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I should say, I do like working through the stacked thirds descriptions, because I like running through all the possibilities for two or three stacked thirds. And, hey, now that I know about extended chords, why stop at just stacking three thirds in four note chords. On to four thirds in five note chords! Etc.!

Yes, agree 100%. The more angles you can see it from all helps, I think.

(Warning: math nerd tangent)

Here is one of the kinds of mathematical musical games I like to play:

0 = m = minor third
1 = M = major third

Counting off chords in binary:

00 mm Cdim
01 mM Cm
10 Mm C
11 MM Caug

000 mmm Cdim7
001 mmM Cm7b5
010 mMm Cm7
011 mMM Cm(maj7)
100 Mmm C7
101 MmM Cmaj7
110 MMm Caug(maj7) (is this the right name?)
111 MMM Caug... with the octave *

* normal spelling doesn't stack as thirds: C E G# C, not C E G# B#.

I don't actually remember most of these combinations of minor and major thirds; I remember the types of chords by the triad plus the type of seventh, and work out the types of thirds if I need them.

I don't claim this is any use for sonata analysis...

Oh my! I haven't seen binary since taking a machine language programming course way back when, in which I barely got a pass. I see what you're doing. You're seeing patterns of majors and minors, rather than literally binary, yet you're also counting them off in binary. That's actually quite cool.

The fault is with the system. When it is built on the fifth degree of the scale it is the dominant seventh of the key. (In the ABRSM Manual of scales and arpeggios GBDF is called the dominant seventh of C not G7).

When it is formed on the tonic or fourth of the key it is a dominant seventh (type) chord.

In letter chord symbols the seventh is minor by default. In RN's the seventh is diatonic by default so C7 in key F is V7 but in C key is Ib7.
________________

Clever work with the binary. A 'mirrored' system might be better; least significant bit on the right being the first third etc. then there's no awkward change in notation from fifths to sevenths.

If you extended this concept into the next octave you will reach a point where a stack of minor thirds has reached a higher interval than a stack of major thirds. Although the chords are tertian (built on thirds) they are actually alternate notes.

So is it conceptually a root, plus a third, plus another third, etc. or is it a root, plus a third (major or minor), plus a fifth (diminished, perfect or augmented), plus a seventh (major, minor, or diminished), etc.? And does it make a difference in practise? It might get rid of sixths, sus2's, and sus4's (but I have a theory about those anyway).


It helps to show the details in the fundamentals of chord construction/naming and the relation to the underlying scale. If it helps to make it clearer for you then it may help to make it clearer for others.

We're analysing sonatas as much to try and learn the musical language as the converse. Your thinking helps.

Agree. Certainly helps me.

So now, testing out my new found wisdom for M21-M27

I will name the chords here, as I believe this may pose a stumbling point for identifying key if I get these wrong.

M21 - E7b5, F
M22 - C#dim7, Dm
M23 - Gm, C
M24 - Dm, F/A
M25 - Want to call this F/Bb, F/C, it is basically the F major scale over Bb and then C
M26 - Fmaj7/A

I can't really account for the C#dim7, but everything else seems to fit nicely with, and indicating F Major.

The C#dim7 comes from the key of D minor, and is making the following Dm chord seem more inevitable. It is VIIdim7 in the key of D minor, and can also be seen as a rootless A7b9, a.k.a. V7b9 in the key of D minor.

Not saying we're in D minor at any point, just pointing out a use of accidentals to make a progression to a particular chord (in this case Dm) seem more inevitable.

I want to say that D is being briefly tonicized here, and C#dim7 comes from the land of secondary dominants, but I don't know if I'm using that language wrong. Greener, I don't know if we've talked about tonicization and secondary dominants in our analysis threads yet. I'll try to explain what I mean better, if someone else doesn't jump in first with a better explanation. Right now I'm trying to think about how to talk about the promised more basic information of chords in minor keys...

Back to my series leading up to dim7 chords.

Before talking about chords in minor keys, I want to talk about roman numerals some more. I'm not sure I need this; I could just avoid roman numerals in what I'm going to say next. But I like roman numerals, because they show me patterns, so I want to be able to use them. So I have to talk about how I will use them in minor keys.

