Talk:Inversion (music)

From Wikipedia, the free encyclopedia

This is the talk page for discussing improvements to the Inversion (music) article.
Article policies

As a total wikipedia newbie, may I suggest that, despite its many well thought out points, there are two possible problems with the page for people in search of basic information:

A) The discussion of notation of inversions is weak & incomplete. It should cover 1/ figured bass 2/ a b c notation 3/ C/E type notation (chord/ bass) 4/ 1 2 3 notation

B) Confusion from a presentational point of view between tonal & atonal theory. For the benefit of the vast majority of users, may I suggest that tonal uasge should come first - or at least they should be clearly distinguished.

I have refrained from making any edits as you guys have evidently have much more experience & history, Many thanks. Reflection

Just wanted to note that I'm still not very comfortable with the idea that inverted octaves become unisons and vice versa (see talk:octave). It's probably just me (though it is notable that most theory textbooks (the ones I've looked at, anyway) tell us what happens when you invert seconds, thirds, fourths, fifths, sixths and sevenths, but not unisons or octaves). --Camembert

Hi Camembert--Maybe it would help resolve the issue by asking what is the purpose of referring to inverted intervals. For all of the other cases of inversion ((1) inverted melody, (2) inverting two parts in counterpoint, (3) inversions of a chord), I can think of cases where the terminology is useful in describing a work of music ((1) "following the aria, the fugal theme reappears inverted" (Beeth. op. 110); (2) "the two themes now appear inverted, with the main theme in the lower part" (Bach 2 pt. inv. E); (3) "the second inversion of the tonic chord is used to introduce a cadenza" (any Classical concerto)). But where do commentators talk about inverted intervals when discussing actual pieces? I don't know the answer, but it seems to me that if commentators do make use of "seventh = inverted second", but never make use of "octave = inverted unison", then that ought to settle the issue in your favor (since our goal is to be useful to readers). Just a thought. Opus33 21:35, 23 Dec 2003 (UTC)
Well, I can't come up with any examples of commentators talking about inverted intervals in practice, but I suppose the most common context in which one would want to talk about them would be when melodies switch places in a contrapuntal texture (your number (2) above) - if you have melody A in the treble and melody B in the bass, and then later you put melody B in the treble and melody A in the bass, then all the intervals between voices in that second version are inverted. In that case it's not possible to generalise about what will happen to octaves and unisons - notes that were previously an octave (or more) apart may remain an octave (or more) apart, or they may become unisons, and vice versa - it all depends how many octaves apart the two voices are. The whole question is irrelevant, really, because the number of octaves apart the voices are is not interesting - only the pitch classes (that is, whether you've got a D or an F sharp or whatever) are. One might also want to speak of inverted intervals in the context of twelve-tone pieces, when again octaves are neither here nor there. So the question of what unisons and octaves become when inverted is really irrelevant, because if you had a C on the top and a C on the bottom before inversion, you do after inversion as well. That's my view of it, anyway. --Camembert
Beginning music theory students are taught about how to invert intervals. Why? Good question.Hyacinth 04:12, 25 Dec 2003 (UTC)
PS. In the last ten minutes I managed to go from complete boredom with this discussion back to complete interest. Anyways, the article is settled, and we could stop talking about this.Hyacinth
Thanks, Camembert and Hyacinth. I'm relieved that there isn't really anything too crucial at stake here, so, as Hyacinth says, we can move on... Opus33 22:03, 26 Dec 2003 (UTC)
See complement.-Hyacinth 07:28, 9 Feb 2004 (UTC)

source for formula definitions: Basic Atonal Theory by John Rahn.

Hope I'm doing the right thing by putting most recent comment at the top. Someone kindly addressed point B/ above with a simple disambiguation at the top of the article, which seems fine. Trying to be a bit more proactively wikipediasical, (a neologism, thinks google - if so, you first saw it here:-) ) I just went ahead & put in something to address the notation issue (point A above). Hope it's useful. Cheers. Reflection.

Thanks for hierarchical heading, Opus 33 - my ignorance.

Great to have Point A addressed. Would it make sense to discuss figured bass in section 1.1 instead of 1? It's really just one of four rival systems, though perhaps the most common. This would keep section 1 nice and simple. (Hope you don't mind my moving your comment to the bottom, Reflection.) Cheers, Opus33 17:09, 25 Feb 2004 (UTC)

Contents

[edit] more on inverted octaves

This question is not addressed in this article, and although it is for self-serving reasons that I add it to this discussion (it was on my theory review paper), I think it should be addressed somewhere in this article. What does an augmented octave invert to? dveej

[edit] Split the article?

This looks to the untrained eye like half a dozen articles lumped into one. --Smack (talk) 01:51, 13 June 2006 (UTC)

Oppose. I think the article is just poorly organized at the moment. It needs improvement, not a split. It is better to keep groups of related information together than to fragment it onto many small pages and make the user have to visit all of them to gain a proper understanding of the subject. - Rainwarrior 03:53, 19 June 2006 (UTC)
Oppose. If this article was split the newly created articles would be stubs which would then need be merged back into one article. Hyacinth 05:06, 19 June 2006 (UTC)

[edit] Figured bass addition

A bit of information about Figured bass was added to this article today. I think it should be trimmed down considerably, as figured bass has its own article that explains it quite adequately, and we are merely trying to compare systems here. Furthermore the information is incorrect. A C in the bass with 4 6 written does not signify a second inversion C major chord (G C E), but rather it indicates a second inversion F major chord (C F A). At least this much must be amended. - Rainwarrior 22:57, 15 August 2006 (UTC)

Kquirici, you seem to be confused about the notation of Figured bass. Check that article, or a nearby harmony textbook. In figured bass, it is the bass note of the chord that is written, not the root note. Thus you may speak of a C major "6/4 chord", but in figured bass it is written as an G in the bass with a 6 4 written below it. - Rainwarrior 17:17, 16 August 2006 (UTC)

Rainwarrior, I agree with your changes. My intent in altering the figure bass notation paragraph was to introduce the inversion of 7th chords, which I do not believe were covered, and make sure that every triad or 7th inversion showed the full inversion as well as the abbreviated version.

I was not aware the inversions were notated with their own bass note. I knew the intervals were counted from its bass note, but not that the 'name' of the chord was the 'name' of the bass. Thus your claim: the first inversion of C is notated E6. I'm still shakey on this point so I'm going to check a text, as you suggest.

Thanks for your contribution. Ken M Quirici 15:01, 18 August 2006 (UTC)

It's not uncommon for someone to say "C major 6/4", meaning G C E, but this is not "figured bass", it just borrows the figures from figured bass. I don't know if that nomenclature has a name, but the confusion with figured bass is quite understandable as it's not an uncommon usage. (Maybe this should be mentioned on the page as well...) - Rainwarrior 22:52, 18 August 2006 (UTC)

Hi, back again (KMQ). More changes. Please consult Ottman's Elementary Harmony, where many examples of notations V6 4, I7, etc., are attested. This is clearly more common than G64, indicating the second inversion of the C chord. I have never in fact seen notation like G6 4, which is I admit derived directly from sheet music notation, but never AFAIK actually used in practice. The scale degree notation is much more common and harmonically makes much more sense, since it places you in the harmonic context of the chord much more clearly than G64, which requires an extra step of mental translation. IMHO.

Thanks.

