is obvious that composers did not move at cadential moments from IV or II$^{6}$ (which usually lead to V at cadences), back to I and only then to V. FraKctured 15:22, 16 May 2007 (UTC)

With due respect to FraKctured and Rainwarrior, as far as WP policies go, there isn't really a "proper" way of referring to this chord or not. We should be reporting common usage and not trying to change the field of music theory, a field in which both I64 and V64 are in common usage. Rainwarrior says that "Roman numerals shouldn't refer to bass, but rather to function," but many music theorists disagree and say instead that the function is read from the roman numeral and any attached arabic numerals. (One example of lack of consensus: at Harvard, at least until four years ago, the first year theory used I64, second year V64, most upper division undergraduate I64, and graduate courses differed by professor). Saying that "WP uses X and X alone" does not exhibit a neutral viewpoint. Mandating one versus the other is also just going to lead to edit wars down the road and senseless reverting. I agree that a style of representation should be agreed upon. We could make (at least) two templates {{cadential-V-6-4}} and {{cadential-I-6-4}} which would insert the proper markup, have accessibility labels, and link to either the stylesheet or the second inversion article.

I will work on spelling out to the best of my abilities the relevant arguments for I and V labels on the page. I think I agree with Noetica that the page can have a broader scope and simply be called "Second-inversion chord," but the main focus will still be on the cadential second inversion. It's the most important usage and the one most in need of an article. I want to avoid six-four in the title, since it's not British/international usage. It'll take a bit longer, since we need a section on the stable second inversion chord after ca. 1950--which I suppose does have a bearing on what we call the dominant 6-4.

(As an aside, when talking about the chord as a double appogiatura into the dominant, some V people are really sticklers for the form $\mathrm {V} _{4-3}^{6-5}$ with the double em-dashes and no repeated V, and consider V $_{4}^{6}$ – $_{3}^{5}$ or V $_{4}^{6}$ – V $_{3}^{5}$ almost as wrong as I $_{4}^{6}$) -- Myke Cuthbert (talk) 17:16, 16 May 2007 (UTC)

One problem created from naming the page "second inversion chords" or anything of that sort is that if you give it a Roman numeral V, it is no longer considered second inversion. Instead, you have a root position triad with a double suspension. Essentially, if you call it a second inversion chord, you are accepting I as the correct notation. However, I can't really think of a better way to describe it, given the language barrier (sorry we Americans don't speak English), so I guess we can call it a second inversion chord in the title of the article and simply explain its function. I also agree that $\mathrm {V} _{4-3}^{6-5}$ is the best possible notation to use on the pages whenever possible because it leaves no ambiguity, and I think that's the main thing we want to avoid. --SockEat 23:02, 16 May 2007 (UTC)

I think we're a bit off topic here. The point we should be trying to communicate here on this page is that the parallel fifths that arise when resolving to V from the German sixth chord are often avoided by using a suspension. Neither notation makes this clear to someone who isn't already familiar with the notation already. To say that it resolves to either I 6/4 or V 6/4 is a poor way to communicate the idea, because this chord is not a point of resolution. A detailed explanation of the two possible notations will not help this article (but it would be very nice to have a note about it in some sort of Cadential six-four article). The reason I suggested I 6/4 instead of V 6/4 before wasn't that I think it's the best notation for a Cadential 6/4 (the figured suspension I think is the best), it was that taken out of context there is no way to intuit that V 6/4 means something other than a 6/4 inversion of a V chord. You have to already know about it to understand what it means (more or less defeating the purpose of the article). - Rainwarrior 05:07, 17 May 2007 (UTC)

"To say that it resolves to either I 6/4 or V 6/4 is a poor way to communicate the idea, because this chord is not a point of resolution." -- good point! An elegant solution to the problem at least here. (I personally believe that there are such things as partial resolutions, but I have no evidence for it, so it's basically OR.) I do think though that anyone who is reading about Aug6th chords will already know about cadential 6/4s (and have their own opinion about nomenclature), just given how almost all music theory instruction is structured. Probably a better use of all our energy on this article is getting more examples of each chord in context. (it was great to find this article already well developed). -- Myke Cuthbert (talk) 05:36, 17 May 2007 (UTC)

If we change the musical example at the top of the page as Tony would like, so as not to introduce "Mozart fifths" right off the bat, I suppose we're back to square one--unless we invert the chord (probably not a good idea) or neglect to label the chords of preparation and resolution (or "partial resolution", if you like)--, but I'm inclined to think that ducking is not a real solution anyway. TheScotch 21:40, 27 May 2007 (UTC)

Parallel fifths in the example

The example at the top will need to be fixed. The last three chords are at issue.Tony 13:25, 26 May 2007 (UTC)

I see that this is alluded to further down. But why what is a relatively rare occurrence, which is problematic in many textures, should be paraded at the top as a basic example, is a mystery. Furthermore, I can't see why all three types of aug. 6th chord are shown together in a highly unlikely and, frankly, unmusical connected passage. Sorry to be critical, but there are lots of misleading things here, and the explanation is overly complex and roundabout. Tony 13:38, 26 May 2007 (UTC)

How do you assert that this is an erroneous issue? Can you point to a text which does not give the German augmented sixth as an exemption to the parallel fifth rule? They even have a name, Mozart fifths, since they are so common. You've left a couple of messages on my talk page asserting that you know how music theory should work and that textbooks and other reliable sources are wrong. On what basis should we trust your knowledge of the topic over peer-reviewed published authorities? -- Myke Cuthbert (talk) 06:24, 27 May 2007 (UTC)

I agree with Tony that it would be better to have three separate examples, one for each "common" augmented sixth chord. The examples wouldn’t necessarily have to be non-contiguous on the page; they would only have to be expressed in a manner that makes it clear they are not together supposed to represent a single musical passage. I take it that the B in the French augmented sixth chord goes to G# in the following E major triad rather than to another B so that the A in the tenor voice of the French augmented sixth chord can go to B so as to avoid a diminished fourth (G# to C) as the tenor voice moves from this E major triad to the following German augmented sixth chord. Separate examples would ameliorate this slight infelicity--if infelicity it be.

You may have overlooked the circumstance that in this example we have a set of parallel fifths besides the "Mozart fifths" created by the resolution of the German augmented sixth directly to the dominant--without a suspension or a cadential I 6/4 chord interposed: The perfect fifth between the bass and tenor voices in the chord that precedes the German augmented sixth chord are also parallel to those in the German augmented sixth chord. (Yes, "Mozart fifths" are common, but arguably not as common as the interpositions I've described.) TheScotch 21:16, 27 May 2007 (UTC)

Um ... don't call it a I 6/4, but just a 6/4. It's clearly not a tonic triad (it's the dominant triad, of course). We really have to move beyond this 19th-century idea (which sadly persists in the 21st century) that you can identify the root by "de-inverting" a chord. It just doesn't work that way, much of the time. Why? Because chord positions are often generated melodically - by linear movement of the voices - as opposed to harmonically. The mere coincidence of G, C and E in a chord doesn't mean that C is the root. It's contextual and functional, not a simple prescription based on a single-chord perview. Tony 06:31, 28 May 2007 (UTC)

Sorry, Tony, but Wikipedia's job isn't to debunk theories which are still active in the 21st century. I realize there are many texts which discourage the description of this chord as a second-inversion tonic chord (and with very valid arguments), but we can't referee different theories. —Wahoofive (talk) 19:19, 28 May 2007 (UTC)

I agree with Wahoofive. That's very POV talk, Tony. I'm sure you know that. A contrary position, current in the literature now and throughout the 20th century, is at least as supportable. A position that combines elements of both extremes is even more supportable. What's more, as I point out below this is a general issue affecting several articles, and it should therefore be dealt with elsewhere if those articles are to benefit from the discussion. There are enough problems specific to this article, of course. I'm with you on that.

– Noetica^♬♩ Talk 23:31, 28 May 2007 (UTC)

Well, I'm not giving in on this one. It's going to fester, I'm afraid. Tony 07:53, 29 May 2007 (UTC)

Ah, I ignored those parallel fifths once I realized that the three examples were supposed to be separate. I admit that I found that confusing at first also, but we've already resolved to change it as part of the general article improvement. -- Myke Cuthbert (talk) 23:43, 28 May 2007 (UTC)

Good.

Re: "Um ... don't call it a I 6/4, but just a 6/4.":

I think I should be allowed to call it whatever I think it reasonable to call it in a discussion page, as long as no one discussing the article in question is confused about what I mean. If I'd put that in the article proper, then we could reasonably (or unreasonably) fight about it. TheScotch 18:34, 29 May 2007 (UTC)

You're "allowed" to call it anything you like, but that won't stop my objecting to your choice of words here. Tony 03:24, 17 June 2007 (UTC)

Opening sentence

Re: "An augmented sixth chord is a chord containing the written interval of an augmented sixth between two of its notes.":

The phrase "between two of its notes" seems to me redundant. Isn't an interval always "between two...notes"?

The qualifier "written" seems to me to war with the next paragraph, which strains to demonstrate that the augmented sixth is functional, rather than merely a notational convenience or tradition. TheScotch 11:17, 27 May 2007 (UTC)

Not sure about the written or not, but I think that the "between two of its notes" is both redundant and simultaneously helpful. Except for David Lewin's generalized intervals, you're right, an interval is generally between two notes, but I think it's worth pointing out that to make something an a6 chord, we just need one a6 and only two pitches need be involved. -- Myke Cuthbert (talk) 15:13, 27 May 2007 (UTC)

Re: "Not sure about the written or not, but I think that the 'between two of its notes'" is both redundant and simultaneously helpful.":

I think redundancy within a single short sentence nearly always creates confusion in and of itself. (It is also, of course, offensive to logic and to a literary sensibility.)

