Talk:Inversion (music)

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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

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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)

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

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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)

[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)