Ken Ken M Quirici 01:12, 19 August 2006 (UTC)

But again, this is not Figured Bass. Figured bass doesn't actually have letter names; they are written bass notes. There are inversional names derived from Figured Bass, and examples where a roman numeral denotes harmonic function but not bass note are also common, but this is not Figured Bass. Figured Bass is a style of score notation that has very fixed rules, and was a big part of performance practice through the Baroque and early Classical periods. Figured Bass is always the bass line of the piece, and the figures indicate harmony above it. Roman numeral analyses and discussions using the language you are talking about do not appear until the later 19th century (Hugo Riemann, for instance) and have nothing to do with figured bass, though they may sometimes borrow the inversional figures.
I have edited the page to reflect both what Figured Bass is accurately, and mentioned that the figures have been utilized as a way of notating inversion. As for something like "C 6/4", if you see this written on a page, it is ambiguous. A written bass note C, however, with the figure 6 4, unambiguously means C F A. On the other hand, roman numerals with inversion figures is not ambiguous, I 6/4 means G C E if in the key of C major; similarly saying C major 6/4 is also unambiguous. However, C 6/4 is unclear, and can only be resolved by the context it appears in. Also, it is not appropriate to include "1" in a figured bass, because it indicates an additional unison note. The bass note is already written, and does not recieve a figure. The only place the 1 appears in Figured Bass is to indicate a 2-1 suspension. - Rainwarrior 08:58, 19 August 2006 (UTC)


Rainwarrior:

Have you ever actually seen the notation E6 to refer to the 2nd inversion of C?

And you refer to historical practice but the article consistently uses present tense. It is clearly, IMHO, referring to current practice, as it must be. You don't want to say inversion notation IS thus and so meaning that's how it was done in 1300 AD.

I do note you mentioned the notation I6/4 or whichever example you use, which seems appropriate.

As for the '1' in figured bass, I think it's a question of interpretation, but I'm willing to go with your strictures since they're coherent and consistent.

Anyway, as you notice I'm not changing anything. The article is reasonable but I don't think it's quite clear or direct enuf, and note that none of mine were either :-)

Cheers.

Ken M Quirici 13:19, 19 August 2006 (UTC)

Yes, when reading figured bass, a written note E with the figure 6 always refers to the 2nd inversion of C. You'll see this in pretty much any Baroque work in C major for a chamber ensemble with keyboard. Figured bass is still used today, and is a part of the training of many keyboard players. As well, the notation of Figured bass hasn't changed in a long, long time. What I am saying is that these other adaptations of the figures of figured bass aren't called figured bass at all. I don't know what their name is, but it's not figured bass. They exist, they're useful, I've seen them, I use them, but they're not called figured bass.
In analysis, often one writes figures below the bassline, as they are an excellent way of notating suspensions and other dissonances, and then below that writes a roman numeral analysis. In this case you have both figured bass and roman numeral analysis together, but in text writing roman numerals with the figures are very often used.
As for the written letters E6, I don't think I've ever seen that notation in music theory, but it is frequently used in commercial chord notation to mean an "added 6th" chord, which in this case would be E G# B C#, which is a second inversion C# minor 7th chord. Why, where have you seen it? - Rainwarrior 20:01, 19 August 2006 (UTC)
I pulled the score for Vivaldi's "Four Seasons" off my shelf to find an example, (I figured if you want to look up some figured bass, this one would probably be easier to find than anything else). In the first movement of "Spring", the first figured 6 appears in measure 47: we have a G sharp in the bass, and above it G sharp, E, E, and B. Thus, this is an E major chord in 6/3 inversion, but what is written is a G sharp with a 6. (Every other figure in the piece follows these same rules.) - Rainwarrior 20:15, 19 August 2006 (UTC)

I made a couple of pictures that would demonstrate the notation clearly. I don't like the layout right now, but I can't think of anything better for the moment. It might also be good to mention that the pictured cadential progression is (by far) the most common place for the 6/4 inversion to appear in classical music, though I'm not sure where on the page this should be mentioned. - Rainwarrior 00:38, 20 August 2006 (UTC)


Rainwater:

The article is shaping up nicely. Excellent diagrams. I assume you used a music notation program for them? Sibelius? Overture? Finale? Igor Engraver? Something else?

Thanks.

Ken M Quirici 01:48, 20 August 2006 (UTC)

I just took a screenshot from Finale and edited in the numbers by hand. - Rainwarrior 01:59, 20 August 2006 (UTC)

[edit] More on Invertible Counterpoint

I think there needs to be more on invertible counterpoint, particularly as it is one of the most important aspects of fugue writing (even though it is not always used), and there are so many examples of its use in baroque music. I think we can then satisfactorily refer back to this page on the countersubject and fugue page. Matt.kaner 14:06, 3 March 2007 (UTC)

I'm a Wikipedia newby, and this is the first time I'm participating in a discussion. I haven't touched the article, but it seems to me that splitting it would be helpful. Inverted counterpoint and inverted melodies are direct and practical applications of inverting intervals. Thus, interval inversions should be introduced first. For chord inversions, perhaps the reader should be directed to Figured bass after a brief definition, and Set theory (music) could be under "See also." What do you think? --Username: Virelai 18:17, 18 March 2007 (UTC)

[edit] the analysis of the 6/4 – 5/3 cadence

It's wrong; the figure needs to be redone. Tony 11:46, 21 May 2007 (UTC)

Ah, Tony. There's been some discussion at Talk:Augmented sixth chord recently about 6/4 – 5/3: its analysis and proper annotation, and also more generally how to mark these things up in articles. Check it out, yes? Your input would be useful. Myke Cuthbert is developing an article on the 6/4 – 5/3 cadence (just in a sandbox, so far). I've offered to help, and I've suggested that we cover also over kinds of progression with 6/4 (passing 6/4, arpeggiated bass including 6/4, etc.), since the different uses have features in common, and sometimes 6/4 is approached as if it's one sort, and left as if it's another sort.
Incidentally, what is your particular objection to a figure here? There are two figures that are relevant, and I can see reasons for objecting to each of them.
– Noetica♬♩ Talk 12:07, 21 May 2007 (UTC)

The first chord: GCE. Roman numeral I indicates a root of C. C is a fourth above the bass, and therefore dissonant. The root of a chord cannot be dissonant. Therefore it's not the root, and I is wrong. It's clearly chord V. Tony 13:18, 21 May 2007 (UTC)

[edit] the only way out of the impending war

... about what I see as wrong harmonic analysis is to present both sides in their context. But I'm going to be particular about how this is done, as I'm sure others will be. Tony 07:59, 29 May 2007 (UTC)