Re: "Except for David Lewin's generalized intervals, you're right, an interval is generally between two notes, but I think it's worth pointing out that to make something an a6 chord, we just need one a6 and only two pitches need be involved.":

There are other ways to express this. If we eliminate both written and between two of its notes we may end with something on the cusp of tautology, but if so, we are merely disguising the banality now, and I don't that there is a rule stipulating that the first sentence of every wikipedia article must be in the form A(n) [title of article] is a(n) [definition]. TheScotch 20:51, 27 May 2007 (UTC)

Re: "I don't that there is a rule stipulating that the first sentence of every wikipedia article must be in the form 'A(n) [title of article] is a(n) [definition]'": Agreed completely! Here's an attempt at a new lede:

Chords containing an augmented sixth became an important compositional device in the late eighteenth and nineteenth centuries. This dissonant interval, generally found between the ♭6 and ♯4 scale degrees, typically resolves via contrary motion (typically outward by half-step), each to scale degree 5 with the new chord implying dominant harmony. Thus augmented sixth chords are usually used as substitutes for more common pre-dominant chords such as IV and ii.

Most augmented sixth chords also include the tonic note of the current key and may also include a fourth pitch. The most common augmented sixth chords have names which imply national flavors (Italian, French, and German), but are not found more commonly in the music of that country. The "Italian" augmented sixth is a three-note chord built on scale degrees ♭6, ♯4, and 1. The French and German chords add to the Italian chord degrees 2 and ♭3 respectively.

Thoughts? I tried to work in a definition (including all three common chords), a period of usage, and how they are used in pieces all in one short section. By the way, just since I was curious, and probably should be added somewhere: Piston, Aldwell and Schachter, and Benjamin et al. use "Augmented sixth chord," while Clendinning and Marvin use "Augmented-sixth chord." I think the latter is more correct English, but the former seems to be the consensus usage of experts. (I'm going to go make the abbreviations It and Ger etc. smaller in the article--they're usually in the normal typeface size.) -- Myke Cuthbert (talk) 23:43, 28 May 2007 (UTC)

Myke, first concerning the hyphen. Yes, conventionally augmented-sixth chord would be more "correct", but usage and other considerations work in favour of omitting the hyphen, I think. Second, I think there are some small infelicities in your new wording, but that's OK. Other things have priority right now, as I see it. Third, I like the change you made to It, Fr, etc. But you might consider making them bold, to match the other chord indications. Fourth, I am mystified by this text:

The doubly-augmented or ♯2 form of the chord combines the sonority of the German chord with the approach and resolution of the French chord. On account of this mixing of national characters, the chord is sometimes called "Swiss" or "Alsatian" chord. The "doubly-augmented" designation comes from the presence of two augmented intervals, augmented fourth and the augmented sixth, and not from an actually doubly-augmented sixth, such as between A-flat and F-double-sharp.

Given practice established elsewhere in the article, you can only mean the raised second degree by ♯2, right? But that would be enharmonically the same as ♭3. So are you speaking simply about a re-spelling of the German sixth chord? Or what? How can it be, in any case, that this variant of the German sixth chord is notable for including an augmented fourth? All of the standard chords discussed include an augmented fourth (1–♯4); and the French chord includes an additional augmented fourth (♭6–2). So what are you saying about this modified German chord, and precisely why? (Note that ♭6–♯2 is a doubly augmented fourth.) :)

– Noetica^♬♩ Talk 05:46, 29 May 2007 (UTC)

Ah, meingott! you are right. I've completely flipped my mind--and will fix--was not thinking straight. The ♯2 form is an enharmonic respelling of the German sixth chord, but it's sometimes treated separately because of the need for ♯2 to resolve upward to 3 which more often takes one to a cadential 6/4 chord than directly to the dominant. Will bolden the It., etc. -- Myke Cuthbert (talk) 17:01, 29 May 2007 (UTC)

No problem, Myke. Easy to slip up on these things. All fixed now. By the way, I have sources for Swiss sixth, but not for Alsatian sixth. Where have you seen that? It's interesting that people want to give novel names to these things, isn't it? I don't see that a mere re-spelling should amount to a new chord, nor that the means of resolution motivating that re-spelling should change the way we name the chord. Not by itself, anyway. (I must look up the Australian sixth that someone proposed a few decades back. I forget the details and the exact name; and I am away from my music-book collection right now.)

– Noetica^♬♩ Talk 01:21, 30 May 2007 (UTC)

• The hyphen: I don't mind either way, although I probably have a slight preference for without, because it looks nicer. Whichever variety this is written in, North American writers nowadays prefer not to use a hyphen unless it's necessary to disambiguate; others if it makes it easier to read (Fowler's prescription). Despite its being a double epithet, it's so up-front in the article that the hyphen is not necessary for easy recognition. But I'm easy. Tony 07:29, 29 May 2007 (UTC)

• I see that "chord" is linked, but the repetition at the start is ungainly. "Written" will confuse many readers; it's more than written—it's conceptually an aug. 6th (as opposed to a minor 7th). Remove "written" and explain later? Tony 07:34, 29 May 2007 (UTC)

• "Voice leading" describes just the movement of parts in relation to each other, which is what is intended at the start of the second para. "Counterpoint" involves rhythmic individuality between the parts, which is not necessarily at issue here. Why is the V7 thing mentioned at the opening? It involves only the German 6th, and is kind of jumping the gun, isn't it, before the typical harmonic function is exposed, as it should be, in the lead. Sorry, extra dot in my edit, I see. Tony 07:46, 29 May 2007 (UTC)

French sixth

Re: "This creates a rather unique sonority that is both inversionally symmetric, and transpositionally equivalent to itself at the tritone.":

If we're going to be sticklers about the spelling--and I think we're obliged to in this article, given its premise--then this chord is not "transpositionally equivalent to itself at the tritone" (B D# E# GX v. F A B D#). TheScotch 12:20, 27 May 2007 (UTC)

I disagree. Not only is the tritone not a specific interval, but also composers use whatever spelling they feel like to communicate augmented-sixth chords, hence the permissibility of the "doubly-augmented" German sixth. This is especially true when the sonorities are taken to have more then one meaning (approached as a German sixth, resolved as a dominant, etc.). Since composers aren't sticklers about spelling, why should we be? The point of the statement in the article is that it can function as the same chord at the tritone, because it's the same set of sounding intervals. maestro 15:52, 27 May 2007 (UTC)

The tritone is an augmented fourth, hence the name. Donald Tovey, for one, is Adam Ant about this, and I think he's right to be. Whether a tritone can also be a diminished fifth is irrelevant to the argument, however: If we transpose F A B D# up a diminished fifth we get Cb Eb F A.

Composers are sometimes sticklers about spelling and sometimes not. When writing augmented sixth chords they generally are, which is rather why we bother to call them augmented sixth chords. Yes, the doubly-augmented sixth chord is often spelled equivocally, but, in the first place, this is merely a quibble, and, in the second place, there is a difference of opinion about whether its equivocal spelling should be permitted; Walter Piston says it should not be.

In any case, I'm not happy about the way the phrase "transpositionally equivalent" is used in this passage either. We can easily side-step both problems simply by remarking instead that we get an enharmonically equivalent chord by transposing at the tritone. In addition to much greater accuracy, we then also have the virtues of greater clarity and ease of understanding, considering that the phrase enharmonically equivalent will be more familiar to most readers. TheScotch 20:40, 27 May 2007 (UTC)

Much more to the point is that it's useless trivia whether it's invertible this way, since such a use is extraordinarily rare (if not absent) in music literature (even in jazz). Contrast this with the diminished seventh chord, whose enharmonic inversional equivalence is often used for modulation purposes in the literature (which, by the way, crushes the idea that the Fr6 is a "unique sonority" in this way). What does appear in the literature (though not in the article) is the exploitation of the enharmonic equivalence between the German sixth chord and the dominant seventh (e.g. in Richard Strauss) and the inverted form of the chord ("diminished-third" chord?), which makes a notable appearance in Bach's B minor mass. I'd much prefer that these articles focus on what composers routinely did with the tools rather than what set-theory games can be played with the simultaneities. —Wahoofive (talk) 15:23, 29 May 2007 (UTC)

Another missing variant: the irregular resolution of the German sixth to the dominant seventh (in which the sharped fourth scale degree resolves down instead of up), creating parallel motion in all voices. This is a very characteristic feature of barbershop music. —Wahoofive (talk) 15:35, 29 May 2007 (UTC)

Re: "...(which, by the way, crushes the idea that the Fr6 is a "unique sonority" in this way)":

Good point. This "unique" must go.

"What does appear in the literature (though not in the article) is the exploitation of the enharmonic equivalence between the German sixth chord and the dominant seventh (e.g. in Richard Strauss) and the inverted form of the chord ("diminished-third" chord?), which makes a notable appearance in Bach's B minor mass."