There are a couple of different ways of using roman numerals in minor keys. The way I'm going to show is not actually how I originally learned these; it's a system I learned later, but I think it's more flexible for the variety of harmonies one might want to analzye. The original system I learned worked best only for highly tonal music with a restricted set of chords and key changes.

In this post I'm going to just talk about roman numeral names for chords with accidentals. The post comes out quite long, and I'm not sure this is the best order to approach this in. So if this just makes your eyes glaze over, skip over it, and the next post will show more examples. It might be easier to pick this up just from examples rather than me trying to give this theoretical explanation first.

That said, here's the theoretical explanation. There's no music in this post; it's purely notation.

Roman numerals for chords with accidentals in a major key

Let's suppose that we're in a major key. Say, C major. Then we've seen, for example, the triads that are native to C major:

C, Dm, Em, F, G, Am, Bdim.

In roman numerals:

I, IIm, IIIm, IV, V, VIm, VIIdim.

Suppose I start to allow accidentals, while staying in the key of C major? What would I call, for example:

• Fm (F Ab C)? Answer: IVm.
• Em(maj7) (E G B D#)? Answer: IIIm(maj7).
• D6 (D F# G A)? Answer: II6.

And so on. I just replace the letter with the appropriate roman numeral.

Roman numerals for chord roots with accidentals in a major key

Now what if I allow accidentals even in the root of the chord, still staying in the key of C major? For example:

• Ebm (Eb Gb Bb)? Answer: bIIIm
• F#dim7 (F# A C Eb)? Answer: #IVdim7
• Bb (Bb d F)? Answer: bVII
• C#m(maj7) (C# E G# B#)? Answer: #Imaj7

For the root, I use the same roman numeral and put a flat ("b") or sharp ("#") on the front to show how the root has been altered from the normal note in the scale. Then I add on the usual chord naming parts.

For example, Ebm. The normal note in C major would be E, roman numeral III. So Eb is bIII. Then add on the decorations "m" for minor: bIIIm.

For example, C#maj7. The normal note in C major would be C, roman numeral I. So C# is #I. Then add on the decorations "m(maj7)" for a minor major seventh chord: #Im(maj7).

Notice that when identifying notes with letter names, we stick "b" and "#" after the letter. But when identifying notes with roman numeral names, we stick "b" and "#" before the letter.

What do "b" and "#" really mean?

I chose my example from C major, but I swept a key fact under the rug: with roman numerals, "b" and "#" mean "lower a half-step" and "raise a half step".

To illustrate, suppose I'm in the key of D major. What is the roman numeral name for Fm (F, Ab, C)?

• The root is F.
• The normal "flavor" of F that appears in the key of D major is F#, a.k.a. IV.
• Plain F natural is a half-step lower than F#.
• So we call F natural "bIV", where "b" really means "a half-step lower".
• So, in the key of D major, the chord Fm is called bIVm in roman numerals.

Still in D major, what about Cmaj7 (C E G B)?

• The root is C.
• The normal "flavor" of C that appears in D major is C#, a.k.a. VII.
• Plain C natural is a half-step lower than C#.
• So we call C natural "bVII", where "b" really means "a half-step lower".
• So, in the key of D major, the chord Cmaj7 is called bVIImaj7 in roman numerals.

Suppose I'm in the key of Bb major. What is the roman numeral name for Bdim (B D F)?

• The root is B.
• The normal "flavor" of B that appears in the key of Bb major is Bb, a.k.a. I.
• Plain B natural is a half-step higher than Bb.
• So we call B natural "#I", where sharp really means "a half-step higher".
• So, in the key of Bb major, the chord Bdim is called #Idim in roman numerals.

Still in Bb major, what about E7 (E G# B D)?

• The root is E.
• The normal "flavor" of E that appears in Bb major is Eb, a.k.a. IV.
• Plain E natural is a half-step higher than Eb.
• So we call E natural "#IV", where "#" really means "a half-step higher".
• So, in the key of Bb major, the chord E7 is called #IV7 in roman numerals.