The image is not "factually inaccurate". The label I 6/4 is used in some textbooks and academic literature. Other authors usually prefer a V with a figured suspension, or some other alternative perhaps. It's a matter of taste, not a matter of fact. The tag is inappropriate. This is akin to the problem described at WP:Mos#National varieties of English. Whether or not you think it's an illogical label, it is known and used (this has already been discussed and sourced at the Augmented Sixth talk page), and I don't see a good reason to shelter the Wikipedia reader from this alternative. - Rainwarrior 08:28, 29 May 2007 (UTC)
  • I disagree, and you can quote textbooks all you like; it doesn't change the fact that it's erroneous, illogical and misleading. The figure with the I6/6 can either be deleted or matched with another illustrating it as V6/4. I intend to delete it if there's no move to produce such a corresponding figure. Tony
Quite so, Rainwarrior. As if there were Platonic "facts" to appeal to here! So far we have no citations or cogent argument to support excluding the I 6/4 labelling at all.
This is, at least, a better forum for the discussion than Talk:Augmented sixth chord, where it was a wildly inappropriate topic. But are you two at all interested in my suggestion that we deal with all of these uncertainties more collegially and systematically, at Wikipedia talk:Manual of Style (music) in the first instance, then possibly elsewhere? It's unhelpful to have all this fragmented discussion about issues affecting several articles.
And Tony, it's only an impending war if some of the participants set it up that way. I'm surprised and disappointed to see you doing that.
– Noetica♬♩ Talk 08:37, 29 May 2007 (UTC)
  • I'm disappointed in you. Tony
  • You are? Why? What have I done? Have I been one-sided, or blinkered in some way? Have I been dogmatic? I have simply been advocating clear well-sourced and reasonable dialogue, to come to a consensual solution – at an appropriate place, so that we can make genuine progress. I have, so far, advocated and worked towards a harmonious process and outcome. I have already said elsewhere (every bloody thing is elsewhere in this discussion!) that I have a certain view, but will accept a reasonable consensus position that is not my own first choice. What do you object to, then, in what I have done or omitted to do? (You might like to think these things through, before offering a reflex one-liner response.)– Noetica♬♩ Talk 11:25, 29 May 2007 (UTC)
  • Because I thought you had a deeper knowledge of music theory. Tony 12:26, 29 May 2007 (UTC)
  • Ha ha! Nice try! Don't let the tolerant and conciliatory attitude fool you. A completely unsupported and unsupportable aspersion, such as we might expect from a lightweight beginner. Unworthy of an experienced and knowledgeable editor. (And a mere one-liner, I observe.) Just get on with dialogue towards improving articles, I suggest. You might start by answering the direct questions I put to you about broader work towards consensus, at Wikipedia talk:Manual of Style (music), instead of perpetuating cheap defensive sniping – and scattered small-time editing in ever-decreasing circles, so far fed by little more than unexamined prejudice.– Noetica♬♩ Talk 00:54, 30 May 2007 (UTC)
Aren't there a couple of citations at User:Mscuthbert/sandbox? Offhand I don't think any of the books on my shelf prefer that notation, but I did find a quote in Robert Gauldin's "Harmonic Practice in Tonal Music" (Norton, 1997) page 212: "We could label the second chord in each group as a second-inversion tonic triad, or I^6_4". It goes on to explain the problematic 4th and the usual use as a suspension, and throughout the book the figured dissonance over V is preferred, but it acknowledges the possible use of that term. In the case at hand, I think the I rather than the V shows better which chord is the second-inversion chord. While I would say in most cases V is more useful, in the very narrow scope of this example I think using I 6/4 is more straightforward than introducing the notation of suspensions over V. - Rainwarrior 09:00, 29 May 2007 (UTC)
  • I've already explained that C can't possibly be the root, since it forms a dissonance above the bass. That's just one reasons that I6/4 is impossible. Shall we go through all of the reasons, or are you interested only in citing textbooks that persist with this falsehood? Tony 11:05, 29 May 2007 (UTC)
Two things in reply, Rainwarrior:
  1. I said So far we have no citations or cogent argument to support excluding the I 6/4 labelling at all. There is nothing to do that at User:Mscuthbert/sandbox.
  2. The fact that we have to refer from here to such a recherché location as User:Mscuthbert/sandbox simply illustrates how this discussion is fragmented!
– Noetica♬♩ Talk 09:10, 29 May 2007 (UTC)
Anyway, you two seem to agree that the following text ought to be deleted:

Similarly, any C major chord with E on the bottom is in first inversion, any C major chord with G on the bottom counts as a second inversion; and analogously for all other chords.

But why (Tony especially) do you take issue with this? Provided we accept that the structure mentioned is a C major chord, as explicitly stated (excluding therefore any sort of a mere non-chordal structure using the notes C, E, and G such as you claim occurs in cadences, when V 5/3 is delayed in a certain way), isn't it true that such a chord with E in the bass is in first inversion, and with G in the bass is in second inversion? (Just asking – because you have not made your position clear, despite all the appearance of being so sure about things.)
In fact, the text deleted is well-motivated and quite useful, because it shows that it is the bass that determines the position (root, first inversion, etc.), not the disposition of any higher components of the chord. Newcomers might need to be told that.
– Noetica♬♩ Talk 08:54, 29 May 2007 (UTC)
It's wrong because this is not always the case for 6/3 chords, and is rarely the case for 6/4 chords. The statement indicates that it's always the case. Tony 11:08, 29 May 2007 (UTC)
I didn't quite like the "and analogously for all other chords" statement, but I wasn't sure exactly what Tony1 objected to. I deleted it because Tony1 should have done so instead of the comments invisible to the reader; if he thinks something is untrue he should remove it outright. (Also it had broken formatting, but that's not a reason to remove something.) There might be some value in what it was saying; replace if you like, but we should be careful about very general offhand qualifiers like "for all other chords". - Rainwarrior 09:07, 29 May 2007 (UTC)
Well, I didn't put it there. But I think it's entirely correct. Especially since it isn't about stipulating what qualifies as a chord (see my remarks above). Can you think of any exception to the addition and analogously for all other chords? I can't!
– Noetica♬♩ Talk 09:18, 29 May 2007 (UTC)
Well, the augmented triad comes to mind. A guitar player might wonder about inversions of a suspended chord. A ninth chord could make the "analogy" confusing, i.e. do the inversions always come in the triadic order or in order of ascending pitch-class? The other part of the removed statement is probably an okay example (though I would have preferred "bass" to "bottom", at least clarify that the bass is the bottom note with the first mention and then proceed to use bass as the term for it rather than bottom). - Rainwarrior 09:37, 29 May 2007 (UTC)
In some cases there may be no clear analogy because there is no clearly identified chord entity; but where there is, the statement holds. Augmented triad? So long as it is identified as having a particular root that gives it a name, the statement holds. So-called suspended chord? Perhaps there is no clear analogy. Wouldn't more classical theory analyse the fourth from the root as a non-chord element (a suspension perhaps, or an appoggiatura; the terminology might depend on the context of use)? With the ninth chord, the very name suggests how that would be treated: ninth, not second. That would settle it, I had thought. But if not, the correct analogising is one thing, and the facts about the second inversion of the chord are settled once that is settled. None of this is a big deal, in any case. Perhaps the statement ought to be restored, without such a broad additional claim as I have been defending here – just to show that it can be defended, really.
– Noetica♬♩ Talk 10:49, 29 May 2007 (UTC)

I 6/4 is complete nonsense. I2 would work (I in second inversion), though it may be confused for the notation for a third inversion seventh chord. Anyone know who uses the "I 6/4" notation?--Roivas 15:43, 5 June 2007 (UTC)

[edit] POV issue: notice of intention to remove figure

It's some time ago that I first raised the issue of the misleading analysis of the cadential 6/4 in the second figure. I suggested then that—reluctantly—I'd accept this if it were accompanied by a similar figure with the right analysis (i.e., V6/4 – 5/3 — I), and an explanation of the two ways of analysing this phenomenon.