Another good point. More common and historically entrenched musical puns--as Tovey calls them--should have priority. TheScotch 18:45, 29 May 2007 (UTC)

That's a nice Toveyism I wasn't aware of. This enharmonic equivalence is used as a fast way into the key of the raised seventh degree, and conversely of the flattened supertonic. Kewl effect. Tony 06:27, 1 June 2007 (UTC)

I’m not quite sure I follow this. If we assume we’re in the key of C minor, our stereotypical German augmented sixth chord in first inversion will be Ab-C-Eb-F# (a raised subdominant chord). If we spell the chord enharmonically as Ab-C-Eb-Gb, then, yes, it becomes the dominant of Db, the lowered supertonic in respect to C minor. I can’t think of a spelling that would make this chord function as the dominant of B, the leading-tone in respect to C minor, however. (Yes, the root of an F# German augmented sixth chord is also the root of the dominant of B, but "a fast way into" a tonicization should depend on chord quality as much as chord root.) Neither am I familiar with this term kewl. What is a “kewl effect”? TheScotch 05:34, 2 June 2007 (UTC)

In C major, go straight to G7. Respell as G–B–D–E#. G slips down to F# and E# slips up to F#, and you have an F# major chord, V of B major/minor. It's the reverse process, and an extraordinary effect of being swung around 180º. "Kewl" is an alternative spelling of the teenybopper's word, "cool", i.e., excellent, desirable. I used it ironically. Tony 06:04, 2 June 2007 (UTC)

Okay, I see: It's the same pun. When you said "the key of the raised seventh degree", I assumed you meant the raised seventh degree of the key to which the German augmented sixth chord is (stereotypically) native. (Actually, I still don't see why you said raised seventh, if you had in mind a major key.) Anyway, thanks for the explanation. TheScotch 09:14, 2 June 2007 (UTC)

I did mean that. B natural of c minor. Tony 00:30, 15 June 2007 (UTC)

Just above you said C major--and "G-B-D-E#" is (stereotypically) native to B minor, not C minor. TheScotch 05:33, 15 June 2007 (UTC)

What is to be done?

A consensus seems to have emerged that this article now needs coordinated and systematic work to raise it to the next level of quality. Like many or most of the music theory articles, it has evolved rather chaotically. It is not surprising, to students of the Way of Wikipedia, that such articles should need rethinking after their first couple of years. What is remarkable is that there is so much good information in them! We should respect the work of those who brought them to their present state, for at least assembling the material, and marshalling and maintaining it as well as they have.

Looking at the discussion above, we see evidence of dissatisfaction with specific content. But we also see some broader and some more basic issues raised, and it is not reasonable to deal with those here. That would be extremely inefficient; and it is not necessary, because there are other substantive articles with talk pages at which these issues are more usefully and effectively discussed (like spellings of the tritone, and precise regimented meanings for that term); and where there are not such articles, they can be made and perhaps should be made (like the article proposed above for six-four chords, whether cadential or not, and their proper naming and indications); and where issues are very broad and affect several articles, there are suitable places for principles to be laid out also (like how to indicate chords generally, with their various modifications and inversions, which is appropriate for Wikipedia:Manual_of_Style_(music): a neglected resource).

I think these issues have priority, and that we should focus on them before attempting to fix relatively complex problems specific to augmented sixth chords. So I suggest we all adjourn to Wikipedia_talk:Manual_of_Style_(music), call in a few other music active editors (by putting notices in the talk pages of relevant articles), and set an agenda for discussion there, and for discussion and action elsewhere as well.

What do people think about that? For myself, I am reluctant to take on much else until we have more orderly ways of operating worked out. Perhaps if we set up some sort of an overall program for the music theory articles, we can respect each other more and waste less time promoting our own prejudices and preferences, and more on making real progress that will be useful and satisfying for everyone concerned. We could then each use the skills we have – writing and improving text; the technicalities of tables, musical examples, etc.; or particular expertise with content – to produce articles that are deficient in none of these departments.

– Noetica^♬♩ Talk 02:35, 28 May 2007 (UTC)

While I support in general your proposal to discuss these matters all together at a central location, the augmented-sixth chord presents unique challenges, because it has been a controversial chord subject to various theoretical interpretations from the 18th century to the present day. What is needed most seriously in this article is a historical overview of theory of this chord, which wouldn't really be necessary for other structures. I took a survey class of the history of music theory in graduate school, but I seem to have misplaced my textbook. —Wahoofive (talk) 04:33, 28 May 2007 (UTC)

Sure, there is specific and specialised work to be done here. I have not said or thought otherwise. It's just that so far we haven't developed a systematic way of discussing these things, and a whole lot of other incidental disputes keep breaking out. Some of those are on more fundamental matters, and it would be profitable to give them some priority. Personally, as I say, I am not interested in development work for an article where we can't even decide on how to label chords at it. That's pretty basic, and failure to address it early means continuing failure in clarity: here and at many other music articles. Hope to see Glad to see you at Wikipedia_talk:Manual_of_Style_(music) also, Wahoofive!

– Noetica^♬♩ Talk 05:11, 28 May 2007 (UTC)

Tony's inline question

The raised sixth indicates its usual method of resolution: it functions as a leading tone, much like the third of a dominant chord, which resolves up a semitone.

Agree with Tony that this is too strong. Chromatically-raised tones do tend to resolve upwards, but that doesn't necessarily make them leading-tones. If I'm resolving C major to F major, and decide to color the C chord by making it augmented, that still leads upwards but doesn't tonicize A. Similarly, the augmented-sixth move to the dominant is unquestionably heard as a half-cadence (generally a variant of iv6-V), not a tonicization of V. —Wahoofive (talk) 15:31, 29 May 2007 (UTC)

I suspect that the article is either attempting to use the term leading tone in a different sense or that it means the raised sixth functions in a way analogous to the way a leading tone functions. In either case, as it now reads it is probably misleading. TheScotch 18:51, 29 May 2007 (UTC)

The closest thing to a leading tone in a +6 chord is when a Ger+6 is used enharmonically to the V/bII or V/N, and in that case it turns the tonic into a leading tone rather than the #4.--SockEat 20:41, 20 July 2007 (UTC)

score excerpt at bottom

There are no clefs. For a scanned file, these would have to be cut and pasted. In any case, why not a short-score example, or one of keyboard music? Tony 22:37, 29 May 2007 (UTC)

Fair criticism. I have re-uploaded the image to include clefs and key signatures (also essential). —Wahoofive (talk) 01:42, 30 May 2007 (UTC)

Thanks for that, but can I be a total bore and suggest that in an encyclopedic article, the examples should be as simple, regular and easy to understand as possible? The problems here are that the "inverted" version in the example is an unwanted complication when trying to get across the basic idea to the readers, many of who won't be good at reading open score. It's such a difficult concept, so why not a straightforward example with the E flat in the bass? Why not use keyboard music (or keyboard reduction)? The chord in question could be highlighted with an arrow. Then there's a niggling issue that a heavily tampered-with 19th-century edition is used, with lots that Bach didn't write (ppp, commas, caesurae). It should be flagged as a vocal score, not a full score. The movement? Perhaps even the year of composition (or the 1730s, given the fuzziness of that notion).

The intent is to show a variant, which is why it's buried at the bottom of the article. Such variants (as well as the barbershop one I mentioned elsewhere) belong in the article somewhere, but I certainly agree that conventional uses should get more prominence. The edition I chose was one with an expired copyright and freely available on the web; if someone has a better example, by all means replace it. And if you'd like to improve the caption, be bold! —Wahoofive (talk) 15:36, 30 May 2007 (UTC)

Sample new opening

This is what I've written off the top of my head, so it probably needs tweaking.

The appendix of Charles Rosen's The classical style may be a good reference for the second statement.

Are there three or four types? It doesn't matter, just change the three to a four if necessary—I haven't looked properly at the rest of the article. I've deliberately restricted the info to what applies to all types of aug 6 chord, and to a basic overview.

The all-in-one figure at the top, I think, needs to go, and should probably be replaced with separate examples of each type in progress to V. Much simpler. In fact, for each type, why not the parent chord first --> the chromaticised version (in closed chords), then a second example on two staves of the aug 6 --> V? Locate them all in c minor?

_________________________

An augmented sixth chord contains the interval of an augmented sixth above its bass. The chord was occasionally used in the Baroque and became a distinctive part of the musical style of the Classical and Romantic periods.[1]

The chord developed as a chromaticised version of two of the three "pre-dominant" chords—ii and iv—in the minor mode. These two chords, in inversion, are chromaticised by the raising of the sixth above the bass. This tone is spelled as an augmented sixth rather than a minor seventh because it rises by a half-step; it is this movement that gives the chord its power, propelling it towards the dominant chord.

Although augmented sixth chords arose from the minor mode, they are used in the major mode as well, where mode mixture is involved in creating a temporary window in the minor by borrowing from it the flattened sixth degree of the scale. Thus, in both modes, the bass provides additional propulsion by semitone towards the dominant tone, from the flattened sixth degree to the fifth of the scale.

There are three types of augmented sixth chord, each named after a European nationality, although the actual names are irrelevant to their origin and function.

_________________________

Since augmented 6th chords often lead to a V $_{4}^{6}$ – $_{3}^{5}$, there's a risk that we'll have to have two examples (one for single-chorders and one for the functionalists, ho-hum), with the same two rationales trotted out here as will have to be put into the inversion article; it would be nice to avoid it, but I'm not hopeful of this. Tony 03:36, 30 May 2007 (UTC)

It would be a good thing to add detailed examples to the individual chord sections, but it is not helpful in the least to remove this image. It is also currently referred to by the text of the three sections. - Rainwarrior 10:48, 1 June 2007 (UTC)

typographical query

Anyone know how to render single-digit numerals with a circonflexe above them, to stand for scale degrees? This thing: ^

And is it possible to render three figured bass numbers vertically, e.g., 7/4/2?