Key point: The roman numerals might have "b" or "#" tacked on in front, depending on if the root of the chord is a half-step lower ("b") or higher ("#") than the normal note as it appears in the major scale. This happens even when the letter name does not have "b" or "#". For example, in D major, Fm, but bIIIm. In Bb major, E7 but #IV7.

Wait, what about the minor keys?

This post is quite long enough, so I'm going to put the minor keys in another post. Poor minor keys, always being deferred.

Just seeing your new note now, PS88 re: series leading up to dim7 chords, but have not gone through it yet.

We had tossed about D minor before for this section. I chose it originally I think because of the Bb, C#. But we are certainly not there long.

Since this section is largely construed from development of movement 1, would it be safe to say that we are passing through D minor, shortly visiting F major and then heading straight home to Bb Major?

Sorry, but unfortunately I mostly think in Black and White and have a very difficult time with Grey.

M21 is Em7b5. Although the third is absent, it wouldn't be G#.

The rest is pretty much there. The C#dim7 in M22 is a rootless A7 resolving to Dm.

We end up in F, yes, briefly via Dmin, but in M26 the E nat makes it F7 the dominant of M27 Bb.

Actually, all clear so far.



Not so clear; Fine with being back to Bb a measure sooner. But, how is (F,E notes) making it a F7 vs. Fmaj7?

Agh! It doesn't. It's a mistake!

Sorry.

I haven't actually looked closely at any of the harmonies in this sonatina, so I based my "brief D minor" comment solely on the short snippet of chords that I saw posted.

I'm about to go on a business trip, and hopefully I'll remember to take my Sonatina scores with me on the plane, and catch up on the analysis you all have been doing.


Do you mean, the idea of briefly touching on a key, but not really being there? If so, I'm with you. I hate having to resort to just saying "accidentals for colour"; I always want to pin them down to some specific harmonic purposed, tonicizing a note being best of all. (Although I'll accept the stray Neapolitan sixth...). But I'm forced to admit that music doesn't always work that way, and I'm having to become more flexible in how I approach harmonic analysis.

Or do you mean some other Grey idea?

And of course that is simply F C G Dm Am Em. So good point.

Another way of looking at it, going the way music usually moves:

B° Em Am Dm G C. And that progression is not the least bit unusual, showing the circle of “fourths”, if you wish.

Then you can tack on F, then show a cadence at the end:

B° Em Am Dm G C F G (or G7) C.

VIIdim7 IIIm VIm IIm V I IV V or V7 I

So it shows that each of the primary chords of a key, except for VIIdim, can become the I or Im chord of a nearby key.

VIIdim can also become VIIm or VII (major), and this is the whole principle of secondary dominance. So in the key of C – I hope I am in the right key! – you can stick to comfortable RNs so long as you use any simple triad that belongs to the keys represented by I, IIm, IIIm, IV, V, IVm. It’s only when you go outside this limit that RNs get really clumsy. Thus a Ger 6th chord in C major, Ab7 or Ab(#6), suddenly leaves behind numbers, and that is my objection. “Ger” is English. We suddenly need something like bVI7 or bVI(#6) to stay in numbers.

I never thought of it that way. I would not call IIm a substitute for the simply reason that IIm V I is incredibly strong. Downward 5th movement. But it does also explain the duality of IIm/IV, and why EITHER chord going to V is about as common. It also intuitively hints at the fact that IIm7 contains IV – Dm7 = D **F A C**.

VIm really doesn’t substitute for I, which is why V to VIm is labeled a deceptive cadence. It’s horribly weak if mistakenly used for an ending, but it is great for delaying. Which is why Mozart and co. so often write G7, Am, Dm or F G(7) C. It’s musically the equivalent of “haha, just kidding, you’ll know where I’m going, and I’m going to make you wait.”

Also, you will not normally hear IV VIIdim I, but you WILL hear VIIdim to I, and even more often VII°7 to I (or Im).

I hope I did not write something totally confusing.