In the absence of such a matching figure (I don't have the software to produce one myself), I intend to remove the figure next Monday 19 June, so that this misleading and, I believe, quite wrong analysis does not stand unchallenged in the article. Tony 09:36, 15 June 2007 (UTC)

I'll also give this article a copy-edit soon. Tony 09:55, 15 June 2007 (UTC)

(Tony, I hope you won't mind that I have fixed a couple of slips in your spelling, above. An itch that I'm sure you can understand!) I have called for discussion of this 6/4, and other broad issues affecting several articles, at an appropriate place: Wikipedia Talk:Manual of Style (music). I have no objection to your removing the figure if there is no sufficient discussion of the matter there, or here. But it may reasonably be reinstated later, if people do in fact start talking. I agree that more than one view can be accommodated; I disagree with your suggestion that there is any single "right analysis". (See Talk:Augmented sixth chord also.)
I still say we need more work towards consensus and coordination spanning several articles.
I'm glad you intend to copyedit the article, too. But those broad issues ought to be discussed first.
– Noetica♬♩ Talk 09:59, 15 June 2007 (UTC)

Yes, spelling took leave. I did raise it a month ago or so, and the POV remains. Thus, it should be removed pending a decision either to have two corresponding figures or none at all. The current situation, as I pointed out, is significantly unbalanced and should not be allowed to continue. No, the fact that mere discussion is occurring is not sufficient to allow POV to continue.

You can disagree with my view that the single-chord analysis is wrong for this phenomenon, but that won't change my intention to wage a permanent war against it on WP's music-theory pages. Tony 10:10, 15 June 2007 (UTC)

I agree that such discussion here would not necessarily justify reinstating that figure, or putting any other competing figure in the article (based on what others will call your POV), or both.
But why do you resist taking that feud to Wikipedia Talk:Manual of Style (music), where it can be played out with a cast of thousands, in Cinerama? Then many articles can benefit from there being an outcome – and you won't have to fight the battle several times?
– Noetica♬♩ Talk 10:21, 15 June 2007 (UTC)
Who said I don't like that idea: it's proper. But it doesn't change the fact that one side alone is presented/privileged at the moment. That cannot be allowed to go unchallenged. The result of any debate will be that both sides will have to be presented, since I can't see single-chorders backing down—or not enough of them. I'm not happy that visitors to the site are curently given wrong information. Tony 10:34, 15 June 2007 (UTC)
Fine. I understand! I can't see anyone "backing down": but there are compromises to find. Several textbooks have ways of notating these chords that give consideration to both stances, and often the authors themselves respect both stances. If you don't start things at Wikipedia Talk:Manual of Style (music), perhaps I will – later. But it might be more appropriate for you to take it up yourself.
– Noetica♬♩ Talk 10:54, 15 June 2007 (UTC)
I might do that. Not keen on two-headed monsters, since these are diametrically opposed ways. But I haven't seen the graphics, so it's hard to tell. It would be much easier with notational facility. Tony 11:23, 15 June 2007 (UTC)
I don't see the advantage of scouring the idea of a I 6/4 chord from Wikipedia. It's out there, it's in the literature. If someone is trying to learn about music theory from Wikipedia, this symbol is going to be missing from what they learn. However, I do notice that no one has yet pointed out the alternative notation in the text of the article at all, so I have done so. - Rainwarrior 15:28, 15 June 2007 (UTC)
Nor do I, since I six-four does occur, although rarely in non-popular music. It's just that by not explaining basic concepts surrounding inversion, this article fails to make necessary distinctions between when a sixth and a fourth that occur above the fifth degree of the scale in the bass produce an inversion and when they don't; that is, when there's a sense of root and when there isn't. Noetica has pointed out an instance of a true I six-four here, where the root has already been established and Beethoven has the bass skip to the fifth of the chord. Another example is at the start of Op 18/2 ii. In these contexts, the fourth above the bass (the root) is consonant (witness the arrival and departure of the bass from the fifth of the chord by leap); the root, of course, must be consonant with the bass—it's fundamental (no pun intended). These are harmonically generated six-fours. So are many six-fours in waltz- and march-time popular music, where the root is established (usually beforehand, but sometimes by back-prolongation) and the bass touches the fifth of the chord momentarily (oom-pah-pah, etc). It is this popular-music context that, I think, has led Gauldin to give oxygen to the I six-four fallacy in other contexts, notably the cadential six-four. In an otherwise excellent text, this is incompetent and a great pity.
By contrast, most six-fours in the non-popular literature are generated purely by voice leading, where there's no sense of root. This fact is partly why these six-fours became more important during the gradual disintegration of tonality during the 19th century. In particular, Wagner elevated six-four chords to a new status in his weakening of goal-oriented cadential expectations: because six-fours that are generated by voice-leading alone lack a root, for him, they were invaluable tools in producing seemingly endless, floating, uncadenced, unphrased passages. They're also useful in that respect because they can be followed by a myriad of chords/keys that would be remote and disconnected from a "rooted" chord.
This article will be superficial until it explicates the two basic ways in which, for example, 6/3 and 6/4 chords are generated: harmonically and melodically. It would be neater not to have to go into this in what might otherwise be a nice, simple, basic article; but, like basic music-theory curricula, to present an easy, "count the notes" kind of explanation is only half the story, and inevitably causes problems soon after in properly understanding harmony.
The figure is misleading, and privileges this misinformation in the absence of a matching figure illustrating what many people see as the right (and more straightforward) way of ascribing roman numerals to the cadential six-four. The recent edits do not solve this problem, and indeed they introduce further problems:
"In the second inversion, the bass is G—the fifth of the triad—with the root and the third above it, forming a fourth and a sixth above the bass, respectively. Thus, a second-inversion triad is known as a {}^6_4 chord. This inversion [no, the interval of the fourth above the bass] is usually [always!] considered a dissonance, and analytical notation will often treat it differently from the other chords (see Notations for inverted chords below)."
This jumps the gun, because it assumes that six-four chords always have a root. In reality, they rarely do. The harmonic/melodic distinction needs to be made here (in fact, before the 6/3 explanation, because it involves those chords as well).
"In addition to this, the numbered figures used in figured bass are often used in music theory to simply denote a chord's inversion. Thus a 6/4 chord refers to a chord in second inversion, and is often seen with roman numeral analyses of harmonic function. For instance, a common cadential progression might be written: I{}^6_4, V, I (see picture). Alternatively, this progression is often written as V{}^{6-5}_{4-3}, I in order to signify that the {}^6_4 chord here is a dissonance resolving to V{}^5_3."
Again, the point of departure is this wrong assumption. "Thus a 6/4 chord refers to a chord in second inversion" is correct only rarely in non-popular music. The last two sentences are garbled, to me.
I see no convincing case that the figure containing the analytical fallacy should remain as the sole illustration, even in the short term, and if it remains at all (with a matching illustration of the correct analysis), it should be put in its proper context, both in the caption and the main text. Tony 04:30, 16 June 2007 (UTC)

People tend not to read and become involved in discussions when responses are longer than stub articles. Try to keep your answers short. It will make your arguments better. Hyacinth 03:30, 17 June 2007 (UTC)

It takes some explaining, and a long entry doing so is better than no stubstantive contribution at all, like yours. This is a repeat of the pattern I'm seeing here: no one engages substantively in the debate, but just flings specious or irrelevant comments in to justify their position. In any case, you can see my argument in a nutshell just above your entry, in two sentences. What more do you want? Tony 03:37, 17 June 2007 (UTC)

What argument of yours are you seeking a response to? I've already said above why I prefer the I 6/4 analysis in this particular case (I think it better indicates inversion, which is the subject of the article). You've made several comments about this, but as my reason hasn't changed I saw no reason to reiterate this again and again. I am not ignoring your argument, I just disagree. I put different weight on the factors involved than you do, and unless I have something new to say or you come up with something I haven't considered already I don't usually think it's necessary to respond. - Rainwarrior 05:27, 17 June 2007 (UTC)

You think that the root can be dissonant with the bass? Hello? Where do you come from?