The circonflexe is easy: <math>\hat{6}</math> = ${\hat {6}}$

You could use a matrix to do 3 numbers: <math>V{\begin{smallmatrix} 7 \\ 4 \\ 2 \end{smallmatrix}}</math> = $V{\begin{smallmatrix}7\\4\\2\end{smallmatrix}}$

If this is used in an example next to two numbered ones, you may wish to use matrices for them as well (the empty cells can be filled in to keep the spacing the same): <math>I{\begin{smallmatrix} 6 \\ 3 \\ {} \end{smallmatrix}}</math> = $I{\begin{smallmatrix}6\\3\\{}\end{smallmatrix}}$

My personal preference was to use the sub/super scripts for one and two numbers: <math>V{}^6_{}</math>, <math>V{}^6_4</math> = $V{}_{}^{6}$, $V{}_{4}^{6}$

If the roman numeral is also included, both will render with the same spacings at least with all the wikipedia renderings of it I've seen (I understand personal settings can affect it though). Without this (as it is at the moment) the two and one numbered ones appear differently where I've seen it. - Rainwarrior 07:02, 1 June 2007 (UTC)

Thanks, Rainwarrior; you're a valuable asset to this project—my attempts to understand how to do these things from WP's how-to guides ended in chaos. My only further issues are how to make them smaller, so they read more smoothly in the lines of text, and how to adjust them so that they don't fall so markedly below the line. This is particularly the case with the ${\hat {6}}$. Thanks so much. Tony 08:13, 1 June 2007 (UTC)

I'm not sure if there's a good way to shrink things. Some of the math markup tags have small versions, but I don't know of a general "make everything smaller" tag. (There might be. Try reading Help:Displaying a formula if you haven't already.) There's also the problem that on different computers with different settings: Wikipedia will pick different things to try to render inline or not. You can force it to render as an image though with the right tag (I don't remember offhand what it is). In articles where it's come up I think I've been using bold instead of a hat and phrasing its first usage something like "scale degree 6". - Rainwarrior 09:05, 1 June 2007 (UTC)

First image

Rainwarrior, while praising your knowledge of markup, I have to bring up the matter of the first image. Although it took effort to conceive and construct it—thank you for that—there are several disadvantages.

• The passage doesn't make musical sense; it's a good example of how augmented sixth chords are not used in the real world. In particular, the movement from V to the augmented sixth chords is the reverse of their function. I don't think even explicitly flagging that it's a laboratory example would save it in this respect.
• There's the problem that parallel fifths are present. This might well be explained as Mozart fifths, but I put it to you that the topic is complicated enough without introducing what will be perceived as a grammatical query right at the start, unexplained (to explain it on the spot would be an undesirable digression).
• It contains nomenclature that is unexplained in the lead, and which would be better illustrated where it is explained, in the body of the article, preferably in a separate image for each type.
• The crotchet rest is apparently redundant.
• The audio excerpt flits past at an impossibly fast speed; I presume the strategy is to allow readers to hear what aug 6th chrds sound like generally, and to distinguish the three chords aurally (rather subtle differences). Either way, it's pointless, I'm afraid.

I'm envious of your ability to use Finale for these attractive illustrations, and would be grateful if you applied this skill to the production of more functional examples that will ease the uninitiated into a difficult concept. A much slower, single audio excerpt could be arranged, with a caption stating the order in which each type appears (each moving to V, I guess, then a pause).

I don't see the point in retaining the image in its present form. Tony 11:03, 1 June 2007 (UTC)

I don't have any notation software currently installed, but even the "Paint" application that comes with windows is quite suitable for making musical examples at a pinch. I encourage you to make some yourself. (I might get to it later if no-one else does, but right now it is not a high priority for me.) Despite the points you have made (and I think you've mentioned most of them already) I still don't agree that the image should be removed. I do agree that better examples for each of the three sections would be very good to have, but until we have these to replace it we shouldn't just remove this visual information from the article; and even then, I think it's a suitable way of summarizing all three in one place. 1. While this passage would obviously never occur in a real piece of music, the individual motion of V to an Aug6 and back does (though yes, 2. the German version would probably never be written with parallel fifth both going in and out like this). To put in a different starting chord for each of them and a suspension for the German would be too cumbersome for the lead image. 3. The "unexplained nomenclature" I don't see as a problem, because the alternative would be the same passage with no chord symbols (which I don't think is better at all). 4. The extra crotchet was just a matter of rhythmic taste, a rest on the weak beat after the cadence. It's not essential and could be removed if you like, but I liked it there. 5. I don't think the audio example is pointless for the same reason I don't think the whole image is pointless. It gives a quick overview of what an augmented sixth chord is. The many details of context and counterpoint are left for the rest of the article and more careful examination, but this image/sound at the top gives the general idea quickly. You seem to expect too much from the image, and then want to replace it with nothing (which is by default, not enough). Please await consensus before removing it again. - Rainwarrior 11:38, 1 June 2007 (UTC)

Well, leave it there for the moment, but I think that when we have individual chord illustrations, it should go, along with the unsatisfactory audio.

Is there a way of producing these notational images with a Mac and no Finale?

I have a crazy idea for a lead pic—from Bergman's Magic Flute film, the opening scene with the dragon and the three ladies—there are a few poignant aug 6th chords for dramatic heightening. But it's probably a copyright problem. Tony 11:44, 1 June 2007 (UTC)

I don't know how to make examples myself, but I want to stress again that we need a separate example for each kind of augmented sixth chord and that it should be immediately clear that each example is separate. TheScotch 05:16, 2 June 2007 (UTC)

Scotch, I agree with you about the need for separate examples. I think we should keep the existing composite one till we have alternatives, but with a caption that tactfully acknowledges its artificiality and error.

For the article as a whole I'd like to see a simplified and paradigmatic example for each of the three types, a couple of real-life examples in context illustrating standard treatments, and a couple of less common examples to show the flexibility with which these chords have been treated – like the rather tubular way Tony discusses above, taking us from C to B via a German sixth.

One or two of us are going to have to get organised with a quick means of making examples, and modifying them as people suggest improvements. In many of the music articles the examples are generated by well-meaning enthusiasts who have not been encouraged to work collegially towards such improvements.

– Noetica^♬♩ Talk 22:54, 2 June 2007 (UTC)

Inversions, occurrence on degrees other than ♭6, etc.

We need to be careful how we present so-called inversions of the standard forms of the augmented sixth chords. As things stand there is some treatment of these, but it's going to be confusing for many readers.

The matter is complicated, for beginners especially, by the fact that the chords can also be founded on degrees other than ♭6. Sure, functionally these might differ from the standard types on ♭6, and their motivations and histories might not be the same; but they still include the defining interval of an augmented sixth.

Different textbooks have managed the problem of classification differently, and the terrain is complex. Consider those allegedly built on ♭2, 4 (yes, Goetschius calls that one an augmented sixth chord, with its 4–♯2), or ♭5 – with or without the canonic major third.

And then of course we might want a more regulated treatment of variants on whatever degree that do not have that major third.

On the matter of supposed inversions once more, I don't think we should be dogmatic about the analysis of some of those. The article at present gives alternative analyses without any citation whatsoever, and I'm sure they are not universally acceptable.

Finally, how about citation in this article more broadly? Like many music theory articles, it has very little. Good to see a couple of sources listed, but with such complex matter we might have to document a bit more; and it is best to do this progressively, because it might be hard later to find support for otherwise sound and useful material in the article. I still think we should first give attention to more basic issues, since this article deals with one of the most complex topics in harmony. For that reason I won't do a lot myself on it, right now.

– Noetica^♬♩ Talk 23:35, 2 June 2007 (UTC)

I can only plead that the complications be dealt with later in time, and in the article, after a plain, simple exegesis of the standard phenomenon has be constructed. Tony 01:08, 3 June 2007 (UTC)

While I think Tony's right that the standard usages are inadequately treated and should get our principal attention, I'd like to ask Noetica if he can provide an example of some of these nonstandard usages, because I can't call any to mind. Anyway, wouldn't an Aug6 chord on another scale degree just be a borrowed chord like a secondary dominant? Don't they just resolve to secondary dominants? (Oops, I notice that the borrowed chord article only considers borrowing from the parallel key. Why can't you borrow from other keys?) —Wahoofive (talk) 15:06, 3 June 2007 (UTC)

There are cases where the aug6 chord is built on other degrees as part of either a temporary or large-scale modulation to another key. Off the top of my head, the quickest to come to mind is the It6 in the Waldstein sonata of Beethoven, mvmt 1, where I (C-major) becomes vi6 (G in soprano to A) which becomes It6/III via A -> A#; the chord resolves normally with an extended passage on the dominant of E-major before the second theme group comes in in E.