No, I'm fine with that. Just mean when I look at, M21-M26 for example, I prefer to know the final conclusion, consensus and outcome of our analysis. Otherwise, I am likely to keep pestering with more questions.

So for example, when you say I think we are visiting D minor, but not saying we are in D minor and then not confirming my F major ... well, that just throws me into a tail spin. But, thankfully, Richard saved the day and confirmed we were pretty close. And VIOLA, my heart rate is back to normal

Rondo: a musical form in which the principal
theme is repeated several times, with short sections
based on different themes (called episodes) in
between each restatement of the opening theme;
sometimes one or more of the episodes is also
repeated, a common pattern being ABACABA. The
rondo was often used for the final movements of
Classical sonata-form works

allegro: cheerful or brisk; but commonly interpreted as lively, fast
vivace: very lively, up-tempo

I have just had a precursory glance at this final Rondo movement. On first glance it looked/sounded involved, but the Rondo definition (above,) explains a bit. There is some clear recognition to 1st movement, not so sure about the 2nd movement yet.

I have not had a chance to identify the sections, keys and where all the content is coming from yet. Starting out, we are back in F Major and in cut time (2/4.)

Unfortunately, I need to be away for a few hours now. But, anxious to move forward with this today and keen to see any further insight upon my return.

Are we all with movement 2 and fine to proceed?

I will take the overwhelming enthusiastic response as a resounding ... YES.

Best I can tell is that this is sonata-rondo form:

A - M1-M10
B - M11-M12
A - M13-M28
Development M28-M52; Key of C Major
A
B
A

Have not seen a movement like this before. It is quite different. But this is my preliminary assessment. It's late, so that is my excuse, if I am entirely off base.

What's a Sonata-Rondo?

A rondo is basically ABACADA etc. The sonata-rondo complements the sonata principle so B is in dominant, C is the development section (usu. in varied keys) and D is the B section in tonic. Most of the rondos I can think of off-hand have a coda section different to the closing cadence of A.

There are no fixed definitions, however. There are many, many variations.

The most famous rondos are probably the third movement of Beethoven's Pathétique, an excellent example of sonata-rondo, and Mozart's Alla Turca from his Sonata K.331, which is not strictly a Rondo. His Rondo an A minor, K511, is a much finer example of the form.

So what do we have here? The structure appears to be a da capo ternary, ABA, form. Here, M28-52 is clearly the development section.

M1-28 are the AB and AD (or AB') combined. M1-7 is our rondo theme, A. Our B section (in the dominant key) is M7-12. The A theme returnes in M13-19 and the remainder remains in tonic, M19-28 so must be our B in tonic.

I don't foresee a struggle finding out where the material comes from for the development section. Tying the piece up to the other two movements is a bit more of a challenge but needn't detain us if it's not obvious.

I'd be as happy with A = M1-12 and B = M13-28 but you do need to make sure you understand why B shouldn't start mid-phrase and if A = M1-10 (10 measures) then A = M13-28 (16 measures) must be wrong. B = M11-12 seems more like a change of phrase ending than a whole section (even without looking at the score). Does that make sense?

If I were to just listen to this, without looking at the score or listening to/for key modulations, I would call this a rondo as the theme is very distinctive and makes four clear returns.

I would treat the terms rondo and sonata-rondo as a vagaries or as a challenge to find the form in that particular instance. I would delight in finding a movement, like Beethoven's Pathétique, when the A section preceded every episode including the coda.

Rondo form is often combined with elements of sonata form to produce the sonata-rondo. The sonata-rondo has a development section similar to that in a sonata form and is outlines A B A -development section- A B A.

I wasn't so keen on the previous definition as I did not see how it would fit. So went searching and found this one, which seemed to me to fit better.



Yes, making more sense. I had a big problem -- as is evident -- in trying to figure out where to put these labels. With the main theme returning I wanted to call this A again.

Can a second A have any extra/fewer measures? I believe we had a couple of extra in the 2nd movement, but it was just a repeat of 2 already used measures and was not as drastically out of whack as was the case here.

The development section is the C section? Would we just call it that "C" and not development at all?

Yes, we should call it C. I got carried away the the sonata-rondo bit...