I'm taking down the figure tomorrow, for this reason alone. It's just wrong, musically and acoustically. Tony 05:51, 17 June 2007 (UTC)

And: "I think it better indicates inversion"—It's not an inversion. Can't be for my reason just stated. So let's not damage the "subject of the article" with this fallacy. Tony 05:53, 17 June 2007 (UTC)

I'm just wondering, if you think I 6/4 is invalid because the root is dissonant with the bass, is the symbol V 4/2 also invalid? I understand that you think it's a better approach to teaching harmony to not use the term I 6/4, and I've heard your reasons, but I don't agree. Your intent to remove it is inappropriate, it is your POV; there is plenty of published precedence for the use of I 6/4. This I've also said repeatedly before. This encyclopedia should reflect the real world usage of these terms. "6/4 is not an inversion" will be directly contradicted by almost any harmony textbook. It doesn't matter if you think you have harmony sewed up into a neat package by making up certain strict definitions for various terms; it doesn't reflect the way these terms are actually used. - Rainwarrior 20:00, 17 June 2007 (UTC)
But your POV is currently on display. And since both systems are quite in evidence in the literature, there's no question that both should be explicated here and not subject to unbalanced treatment. The sole illustration of YOUR method is POV. And doing a straw poll of how many crappy textbooks tout the simplistic fallacy will not do.
I'm glad you raised V 4/2, because thus far we've discussed only triads. Seventh chords are a different matter. There, the existence of the seventh is a strong identifier of the root, even if it is dissonant with the bass. Remove the seventh from V 4/3 and you remove the sense of root (unless the fourth is consonant, in the contexts I've pointed out). So we're back to the same old problem in your POV figure. It HAS to go, unless you want to produce another with the correct notation and put them side by side with explanatory text (that's the way I'd go, but I don't have the software to create a figure).
You see, harmony is not as simplistic as you make out. Tony 00:39, 18 June 2007 (UTC)
The alternative is clearly pointed out in the text. I don't see why we should clutter this with another image; what we should have is an article on the cadential 6/4.
What's this about harmony being simplistic? Could you can the insinuations and insults for a while? They make it harder to see where you're actually making an argument and where you're just trying to be annoying. - Rainwarrior 04:12, 18 June 2007 (UTC)
It's not clear, and even when it's made clear, the fallacy should not be dignified by an illustration where the correct method is not. Both or neither. If you want an article on the cadential 6/4, the illustration might go there as an example of how not to analyse it. Not here. Tony 05:18, 18 June 2007 (UTC)

You know, Tony, it's weird that someone with your experience on Wikipedia, which is quite extensive, doesn't understand how this works. And it's frustrating, because I totally agree with you that dignifying that cadential pattern with the pretense of the presence of a tonic chord doesn't help further understanding. We need to include solid counter-arguments from other sources. But I also know that plenty of reputable theorists, theory teachers and textbooks present it that way. And whether I think it's wrong or right, it deserves to be mentioned in Wikipedia. Our articles have to be about how things are, not how they should be. And how they are is that the I64 notation is used extensively. And I must remind you about WP:3RR. —Wahoofive (talk) 05:00, 20 June 2007 (UTC)

And I say to you to keep your bib out of this unless you remind your own friends of the same rule. Your bias is very disappointing. I'll be taking steps to have Rainwarrior banned if s/he reverts once more. I see that an anon. clearly sees the POV in privileging the fallacy with the sole illustration. I'm perfectly aware of how NPOV works: it's my ENTIRE argument here. I regard your entry as offensive. Tony 05:33, 20 June 2007 (UTC)

I've only reverted twice here. One of the three edits I made to the page today was correcting a mistake made by a bot. At any rate, you're threatening to have me banned if I break a rule that you've already broken yourself. If emotion is getting the better of you here, I think it would be better for the discussion and better for you to take a few days off. - Rainwarrior 06:45, 20 June 2007 (UTC)
Take a few days of yourself. In fact, the project would be better off if you left for good. Tony 07:31, 20 June 2007 (UTC)

[edit] Rameau

Rameau (surely a significant source on this topic) seems to indicate that he considers the fourth not to be a dissonance, but a "secondary" consonance like the sixth:

Il faut conclure de tout ce que nous venons de dire, qu'il n'y a que trois Consonances premieres, qui sont la Quinte et les deux Tierces, dont se compose un accord qui s'appelle naturel ou parfait, et d'où proviennent trois Consonances secondes, qui sont la Quarte et les deux Sixtes, dont se composent deux nouveaux accords qui sont neanmoins renversez du premier, laissant à part l'Octave qui doit être sous-entenduë dans chacun des ces accords, et pour qui le terme de Consonance n'est pas aussi propre que celuy d'Equisonance, dont la plûpart des meilleurs Auteurs l'ont orneé.

Source: Traité de l'Harmonie [1] That's why he didn't have any problem with second-inversion triads (he also seems to think we should be able to hear the root as an "undertone"). Rough translation of the above:

It is necessary to conclude, from all that has just been said, that there are only three primary Consonances, which are the Fifth and the two Thirds, of which a chord is composed which is called natural or perfect, and from which issue three secondary Consonances, which are the Fourth and the two Sixths, of which two new chords are composed which are nevertheless inversions of the first, leaving aside the Octave which must be heard below tacitly assumed ["Sous-entendre" means "Avoir dans l'esprit sans dire expressément, laisser entendre" (Petit Robert); the form with ë is old-fashioned.] in each one of these chords, and for which the term of Consonance is not as clean appropriate [in this context] as that of Equisonance [very rare in both French and English; it means "the consonance of an octave"], as most of the best authors describe it have styled it. [I have boldly amended and annotated, using underlining, Wahoo. Nice work, though! I'll not join the substantive discussion of this, right now. – Noetica♬♩ Talk 07:40, 19 June 2007 (UTC)]

—Wahoofive (talk) 06:20, 19 June 2007 (UTC)

Yes, no wonder music analysis didn't come of age until centuries later. But he does have a point, if we read between the lines. Apart from the fact that the fourth was treated as stable in the early stages of medieval polyphony (just an inversion of the stable perfect fifth), the fourth in tonal music is unique in that it's sometimes consonant (stable) and sometimes dissonant (wants to move urgently).
Thus, six-four chords can be consonant or dissonant, depending on their context. The cadential six-four is dissonant, because the fourth urgently moves to the third over a a stable root in the bass. It's just like a 4–3 suspension, except that instead of 5/4 moving to 5/3, it's 6/4 moving to 5/3. They're both intensifications of V: the root is the same, and the only difference between them is a relatively trivial one—whether or not the fifth is embellished by moving in parallel thirds/sixths with the unstable note, the fourth. Tony 06:55, 19 June 2007 (UTC)
Perhaps we could replace the disputed figure with one which includes a pattern where the notation would be more widely acceptable. Would a passing V64 (such as between I and I6) qualify? —Wahoofive (talk) 05:03, 20 June 2007 (UTC)
Great translations--should definitely include it. Rameau felt that inversion could not affect the fundamental qualities of notes or chords. Hence if interval X is consonant, so must its inversion. Which also lead him to believe that the second inversion was consonant. Put that together with his thought that melody comes from harmony (and not vice versa) then all(*) 6-4 configurations must be second inversion chords and thus consonant. (*)well, not the diminished triad. (6-4 update: I think I now have the seventeenth and eighteenth century views done--many of which are still with us. On to the 20th century). -- Myke Cuthbert (talk) 05:17, 20 June 2007 (UTC)
No, don't include it, because it hasn't got consensus. I'll just revert if you do. Citing Rameau's philosophical dawdlings as fact in a modern context, just as you cite your own take on cadential 6/4s as fact, is unacceptable. Tony
Oh, and "lead" is a metal, did you know? Get it right. Tony 05:25, 20 June 2007 (UTC)

I agree that Rameau's analysis should not be taken as fact over a controversial topic. I also agree that in a cadential 6/4, the tonic scale degree is definitely not the root. However, this does not mean that I 6/4 is a completely false notation; it specifically denotes what notes are in the chord, although it says nothing about the function of the chord. That being said, the article states that the cadential 6/4 chord is an inversion of a tonic triad. This is disputed if not downright false, so the article at least needs to mention that there is dispute upon the issue. I agree that a main article on cadential 6/4 chords would be nice, but the text in this article definitely needs to be changed.