It's a great example of an aug6 in major which is not a borrowing from the minor, nor a temporary elaboration of a pre-dominant. -- Myke Cuthbert (talk) 16:43, 3 June 2007 (UTC)

I'm not on that track: aug 6th chords developed out of the minor mode and are used also in the major mode. Why is this an example of not "borrowing" from the minor? C natural is still the bass. That's degree 6 in e minor, even though the destination is E major. Tony 00:29, 5 June 2007 (UTC)

Myke, the modulatory examples are worthy of note, of course. But there are many non-modulating cases – from the Renaissance onwards – of augmented sixth chords occurring on degrees other than ♭6. Look at the last couple of chords in Schubert's great String Quintet: a huge Fr$_{}^{6}$ on ♭2, followed by a final tonic chord.

I am busy with other things for a while, but I have several other examples, and I'll present them here soon.

– Noetica^♬♩ Talk 00:22, 5 June 2007 (UTC)

Yes, I know about these chords -- I'm wasn't saying that there are only modulating cases, I'm just saying that these are another very common place to get aug6 chords not between #4 and b6. To respond to Tony--in retrospect, we can see the C as a borrowing from e-minor, but if you trace how the chord emerges in this case (and many others), the C is the (major) tonic at the moment the chord appears.

• But that's not relevant to the emergence of the chord from the minor mode, conceptually. Tony 05:46, 5 June 2007 (UTC)

Oh, and I have enough of a "don't care" attitude toward getting my edits in Wikipedia, that it doesn't really bother me, but Tony, I think it might have been common courtesy to have commented on my sample lede before writing your own and putting it up. I think that a lede that doesn't mention the "names" of the three most common augmented sixth chords and how they differ is a step backwards. -- Myke Cuthbert (talk) 03:13, 5 June 2007 (UTC)

• Where is your sample lead? Mine was posted on this talk page for quite a few days, and no one bothered to comment. What are you talking about? Tony 05:46, 5 June 2007 (UTC)
  • Above, under "Opening sentence," where the discussion of rewriting the opening was going on. -- Myke Cuthbert (talk) 21:05, 5 June 2007 (UTC)

Myke, your earlier post: Yes, I know about these chords -- I'm wasn't saying that there are only modulating cases,[...]. O sorry, I didn't intend to be taken as saying that you didn't know about them. I just wanted to answer Wahoofive's query about 6⁺ not on ♭6; and I thought that mention of non-modulating cases would answer that query most directly. Anyway, more examples of them soon.

– Noetica^♬♩ Talk 12:30, 5 June 2007 (UTC)

The reason I asked about modulation and "borrowed" chords is that those uses apply to any chord, so it's not really necessary to discuss them in this article. If the Aug6 can be used on scale degrees other than b6 in a non-modulating, non-borrowed context, that would be much more germane. —Wahoofive (talk) 15:07, 5 June 2007 (UTC)

OK, Wahoofive, here are some examples of the use of 6⁺ chords on degrees other than ♭6, in answer to your earlier request.

On ♭2:

• Fr$_{}^{6}$ at the very end of Schubert's String Quintet, IV, as already given above. (C major: the two cellos ornament the ♭2 with a trill with ♭3 as the upper note; the chords are followed by a unison and octave tonic in all parts, itself then repeated but with a ♭2 appoggiatura in all parts. Source: Aldwell and Schachter.)
• It$_{}^{6}$ at the end of Schubert's piano sonata D. 959, I, composed in the same year as the great Quintet: 1828, the last year of his life. (A major: the 6⁺ chord is followed by a long rest, then three bars of arpeggiated tonic major chord, then two final tonic chords. Source: Aldwell and Schachter.)
• Ger$_{}^{6}$ in Bach's "48", Book II, Fugue 8. (G♯ minor: tonic suspension in the top part, and $_{4}^{6}$ suspension over the chord of resolution: I$_{3}^{5}$. Source: Andrews, HK, The Oxford Harmony, vol. 2. Andrews calls this "a definite and regular use".)

On 4:

• It$_{}^{6}$ in Beethoven's string quartet Op. 18, No. 5, III. (D major: the chord resolves to V/vi – that is, to a III major chord. Source: Christ, Delone, Kliewer, Rowell, and Thomson, who comment: "Despite this apparent remoteness from the tonic, the tonal center is never in doubt.")
• Ger$_{}^{6}$ in Brahms' string quintet in G, adagio movement (II?). (C major: the bass starts in "inversion" on 6, then moves through 1 to 4, then the chord resolves to I$_{3}^{6}$, with the bass descending a ninth to 3. Source: Andrews, who writes concerning the three notes common to all 6⁺ chords on 4 – 4, 6, and ♯2 – constituting It$_{}^{6}$: "To describe [these] as a selection of notes from dominant harmony with the fifth sharpened is grotesque.")

There are several more examples in these sources – especially in Andrews. And some of these chords are also shown in various inversions. All of these examples are non-modulatory, and non-"borrowed".

– Noetica^♬♩ Talk 07:48, 6 June 2007 (UTC)

Thank you. These are very interesting. The Andrews quote is hard to understand out of context -- must be some straw man he's knocking down. I'd dispute your assertion that the Beethoven example isn't a borrowed chord, since it's part of a progression tonicizing vi. —Wahoofive (talk) 15:11, 6 June 2007 (UTC)

Here's one of your examples, from the end of the first movement of Schubert's D. 959 (chord highlighted in pink):

Here's another:

This last one could be argued to be an incidental simultaneity caused by the chromatic counterpoint, rather than a chord per se, but that's a long and boring argument regarding many of Bach's simultaneities which isn't worth rehashing in Wikipedia. —Wahoofive (talk) 16:02, 6 June 2007 (UTC)

Fine, Wahoofive. Thanks for putting some actual score here.

I thought the motivation for Andrews' note was clear enough, since I thought there are indeed those who would analyse chords with 4, 6, and ♯2 as having 5 as a root. They certainly might if 5 itself were present, after all. Compare common analyses of the diminished seventh chord on 7, etc.

Please don't take me as making hard assertions about whether the Beethoven chord, for example, is "borrowed" (perhaps a contested term – see a comment somewhere above in this discussion). I'm presenting all of these on the authority of the sources, and I am not completely convinced by all that they say. But it is interesting that Christ et al. see fit to make specific comment on the stability of the key centre, isn't it? Would you like me to put some more examples here when I have time, or does that meet the present need? There are others from Bach, for example.

– Noetica^♬♩ Talk 01:08, 7 June 2007 (UTC)

Priority at the moment should be to improve the article regarding standard usage, before we worry about these fringe cases. I was just curious. I don't recomment putting even these examples in the article until we have improved what's already there. —Wahoofive (talk) 03:53, 7 June 2007 (UTC)

I agree absolutely, Wahoofive. In fact I go further, as you know: there are broader issues that need to be settled before this article can be straightened out reliably. I have called for discussion of these at Wikipedia_talk:Manual_of_Style_(music) (in the first instance), and you are the only one to respond there so far, in the ten days since I made the call. Too little coordinated action! As one who works hard to answer people's requests for help – often in detail and at length – I would appreciate more of that from others.

As for the cases I present being on the fringe, certainly that applies to some; but not to all, by any means. The texts I cite take them quite seriously, and give numerous examples – especially for 6⁺ on ♭2. Andrews devotes twenty-two pages to 6⁺ chords, and fully ten of these are concerned either with inversions of the chords built on ♭6, or chords built degrees other than ♭6 (with their inversions, too).

– Noetica^♬♩ Talk 04:29, 7 June 2007 (UTC)

you can't resolve to a dissonant chord

Thanks for your notational figure, Wahoofive. However, I have a basic issue with the caption: "German sixth resolving to a 6/4 chord". A 6/4 chord in this case is dissonant (it's the fourth above the bass (and root) that defines this dissonance—it resolves to the third, naturally). The resolution of the augmented sixth chord, then, doesn't occur until the sixth releases to the fifth, and the fourth resolves to the third. It would be correct to talk of the augmented sixth chord resolving to V; otherwise, "moving to a 6/4" is correct, but not as useful to the reader as having pointed out the functional goal—the harmonic "vector", if you like; the 6/4 position that starts V is not a goal, but an ornament, as it were, and of course a technical way of easily avoiding parallel fifths.

It doesn't matter where those two unstable parts move during V—they could wobble back and forth between 6/4, 7/5, 6/4 and 5/3, more than once—the sense of V starts on the 6/4, and normally continues until the end of the phrase or the further resolution to I. Tonic harmony, of course, is not present in this example, but for that further expectation. Tony 23:55, 14 June 2007 (UTC)

First let me take issue in this way: you can resolve a dissonant chord to another dissonant chord. Sequences of seventh chords do just that. Now let's move on.

As we should all know, much theory concerning augmented sixth chords is disputed. Add to that the disputes about the status of 6/4 chords, and you have a recipe for endless uncertainty in the article. A practical solution here might simply be to avoid talk of resolution in controversial cases, as Tony more or less suggests. So: "German sixth moving to a 6/4 chord"; or "German sixth followed by a 6/4 chord". For none of the other figures does the caption use resolving, anyway.

In all the cases we consider so far the augmented sixth interval does resolve to an octave, yes? This includes all of the "inversions" we consider. An example of our speaking this way already in the article: "these two voices resolve inwards to an octave". So perhaps this is a better way to go throughout. Just speak of intervals resolving, including the augmented fourths. (By the way, not all 6⁺ chords discussed in the literature have the 6⁺ interval resolving to an octave.)