--SockEat 17:41, 28 August 2007 (UTC)

[edit] Mediation Offer

Hi. I'm Ed Poor. I'm user #188, which makes me just about the most experienced contributor to Wikipedia. Not that I haven't made my share of mistakes along the way, of course. I've been called "tendentious", but since I don't know what that means, it didn't bother me! :-0

I am one of the original members of the Mediation Committee, and I've hardly ever had a case that didn't come to a happy resolution. So, if you'd all like some help from an experienced mediator, please let me know. I have email, and I can even boot up my IRC program. --Uncle Ed 20:36, 20 July 2007 (UTC)

[edit] Inversions in chord charts (or "slash chords")

I'm surprised the article makes no mention of how chord inversions are commonly expressed in chord charts in popular music. (i.e. An A major chord in first inversion is written as A/C#. A D major chord in second inversion is written as D/A. Etc.) It is mentioned briefly in the main chord article. Chord (music)

I was a music major once, and used to use the more "academically correct" chord inversion system all the time, but that was ten years ago. Now as a music teacher and musician, I never touch it anymore.

If someone would like, I'd be willing to do the research and write the section on "slash chords." --Guitarlesson 03:06, 11 October 2007 (UTC)

I just found an existing article on the matter. It could be cleaned up or integrated with the Inversion article. The link... Slash_chord --Guitarlesson 03:10, 11 October 2007 (UTC)
Thanks for this. We do need to reach some kind of consensus in the mediation before anything is added. I hope it doesn't drag on for too much longer. Tony (talk) 07:11, 11 October 2007 (UTC)
I would suggest the addition of a {{main|Slash chord}} where it appears in the text. Also, what are the sources for the third and fourth systems of chord inversion notation? I'm not familiar with either. Rigadoun (talk) 19:01, 11 October 2007 (UTC)

[edit] Wikipedia:Requests for mediation/Inversion (music)/Sandbox

It's sad that the mediation failed, however, I would suggest you guys edit the above page with the disputed paragraph in to try and thrash out a consensus. Edit warring isn't usually condoned, but it could make sense on this particular page as it won't effect any article. I'll keep an eye on it to make sure it doesn't get out of hand. Ryan Postlethwaite 12:42, 26 October 2007 (UTC)

Cadential .
Cadential {}_4^6.
Since I don't have the Piston source onhand, and we have not heard from Mscuthbert in a little while, I have modified my earlier example to take after its example, creating more or less the example I had suggested shortly before leaving the mediation. - Rainwarrior 03:46, 27 October 2007 (UTC)
Looks very good to me. I wonder whether we can negotiate the text around this? I'd like to propose a draft from the top down to the current "Notation" section, which I've not yet finished. Tony (talk) 08:09, 27 October 2007 (UTC) PS And I'm wondering why you took issue with the term position some time ago. I've googled "chord position" and was met with an avalanche. I've always been taught to say 6/3 position, inter alia, rather than 6/3 inversion. I guess there are two reasons: (1) it gets around the belief by many theorists that not all 6/3 chords are in first inversion, and likewise with 6/4 chords; (2) it embraces root position in the set along with the inversions (whereas the article currently presents a category problem at the top and further down by opening, for example, the section named "Inverted chords" with a discussion of a chord that is patently not inverted. However, all chords have positions. So is it going to be a problem to rename that section "Chord positions"? Tony (talk) 08:29, 27 October 2007 (UTC)
We probably don't need to be using the terms "6/3 inversion" or "6/4 inversion" at all, as after looking at a few sources, I don't think this is a typical description. "Root position", "first inversion" or "second inversion" are common, as are "6/3 chord" or "6/4 chord". I'd rather keep the language as normal as possible, rather than resorting to the use of the term "position" as you suggest, which I find unusual (except for the term "root position"). As it stands, the passage which explains the image is not at all compatible with the new image, since it is attempting to explain the use of figures in a roman-numeral analysis. I'm not sure whether it would be better to add figures to it, or to simply replace the explanatory paragraph with something else that doesn't cover that idea. - Rainwarrior 04:03, 29 October 2007 (UTC)
Also, does anyone have a source for the "a b c" or "1 2 3" notation discussed in parts iii and iv? - Rainwarrior 04:05, 29 October 2007 (UTC)
a, b and c are used by major examinations boards and in all of their publications, such as the Associated Board in the UK. I know of a specific harmony book if necessary, but it's an old publicaiton. I've never seen 1, 2 and 3 used in this way. Did you google chord position? It's pretty commonly used, and could be used as a category that includes root position. "Inversions" doesn't include root position. However, I have a structural solution if you really object to "position"; but the term is "normal", I think. Tony (talk) 06:06, 29 October 2007 (UTC)
Googling "chord position", for the most part I find pages about guitar chords (where position generally means "hand position", and is not directly related to the bass of the chord). Buried amongst these are indeed pages that use "position" in a way that describes root or inversion etc., though of the ones I found, they used it either as "root position" or "position", and then resorted to "first inversion" or "second inversion" when speaking of a specific one. Two harmony books I have on my shelf at the moment, Gauldin's and Schoenberg's, discuss the triad in "root position" and then "inversions" in a separate block, which more or less avoids the inability of the term "inversion" to cover root position as well, but neither ever refer to a chord's inversion as a "position". (Perhaps this is the "structural" solution you describe?) I'm sure there are sources out there which use "position" the way you describe; as I have said, though, I am unfamiliar with its use this way and would like an elementary source to be able to verify and understand its connotations. (As a musical term it is quite overloaded with other meanings, and should be defined here with care.) In some textbooks "inversion" is also used in the categorical sense as you are suggesting for "position" (e.g. Gauldin "identify the inversion of each triad", p.45).
I don't really think we should rename the section "inverted chords" to "chord position", but we should acknowledge and define the word "position" and clarify which chords discussed are inversions and which aren't (if not already clear). If you like, breaking out the root position chord from the others and discussing it separately may help make this distinction (though it doesn't bother me as-is to lump them together either). - Rainwarrior 16:38, 29 October 2007 (UTC)
Much as I think position would be neater in this sense—if defined at the top—I've hobbled through with a longer phrase to encompass root position and the inversions. The first draft of what I hope will be the resolution to this dispute is done in the sandbox. I've borrowed references from Cuthbert's proto-article (I've had the Beach article for 15 years). Tony (talk) 12:59, 30 October 2007 (UTC) And I see that position is still used in two of the captions. In addition, I first had the "Contrasting views" section under the "Notation" section, but moved it to be above it. I can't work out which is better. Tony (talk) 13:09, 30 October 2007 (UTC)
This looks okay, though I have a few points: 1. Maybe a brief introduction to the term "inversion" as it applies to chords is in order at the top of the section, before "root position", which would also be an ideal place to define "position". 2. The discussion of the cadential six-four would be better placed after discussing basic notation, rather than before, since this is a refinement of notation rather than an exposition. 3. The statement about "most harmony textbooks" was maybe true at the time of writing for A&S, but I doubt that holds now; I don't know quit when the balance shifted, but something like "most harmony textbooks before 1970", or a different way of phrasing this would be more appropriate. - Rainwarrior 03:40, 31 October 2007 (UTC)
Also, would you mind if I slipped a little figure 7 under the second last chord in the Rustington example? - Rainwarrior 03:42, 31 October 2007 (UTC)

(Outdent) All good, except that I'm unsure about the 7 in the Rustington. It's only a passing tone, figures are lacking from two other chords (a 6 and a 6/5), and it doesn't seem to be relevant to the concept. But in the larger scheme, it doesn't matter. "Older" textbooks is OK, except that it's chronologically vague. Let Cuthbert decide? The arabic-numeral system that needs a citation: who put this in in the first place? Maybe it exists, but it's news to me. Seems to have issues, but I don't care in the end. Tony (talk) 10:19, 31 October 2007 (UTC) PS The overtly christian dogma would be much better removed from the Rustington example; that would avoid an obvious culture-centric stamp in the eyes of, say, Chinese or Indian music students who are unlikely to be christians and whose parents and teachers may prefer a more neutral example. Tony (talk) 10:30, 31 October 2007 (UTC)

"Older" is indeed vague; I considered it a temporary solution. No one has defended the numeral designation, and it should be deleted before too long. Which figure 6 is missing from the Rustington? I added the 6/5 I had neglected earlier. As for the lyrics, I like the cultural context they add, it distinguishes this as an excerpt from a real piece of music rather than a generic example. Its genre and its composer have ties with Christianity, and I see no reason to censor this fact. It's not even an evangelistic piece of text. If you really want to get rid of the text, take it out, and I won't revert you on it, but I'd rather it stay in. - Rainwarrior 16:47, 31 October 2007 (UTC)
Also, I'm wondering about the term for "popular" or "commercial" music notation. Gauldin refers to "Chord Symbols for Jazz and Commercial Music" (appendix 4, p. 646) but not to "popular" music. I've always used the term "commercial" for it, though I'm sure preference varies. Where is the term "popular" used? - Rainwarrior 17:17, 31 October 2007 (UTC)
I think that between the two of you such great progress is being made now, that adding another voice will only stall our move toward reconciliation.  :) (okay, I'm just making excuses for being over my head in grading today. Though I did teach the 6-4s that everyone agrees on this morning: neighbor and arpeggiating). The chronological trajectory of textbook usage, that I thought would be so clear, ended up not being as clear as I'd like--for instance, that Piston small-I64 with BIG-V is from much earlier than I would've expected it--and in fact the later editions tone DOWN slightly the V side of the chord in favor of I (which seems odd--I'll ask Mark DeVoto about it sometime). And I would have thought that every book using I64 today would at least acknowledge V64 or the "dominant sound of the notes of the tonic" or something like that. But then Benjamin et al. (copyright 2008 [sic]) doesn't at all (though they do put it in brackets which is their way of saying "chord formed by voice-leading"), so it shows how hard it is to make any categorical statements about where the field is heading.
I'm going to basically keep quiet unless my name is specifically invoked. However, please keep taking anything from the six-four sandbox page. I'm happy that progress is being made. Hoping that bygones can be bygones etc. -- Myke Cuthbert (talk) 19:00, 31 October 2007 (UTC)
Actually, looking more closely, I think the vague "older" seems not so bad, maybe "most older and some recent" would be the clearest? Unfortunately "some" seems like the clearest statistical evidence we can find. (Esp. since I've made no attempts to look much beyond Anglophone world (or even North America, really) to see how other textbooks call this). The section as a whole is really well written and the two contrasting points both seem treated fairly--kudos to both. Could the caption "a cadential 64" be expanded to give the citation of Piston?
If we do update the Perry example, I think we should remove the lyrics if we can give a measure number from a published edition instead--it's really important to me to be able to find these examples in the context of the piece, but there are probably some ways to do that which also remove the text. -- Myke Cuthbert (talk) 19:10, 31 October 2007 (UTC)
I've provided a reference for the Parry that has no linguistic text on the score; all that remains is for the words to be removed from the illustration. I've filled out the reference details for all of the books, and linked names. Is there need for further details? What is there now may be sufficient in the context; however, I felt it necessary to add a sentence reinforcing the relevance of the "Two contrasting views" section to the topic of inversion. Tony (talk) 03:35, 1 November 2007 (UTC)

Some questions about quotes and sources: 1. "A different analysis of this harmonic phenomenon also arose in the early 19th century." In what sources does this appear? The only thing referenced is J T Arnold's book about Thorough Bass, which if I am not mistaken was published in 1931. Was this supposed to be "early 20th century"? 2. Does the quote "may be helpful for identification" really belong? It doesn't seem to clarify the I 6/4 symbol, or why it is different from the alternative. 3. Could we just put the "does not act as an inversion" in another footnote? Saying this yet again at the end of the paragraph seems pointlessly redundant. It's fine to have another referenced source, but do we need to quote it? It seems awkward. - Rainwarrior 09:01, 1 November 2007 (UTC)

I take it that your recent edits have addressed these points ...? Tony (talk) 13:03, 1 November 2007 (UTC)
No, I didn't alter any of those three things. I could make changes (i.e. 1. change "also arose in the early 19th" to "arose in the early 20th". 2. trim the "may be helpful for identification" quote. 3. move the "does not act as inversion" into a footnote that becomes another citation, probably another footnote number immediately after the Forte citation, or wherever it belongs), but I wanted to know if you'd object to 2/3 (are they essential in a way that I've missed?), and whether 1 should really be 20th century? - Rainwarrior 17:07, 1 November 2007 (UTC)
Please fix. WRT 20th century, it was Albrechtsberger quoted in FT Arnoled quoted in Beach. When you hit Albrechtsberger, you find that his work was likely to have been in the early 19th century. Here's the text from Cuthbert's article:

Johann Albrechtsberger followed Sorge and Rameau in writing that second inversion triads are consonant, but disagreed in part by suggesting that six-four chords on strong beats in which only the bass can be doubled (i.e., cadential six-fours) are essentially root position (five-three) chords delayed by suspension, and thus dissonant

Tony (talk) 23:59, 1 November 2007 (UTC)
Ah good. The original source should be mentioned somewhere then, either in the article or in the footnote. I find this little snippet of information quite interesting, and it would good to be able to bring some of it to the article (or if a real cadential six-four article is forthcoming, it can go there). - Rainwarrior 03:47, 2 November 2007 (UTC)
I've rearranged and rephrased the cadential 6/4 section a bit. My goal was to present both of them in a similar fashion, so as I've left it now in a form that for both of them first explains what the symbol is, then explains any consequences that need explaining, and then finally use and history. This, I hope, makes them easier to compare. I've kept all of the citations and tried to keep all of the important information, but I seem to have made it a little more concise, and may have left something out. Please look it over. - Rainwarrior 05:55, 2 November 2007 (UTC)

Also, when should we unlock the article? - Rainwarrior 03:48, 2 November 2007 (UTC)