In some of the inversions of the 6⁺ on ♭6 you can move to a tonic chord, without then moving to a dominant chord. Consider, in C major, a progression of these chords: C–G–C–E, D–A♭–C–F#, E–G–C–G, F–C–F–A♭, F–A♭–C–F, C–G–C–E. Why not? The second chord is quite naturally analysed as an "inverted" French 6⁺; it moves to a tonic chord, which is then not at all constrained to move to a dominant. Transferring such an experiment to the "root" position of a standard 6⁺ chord, and allowing that the standard move to a 6/4 chord is a move to tonic chord in second inversion, we get a certain consistency that we do not get if we insist that the 6⁺ is not in any way resolved until we hit a dominant chord.

– Noetica^♬♩ Talk 02:25, 15 June 2007 (UTC)

Re: "you can't resolve to a dissonant chord...I have a basic issue with the caption: 'German sixth resolving to a 6/4 chord' ":

I think this remark demonstrates that the cop-out designation "6/4" hasn't got us anywhere. Tony will never be happy until we in some manner assert that the chord in question is a V chord.

Re: "It would be correct to talk of the augmented sixth chord resolving to V."

Doesn't the V chord resolve to the I chord? TheScotch 04:48, 15 June 2007 (UTC)

Well no, it doesn't. Have you gone back to de-inverting a vertical coincidence of notes and ... aha, that's chord I, have you? It makes no functional sense where that vertical coincidence arises through horizontal movement of the parts rather than underlying root movement. See my point above about the wobbling about of inner parts back and forth along the 5/3 — 6/4 — 7/5 — 6/4 — 5/3 track. They're free to do so without threatening an underlying, "prolonged" root.

In response to Noetica's points above: (1) Yes, you're right in that instance, but it doesn't change my substantive point about the impossibility of conceiving a "resolving" onto a dissonant 6/4. (2) In your spelt-out example, the inverted Fr4/3 is in root position (chromaticised ii7), not in inversion; because its bass can no longer move to the dominant tone by step, it has lost its pre-V function; instead, it's a chromaticised passing chord between I and I6. Yes, it's not constrained much at all in where it moves then. (3) Tonic chord in second inversion? I don't think so, but I'm not entirely sure of what progression you have in mind; can you provide the actual notes? Tony 04:56, 15 June 2007 (UTC)

Re: "In your spelt-out example, the inverted Fr4/3 is in root position (chromaticised ii7), not in inversion; because its bass can no longer move to the dominant tone by step, it has lost its pre-V function; instead, it's a chromaticised passing chord between I and I6. Yes, it's not constrained much at all in where it moves then.":

Petitio principii, begging the question: it's "lost its pre-V function" because you can't find a way convincingly to call its following chord a V chord. Of course its movement is constrained, constrained by the tendency of chromatically lowered pitches to resolve downward, chromatically raised pitches to resolve upward, and diminished fifths to resolve inward.

Re: "Have you gone back to de-inverting a vertical coincidence of notes...?":

A chord is both a wave and a particle, so to speak, both a "vertical coincidence" and an "underlying root movement". Without voice leading, "underlying root movement" would never have historically evolved. In any case, even if we ignore utterly "vertical coincidence", a dominant chord does (stereotypically) resolve to a I chord. (I framed the remark as a question for rhetorical purposes only.) TheScotch 05:50, 15 June 2007 (UTC)

If you don't like the wording of the captions, change 'em to something unambiguous! We can't resolve (ha ha) the question of the interpretation of 6/4 chords on this page. —Wahoofive (talk) 06:10, 15 June 2007 (UTC)

"... not contrained much at all in where it moves THEN. That is, in where I moves, not the chromaticised passing chord. I'm not trying to call its following chord V, as you accuse with your italics. Read what I wrote and you'll see that your response is irrelevant.

We seem to be at cross-purposes here. Of course both the horizontal and the vertical are at play in forming (and analysing) chords; my problem is the unerring ascription of root for every vertical coincidence, regardless of the voice-leading context. Sometimes, when you put a microscope up to a "chord", the root appears at odds with the notes. Take one step back and see the context, taking into account the freedom of voice leading above an underlying root. Then the harmonic scheme makes sense. Tony 06:51, 15 June 2007 (UTC)

I've taken the liberty of placing your most recent remarks where they belong chronologically. Please do not interpolate any of your reply into the body of one of my replies. TheScotch 07:11, 15 June 2007 (UTC)

Re: "I'm not trying to call its following chord V, as you accuse with your italics. Read what I wrote and you'll see that your response is irrelevant."

I did read what you wrote, and I did not accuse you of "trying to call" the chord a V chord. I accused you of circular reasoning, and I stand by that accusation.

Re: "... not contrained much at all in where it moves THEN. That is, in where I moves, not the chromaticised passing chord.":

If you meant the I chord, you ought to have said the I chord, but if you meant the I chord, you're arguing in circles in this respect as well.

Re: "my problem is the unerring ascription of root for every vertical coincidence....":

Then your "problem" is a straw man. TheScotch 07:24, 15 June 2007 (UTC)

Please do not interpolate any of your reply into the body of one of my replies.

Oh sorry, let me polish your shoes.

Then your "problem" is a straw man.

Your problem is your superficial understanding of music. There's an attitude problem there as well. Tony 07:44, 15 June 2007 (UTC)

Tony, you wrote:

Tonic chord in second inversion? I don't think so, but I'm not entirely sure of what progression you have in mind; can you provide the actual notes?

That was about what I had written:

Transferring such an experiment to the "root" position of a standard 6⁺ chord, and allowing that the standard move to a 6/4 chord is a move to tonic chord in second inversion, we get a certain consistency that we do not get if we insist that the 6⁺ is not in any way resolved until we hit a dominant chord.

Well, I simply meant the standard cases, such as we have illustrated in the article. You don't think so, hmm? We already knew you didn't think so! I have to say, Scotch and I are in some sort of agreement here (Scotch, above: "a chord is both a wave and a particle, so to speak"). I really don't think there is a single right understanding of some matters hereabouts. That often happens with music theory: it's such a jumble, and is evolved organically and chaotically rather than engineered top-down, on good design principles. (Ahem... compare Diatonic and chromatic.)

Tony! Behave yourself! Not everyone who has a contrary opinion to your own is on that account an ignoramus. Attitude? Perhaps that's another matter. But more than one of us here still could do with some lessons in manners.

The dispute tag? I would not have put it there myself, but I have no objection to it – for the time being.

As I have said to Tony elsewhere, I'm too busy in the world to do much more on Wikipedia for a few days. (Or should be, anyway, dammit!) I'll try just to watch for a while now, and comment later.

– Noetica^♬♩ Talk 07:54, 15 June 2007 (UTC)

It took quite a long time to rise to an overt squabble; I'm surprised, coz I was willing it.

No, on this matter, I don't agree that there are two legitimate ways of seeing things. On other matters, I do; but not on this one. So this and other pages are set to be the site of sustained battles. Tony 08:10, 15 June 2007 (UTC)

At the risk of fanning the flames here, I'd like to calmly point out that your opinion on whether a viewpoint is "legitimate" is irrelevant to WP editing. If you can convince us that a consensus of experts in the field is centered around a particular position, that's different. —Wahoofive (talk) 00:22, 16 June 2007 (UTC)

Gee, that was a really useful contribution. Tony 03:46, 16 June 2007 (UTC)

I thought it was!

– Noetica^♬♩ Talk 04:15, 16 June 2007 (UTC)

They'd have to be experts, then, as you say. Anyone who subscribes to the I six-four fallacy for the cadential six-four phenomenon is not an expert, but a well-meaning fool. Simple as that. Tony 04:39, 16 June 2007 (UTC)

6/4 chords

Actually, I was rereading the Beach articles in Music Theory on six-four chords, and he gives a great summary of the current views of the chord and how to understand it. He's clearly in the V64 camp, but gives plenty of weight to I64 views today. Really great read. No fools there. Also there is a pretty large school of thought that different chords have gradations of dissonance such that a more dissonant chord can partially resolve to a less dissonant chord or that a dissonant chord of ambiguous interpretation can resolve to a dissonant chord of obvious interpretation (such as the Fr6 to cadential 6-4. (And I too thought Wahoofive's point was useful) -- Myke Cuthbert (talk) 16:16, 16 June 2007 (UTC)

Let's be sure we keep separate the two issues (a) how a 6/4 chord functions and (b) what symbol we use to notate it. It doesn't matter if you use the symbol I64 to indicate that it contains the same notes as a I chord as long as you acknowledge it doesn't provide the stability of a tonic triad. And it doesn't matter if you use the symbol V64 as long as you acknowledge that the figured bass symbols then don't have the same relationship to the Roman numeral as they do in other contexts. Remember that the combination of Roman numerals and figured bass symbols is a 20th century invention, and arguably one which harms as much as it helps. I don't think we really have any disagreement about how these chords function, just what terms and symbols we are to use to represent them. —Wahoofive (talk) 21:16, 16 June 2007 (UTC)

I reiterate that Wahoo's point was absolutely useless, since it provided nothing substantive that will resolve this dispute. What would be helpful is if someone can take issue substantively with my reasoning above. I don't see anyone engaging with me on the theory. Just mindless dogma from the Associated Board, the AMEB et al.

No, the functions and the symbols can't be separated: that's why we have the symbols—to describe functions. It certainly does matter that you want to use I to describe the six-four position in a cadence; it says that the root is the tonic, when it's clearly NOT. That's my chief complaint about the way you guys treat roman numerals—in this narrow, vertical sense, without regard to the harmonic function. I will keep fighting you forever on this point. Nothing is going to sway me, and these articles are going to be unstable and unpleasant permanently because of your stance.

When roman numerals and figured bass arose is irrelevant. You provide no reasoning that the combination harms, just as you provide no reasoning that the tonic is the root in the disputed chord (beyond your simplistic, erroneous mindset). Yes, we do disagree about "how these chords function". II does not go to I—certainly not in this context, yet you would have it so. This defies the primary function of II as a pre-V chord. (It does have other functions, but the pre-V function is by far the most important.) Tony 00:23, 17 June 2007 (UTC)

Postscript: And I'm sorry that reading back over this I sound so pushy and rude. I don't mean personal offence, Wahoo, so I withdraw any language here that looks like it—here and previously. The gist of my entry a propos the subject of our dispute remains, however. Tony 01:54, 17 June 2007 (UTC)

Well withdrawn, Tony. I say yet again: take the dispute about six-four chords and their notation (and all matters of chord notation) somewhere else! Even if we did achieve an understanding, a compromise, or a capitulation here, it would not transfer to other pages, and the hard-won results would be lost. Think about it; act on it.

(Now I'll disconnect my modem and get on with worldwork, Sunday though it be.)

– Noetica^♬♩ Talk 02:00, 17 June 2007 (UTC)

No, I'm quite happy to fight it out here, where the issues need to be fixed urgently. Take it to the other page and it will be mired in argumentation by those who are not working on an article where it's at immediate issue. You're quite welcome to take it there yourself, but I won't initiate a debate there.

Again, I see no counterargument—on the theory at issue—to my announcement that I'll remove the offending figure tomorrow. To lable the chord as I is simply wrong, because it indicates a root that is dissonant with the bass. That's simply impossible, and I'm not willing to mislead our readers. Tony 03:23, 17 June 2007 (UTC)

Tony, what you want to do is have your original research trump other's citation of reliable sources which say that I is a perfectly acceptable labeling. For instance Thomas Benjamin, et al. Techniques and Materials of Music, (Thompson 2007), chp. 8 "The Cadential Tonic Six-Four Chord". There is even debate in Schenkerian circles about the propriety of the V label for it when it supports ^3 in the urline (discussion and possible resolution in Allen Cadwallade, "More on Scale Degree Three and the Cadential Six-Four" Journal of Music Theory 36.1 (1992), pp. 187-198). Besides your expertise, what are you arguing from that could possibly justify silencing other viewpoints? I think I'm getting a little tired of being called a fool or ignoramous for having read the literature. -- Myke Cuthbert (talk) 14:09, 17 June 2007 (UTC)

Why is it my original research? I'm only mouthing well-established theory; you just happen not to get it, whether or not you're a fool or an ignoramus (irrelevant). It's of absolutely no consequence how many textbooks you can find that subscribe to this fallacy—most music-theory textbooks are written by mediocre fools, anyway, and as with all articles, WP has to select. I'd hope that the selection was going to present a viable analysis, not one that defies the basic precepts of music and acoustics. WP should not be privileging this fallacy by displaying it alone in a figure. That's my objection: (1) that there's no figure with the correct notation to counter it, and (2) that the text doesn't explicate the background reasoning for the fallacy.

The reason people object to one six-four is that it's impossible for the root to be dissonant above the bass. End of story. You just can't construct a triad on a dissonant note. In first inversion, the root is a consonance above the bass; thus, it is not ruled out acoustically in its role as the fundamental. In a true second inversion (see Noetica's talk page for examples), the fourth is consonant. Here, it resolves over a stable bass, 4–3. Now let me get this right: are you saying that you can build a triad on a dissonant root? Tony 15:12, 17 June 2007 (UTC)

Do you understand the wikipedia policies WP:Verifiability and WP:No original research? I 6/4 is verifiable. There are many reputable published sources which use it. Your attempt to exclude it is inappropriate. You may think it's better to redefine a few terms more strictly to make harmony easier to teach, but I don't. If you don't use the real world meanings for these terms you are sheltering the Wikipedia reader from it, leaving them unprepared to understand the literature outside of your strict circle of music theorists that you approve of. There are better ways to teach someone about the way a 6/4 works than scouring the symbol from this encyclopedia. - Rainwarrior 20:10, 17 June 2007 (UTC)

You misquote me on a number of counts, and I wonder whether you've read what I write here. This has absolutely nothing to do with original research, nor verifiabilitly. Stop wasting my time. Consult major texts such as Aldwell and Schachter or Forte, and you'll see what I mean. Now, either you tell me how a root can be dissonant with the bass, or it goes, on the basis of POV. You've got 24 hours, since I flagged some days ago that I'm removing the biassed figure on Monday. Both sides must be presented with balance, and by having a figure with the fallacy glaring out, it's not balanced without a countervaling figure with the right analysis. Both or neither. I don't mind an explication of both systems, but the fallacy ALONE will not do, not for a minute. Tony 00:28, 18 June 2007 (UTC)

What goes? Have you even looked at this article lately? - Rainwarrior 04:17, 18 June 2007 (UTC)

Oh, and your claim that the fallacy is verifiable because it's trotted out in print is laughable. So were Hitler's ideas on race; but that doesn't mean they should be endorsed by WP—merely explained as an historical vagary. Tony 00:30, 18 June 2007 (UTC)

It's fine to put up Hitler's ideas on race as long as you attribute them to Hitler. (Thanks for validating Godwin's Law.) - Rainwarrior 04:06, 18 June 2007 (UTC)

E.g.: Nazism and race —Wahoofive (talk) 05:49, 18 June 2007 (UTC)

Which is why your fallacy needs to be attributed, or at least the technical misunderstanding explained. At the moment, it's shoved up in the inversion article as though it's god-given truth. Tony 07:00, 18 June 2007 (UTC)

Several examples have been listed at User:Mscuthbert/sandbox/Six-four chord, earlier on in this discussion, the most prominent source listed that uses I 6/4 was probably Walter Piston's Harmony. Off the top of my head, I know that Arnold Schoenberg used it consistently as well in his Harmonielehre. I could go to a library and find a pile of examples, but this is beside the point. I know that you understand that this symbol can be found quite availably in music theory literature; the issue is that you don't like it. It's not a technical misunderstanding. Those who use it just don't define the symbol the same way you do. I 6/4 doesn't have to imply the things that you insist make nonsense of it. - Rainwarrior 06:41, 19 June 2007 (UTC)

Sure, the fallacy is everywhere. That doesn't mean that WP should mouth it uncritically. I'll be scrutinising your six-four article if it makes it out into WP space. I don't like it because it's wrong, and befuddles the poor people who find harmony difficult. Those who misuse it do define the symbol as I do: it stands for the root. At least on that count, we all agree. Tony 08:14, 19 June 2007 (UTC)

The argument is about the NOTATION, not the function, of a cadential 6/4 chord. You relentlessly assert that I6/4 is wrong, and yet it's quite clear that V6/4 is a very misleading notation given the meanings of the numerals in Roman Numeral notation. Furthermore, there are many different degrees of dissonance, and of intervals labeled dissonant in a consonant harmonic context, the perfect fourth above the bass note is by far the least dissonant. To say that I6/4 is wrong notation because the root cannot be a dissonant interval over the bass note is absurd; in a V4/2 chord the root is a ninth above the bass note, but it is indisputably still a V chord.

Um, it's a seventh above the bass, isn't it? I've already explained how the presence of the seventh above the root is a strong definer of the root in V4/3 and 4/2. Tony 06:17, 21 July 2007 (UTC)

Now, I am not saying that I6/4 in the cadential context functions as a tonic chord, because the harmonic context itself clearly shows otherwise. But the truth is that while I6/4 does not describe the function of the chord, V6/4 describes a dominant triad, which a cadential 6/4 chord clearly is not. So even though a cadential 6/4 chord is dominant in function, the Roman Numeral V indicates a dominant triad. V6/4 is no more correct that I6/4 because both are misleading in separate ways, and so for you to say that I6/4 is wrong notation is extremely pompous. Ah, and you're not pompouse for proclaiming the opposite, of course. You talk circular rubbish, I'm afraid. Your final sentence below is true, but irrelevant. Tony 06:17, 21 July 2007 (UTC)

For a final thought, saying that one notation is exactly correct for a chord is ridiculous since our harmonic analysis was derived after what we use it to analyze was written. If Bach were brought back to life and we asked him what notation to use, he would have no clue what we're talking about. --SockEat 22:28, 20 July 2007 (UTC)

Hi SockEat -- in order to centralize discussion of this dispute, we're mostly talking at Talk:Inversion (music) based on some things that are happening in Wikipedia:Requests for mediation/Inversion (music), which you're welcome to contribute to. Best, -- Myke Cuthbert (talk) 03:05, 21 July 2007 (UTC)

added tone

Don't like this term in the captions. For the French, the D is the original root (of ii4/3). In what sense is it "added"? If the purpose is to make it easier to remember the distinctions between the three versions, it would be better to label the blue notes as the "difference", rather than "added". The best way of all to remember them is to know their origins in iv and ii. That underpins their pre-V function, even where this is subverted. Tony 00:11, 15 June 2007 (UTC)

And sorry, more problems in these otherwise excellent figures: the alto E is flattened in the German 6/5 example (I guess we can assume that in the absence of either key signature or bar-lines), but is presumably E natural in the Alsation example, i.e., it occurs in the major mode. This will not be clear to the learner, and should be disambiguated for all, possibly with a natural sign in parentheses.