The caption was pretty long, so now some of it is in a footnote; unfortunate to have two superscript numbers in the caption, but can't see how else. A 6 is missing from the second chord, if all other chords are to be figured. It should remain black. Pity the Roman numerals can't be smaller on WP, and not italic. Also pity it's necessary to insert commas between them in progression; I hope students don't think the commas are necessary in application. Tony (talk) 14:21, 2 November 2007 (UTC)
I'm trying to find my copy of the Beach article, so Albrechtsberger's (translated) statement can be ultimately sourced in the reference citation. Tony (talk) 04:22, 3 November 2007 (UTC)
The second chord in the Rustington example contains the tones F A C F from bottom to top. Are you actually referring to this chord as requiring a 6, or are you talking about something else? - Rainwarrior 05:35, 3 November 2007 (UTC)
I misread it. Tony (talk) 11:39, 3 November 2007 (UTC)
  • See whether the parentheses are OK. I can't cope with the possessive apostrophe in "inversion's", and it's already and "of" phrase in the subsequent para. We are disadvantaged by the size of the roman numerals, the size of the figures, the poor resolution of both, and our inability to render three vertical figures. Tony (talk) 14:07, 3 November 2007 (UTC)
Parentheses are fine. Three vertical figures can be done (we talked about this a long while back at Talk:Augmented sixth chord). I'll repost what I said there here for convenience:
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{}^6_4
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)
Let's put the roman numerals in Template:Music so that we can write {{music|roman|V42}} (or {{music|roman|V|4|2}} or something like that) and get the proper result. The only problem I've found with the math symbols is that we can't put in things like ♯4 or ♭5 in the math.
Hats are already implemented: {{music|scale|5}} gives scale degree 5. -- Myke Cuthbert (talk) 03:53, 5 November 2007 (UTC)
Now, I don't think there's any real way to directly alter the size of the <math></math> generated images, though there is way to get around this (which is more annoying to execute and to edit later) by creating the image with math tags, saving that image, uploading that image to the media commons, and then using that image inline with the text at whatever size you wish to specify. The thing is, though, since Wikipedia appears differently depending on an individual's settings (monitor resolution, font sizes, browsers, computer, et cetera), it's not quite possible to create one that will render the same way on everyone's computer. Making an image will fix the pixel size of a figure, but the size of everything else around it can't be fixed. - Rainwarrior 18:00, 3 November 2007 (UTC)
I've unprotected the article for now - there seems to be real progress made. You can't just cut and paste the information from the mediation sandbox as that would be a GFDL violation, so would you like me to do a history merge of the sandbox and the article so the histories are merged? Ryan Postlethwaite 18:32, 3 November 2007 (UTC)
Sounds good to me. - Rainwarrior 18:54, 3 November 2007 (UTC)
The sandbox and article have now been merged, so I'll delete the redirect from the sandbox to the article. Ryan Postlethwaite 18:59, 3 November 2007 (UTC)


I have put on a brave face to finally resolve the matter of the cadential six-four in an article on inversion, and everyone seems to have agreed on an illustration that does not privilege one view over another, the issue that sparked the dispute. We have even demonstrated that we are capable of collaboration in a mechanical sense, just as anywhere else in the project.

However, I am deeply distressed at the pursuit of an official page last week in which I was pubicly vilified. I can’t imagine what you thought it would achieve aside from alienating me forever, which is the result. It was unconscionable—out of proportion, bizarrely timed, and without legal basis. If it had happened back in June, it might have been more relevant, and I might well have launched counteractions against you—but I’m just not that nasty, and, frankly, I couldn’t be bothered. The action seems to have been conceived as some kind of pay-back for my role in the mediation that you killed off by walking out of it just as a resolution was in sight.

If I had seemed to be snippy at times, it may just be that the memory of being accused of employing a sockpuppet back in June is still sticking in my throat. It was a public accusation—which apparently still stands—of dishonesty (and stupidity, since to have engaged an anon user at that time would have been patently transparent). Snippiness might also have been a response to stalling, including refusals to negotiate a time-line and objections to sources that I see are now on the page by agreement.

I had been looking forward to constructing an environment in which we might all now collaborate for the benefit of music-theory articles on this project. But everything has been ruined by the gang-like actions last week. Just why you think I would happily engage in collaboration with you after this wanton abuse is beyond me. And to blithely hope that “bygones can be bygones” and to refer to me as “friend” in an edit summary a few days after signing up to the public vification is simply galling. Friendship is not switched on like a light bulb; on the contrary, it can hardly be a surprise that I feel intense bitterness towards the three of you. I can only conclude that that was the intention. Tony (talk) 08:33, 5 November 2007 (UTC)

[edit] Set theory

That section is gobbledygook to me. It needs to start with a big picture statement about WTH it is, why it was developed, and why you'd use it. Otherwise, it assumes way more than the opening sections just merged. Tony (talk) 00:45, 4 November 2007 (UTC)

I think it's worth having a section on inversion in set theory, but this section as is is almost worthless. Inversion in set theory is identical to the usual concept of interval inversion, there's nothing new there. The only thing that's different, really, is the notation, and that's what that T(x) stuff is (it's a fairly standard notation for it). The passage we've got doesn't really explain the meaning of those terms very well though. - Rainwarrior 09:16, 4 November 2007 (UTC)
Agreed--at this point, thanks to the hard work esp. of Rainwarrior and Tony, the chord inversion section is probably the best part of the article, so the other parts should be thought about (but maybe after some break to catch our breath?). My suggestion would be to move melodic inversion to the top of the page, and begin with a basic explanation of the concept WITHOUT using music notation (but probably with audio examples). Then follow with melodic inversion in a diatonic context: first a (simple) technical explanation, then usages in the West (chronological?). Then follow with melodic inversion in a chromatic context, including inversion of a tone row. I think only then is someone reading the article ready to understand inversion of an arbitrary set around a fixed note. -- Myke Cuthbert (talk) 03:53, 5 November 2007 (UTC)

[edit] (a), b, c ; theory texts, etc.

The New Grove article (William Drabkin, "Inversion") can be used as a citation for using letter names for various inversions. However, the letter "a" seems to be omitted:

  • in a C major context, for example, the three chords in ex.1 are either I, I6 and I6-4 or I, Ib and Ic, while ex.2 [I7, I65, I43, I42 -- MSC] shows I7, I7b, I7c and I7d.

Unrelated -- I was just at the American Musicological Society meeting all weekend. I spent some time looking through the theory textbooks that were being marketed there. Looking through about 10 books, there's of course no unanimous consensus, but it appears that at least 50% of them discuss the controversy around cadential 6-4, admit that all the designations require some sort of compromise, and use the symbol I64 in some sort of adapted form. One used (I64) -- similar to Benjamin et al.'s [I64], meaning "voice-leading" chord. One used a small font for I64. And one (similar in spirit at least to the Piston example we're currently using on the page) used I64 - V with a large brace under them and a bigger V placed below it. Most of the writers were careful either to completely avoid or drastically reduce the use of the word "chord" when discussing this 6-4, and/or did not talk about the term "inversion"; yet many of the same books placed this whole discussion in chapters or sections called "Second Inversion Chords."

There's food for all sides of the debate in there, but I think it mostly shows that textbook writers are trying to find a position that both sides can live with.

(I copied down the passages on the cadential six-four from a couple of books and I'll add them to my six-four sandbox page and post them here soon; I asked for sample copies of other books, so I'll add their thoughts too when they arrive in a month or so). -- Myke Cuthbert (talk) 03:53, 5 November 2007 (UTC)

[edit] Tonal vs Post Tonal

I think the few bits of post-tonal theory scattered through the article should either be removed or brought into a new subsection clearly delineating it as such. I was going to jump in but considering alot of good work has been put into this article I refrained. Since most of the article is about the tonal conception of inversions I think its confusing for students or non-specialists to have bits of post-tonal theory there. Post-tonal is quite esoteric, and would only be familiar to those involved with music academically. --Loksu (talk) 01:15, 6 January 2008 (UTC)