The Alsation is hardly worth the different name, which is why many theorists dispute the handle. It's just a respelling of the German 6/5 in the major mode, isn't it? That point is not quite :clear enough in the main text; neither are the derivations of the chords explained (which underlies, of course, their figured-bass names and functions). Tony 00:28, 15 June 2007 (UTC)

The roots of these chords are disputed. Whether they have roots is disputed. Some say they each have two roots! The origins of these chords in IV and II are disputed. They may not be founded on any other (modern) chords; they go back to the Renaissance after all, not just to the Baroque as the article says. Tony, good point about the lack of a ♮ for the second E in that figure, if that's what you meant. By the way Tony, a simple slip in your spelling: Alsatian. I have no source for the respelled German chord being called Alsatian (though I can find one for Swiss on the web). Anyone got one?

– Noetica^♬♩ Talk 02:37, 15 June 2007 (UTC)

Well, the dispute tag is going to be a permanent fixture, I'm afraid, unless there's a convincing case for an alternative derivation of these chords. Tony 04:57, 15 June 2007 (UTC)

I don't think this has anything to do with "disputed roots". If you compare the caption to the text it will be clear that in this case "added" is an abbreviation of "additional"--whether or not this is the best way to put it. In other words, we're simply saying here that the French augmented sixth chord has one more note than the Italian augmented sixth chord.

The second example does need to specify clearly whether its ambiguous second chord is intended to be C major or C minor. It needs either to repeat the flat sign before the E or else to put a natural sign there. I'm guessing it's supposed to be a C minor chord, but I can't tell for sure.

I'd never heard the chord in the third example called Alsatian either (or for that matter Alsation). The term strikes me as a bit rarefied. TheScotch 05:23, 15 June 2007 (UTC)

There are so many different topics in this section already it's hard to know how to respond. To start with, feel free to edit the captions -- nothing's a final draft in Wikipedia! Second, it's not really appropriate to put a "disputed" template when it's the sources themselves which don't agree -- we could easily find sources for half a dozen different theoretical analyses of these chords. There's no consensus about roots. All of the analyses should be explained as best we can. Although I've never heard of "Alsatian" or "Swiss" sixths, if you've got a legitimate source, it's a valid piece of info. Third, I was thinking of an E flat (as if in C minor) for the second German sixth example, simply to avoid the doubly-augmented-fourth issue (which doesn't arise in minor). If you think it could be done more clearly (or if you'd prefer all the examples to be in minor, like the one in the intro), I can upload updated versions. —Wahoofive (talk) 06:06, 15 June 2007 (UTC)

The Swiss designation comes from Piston/DeVoto. It's in the 5th edition, and possibly also in the 4th--that one is easy to put a cite on next time I'm in a library with that edition (I loaned mine to someone and never got it back). The Alsatian comes from the followers of Schachter who disliked "Swiss" on the grounds that it is a mixture of French and German qualities, as opposed to Alsace which at one moment is fully French and at the other is fully German. However, a quick look through A/S and JSTOR doesn't find the term, so it might need to go. I can ask David Cohen (Columbia) next time I see him, since he's one of the big proponents of the term. I don't think that all the examples need to be in minor. Whether the chords "actually" exist in major or whether the chords only exist by borrowing from minor is largely irrelevant since there was never an evolutionary stage in the development of the chord where composers only used it in a minor mode context. -- Myke Cuthbert (talk) 15:08, 15 June 2007 (UTC)

Either give the second example a key signature of three flats, please, or put a flat before its second E. Since there are no measures here, that flat will not be redundant (nor is the existing natural sign before the D in the third example superfluous). TheScotch 06:44, 15 June 2007 (UTC)

I have added the key signature in this one example. It's a little confusing in my view for users to compare this example with the previous one, though, now that they're in different keys. I'm not sure Myke's last statement is correct; I suspect these chords were used almost exclusively in the minor mode at first. —Wahoofive (talk) 15:28, 15 June 2007 (UTC)

I put the dispute tag there because Noetica said that the derivation of aug 6 chords is in dispute. The current explanations are most unsatisfactory. Tony 06:55, 15 June 2007 (UTC)

Bold and worthwhile edits Wahoofive. Myke, thanks for the further leads. Yes, more would be handy, if you can conveniently track it down. I have only the second edition of Piston, and Swiss is not found in it.

– Noetica^♬♩ Talk 23:35, 15 June 2007 (UTC)

Recent editing, and removal of the "dispute" tag

OK, I have broken my rule and spent time editing here. I like a lot of Wahoofive's changes, but I have supplemented them. I could do more, and would do more, but I just have to stop. Tony will probably come in and smooth things further. I have removed the "dispute" tag. The mere fact that the sources don't agree about a lot of things does not justify its imposition. The dispute about the status of six-four chords is not a dispute focused on this article, and it hardly makes an appearance in here anyway, now. Take it elsewhere!

– Noetica^♬♩ Talk 01:14, 16 June 2007 (UTC)

Something needs to be added to the "roots" section, which is a microstub. I don't have any reference sources here to work with. Here's where Tony can convince us that A6 chords are definitively second-inversion chords, and back it up with sources. —Wahoofive (talk) 01:24, 16 June 2007 (UTC)

No, not all three aug 6 chords; just the French, which is derived from ii 4/3. What else would it be derived from? The notes are exactly the same before the fourth degree is raised. Tony 00:39, 17 June 2007 (UTC)

In isolation that analysis is plausible, but another consideration is that the three A6 forms are functionally equivalent, and at least in most cases pretty interchangeable, so asserting they have different roots is less intuitively satisfying. It's fascinating that you take such a note-literal approach to analyzing the Fr6, but reject the similarly literal approach to the I64 chord. —Wahoofive (talk) 03:57, 17 June 2007 (UTC)

copyright issue

The Michael Haydn excerpt with analytical symbols beneath: I wonder where it came from (the edition, not the work—it looks as though it's been stolen from a textbook)? There's nothing about it on the info page, so the free-use police here will take it down sooner or later for that reason alone.

The audio: Pity about the copyright restrictions, because I just hate those electronic choral sounds. Makes Michael Haydn's music sound like the sound-track from a cheap sci-fi movie from the 50s. And another thing: when you play it, you lose the score, at least on my computer.

Note that the notation is CORRECT with respect to the cadential six-four. Thank the lord. Tony 00:37, 17 June 2007 (UTC)

I myself have done the analysis, and did not "steal" it from any text book or any other source for that matter. FraKctured 06:11, 19 June 2007 (UTC)

Image placement

On my monitor the images on this page appear to be placed horribly. Wide images should be placed center. The smaller images screw with the text. I don't remember much about image markup anymore. Hyacinth 03:19, 17 June 2007 (UTC)

Can you email me a screen shot? —Wahoofive (talk) 04:00, 17 June 2007 (UTC)

Tritone Sub?

The article states that the Fr$_{}^{6}$ is similar to the Tritone Sub, but I'm pretty sure the author means Gr$_{}^{6}$: Ab C Eb F# is enharmonically Ab7 which substitutes D7 (Ab being a tritone away from D), the V7 of G. The Fr$_{}^{6}$ would be spelled with a D natural. Jmckaskle (talk) 19:33, 12 December 2007 (UTC)

Here's another possible interpretation, though: in jazz, the dominant chord of C major would be G7, but Db7 (tritone sub) may be substituted for it. Commonly in this case the Db chord has an augmented eleventh added, making it Db7#11. This chord is enharmonic with the French sixth.

That said, however, most of the junk in the last section about the Hollywood sixth and so on is OR. —Wahoofive (talk) 01:26, 13 December 2007 (UTC)

Is there a Culver City Sixth?--Roivas (talk) 16:27, 13 December 2007 (UTC)

My Bad - I was suffering from a bout of lazy eye. I got the Gr and Fr mixed. The Article is correct. Good article, and point about the #11.

128.83.160.235 (talk) 16:55, 13 December 2007 (UTC)

Clarification: the Db7#11 could have other notes included (a major ninth, e.g., or even a perfect 5th), so it's not necessarily identical to the Fr6, but it has all the Fr6's notes. —Wahoofive (talk) 19:03, 14 December 2007 (UTC)

I've gone ahead and added some clarification regarding the most common functional difference between a tritone sub and an augmented sixth chord, and included a simple example. Hopefully without going into too much detail. Its the last paragraph in the article. Feel free to argue about it. :-) Ormaaj (talk) 07:21, 4 April 2008 (UTC)

I have never heard anything about the chords in the last section which are, in addition, are respellings of the Italian ('Canadian'), German ('Norwegian') and French ('Hollywood') Augmented Sixth chords.

190.77.117.1 (talk) 18:46, 10 January 2008 (UTC)

• I hope there's no mention of Hollywood, Norwegian, and other odd terms; it's hard enough for readers to understand conceptually without unnecessary clutter. Tony (talk) 01:53, 11 January 2008 (UTC)

• These excess nationality chords are simply a misconception; they are augmented sixth chords as applied to the tonic resolution instead of to a dominant chord, a concept which is already addressed earlier in the article. I removed that unnecessary and factually unverifiable section. Killervogel5 (talk) 19:31, 9 February 2008 (UTC)

• I removed this same content for the second time. It is unsourced and not verifiable. Killervogel5 (talk) 02:43, 15 April 2008 (UTC)