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keystring, although I used natural, harmonic, and melodic minor scales as stages to build the types of chords in minor keys, ultimately I mostly just use the resulting ensemble of notes and chords:

D minor easily includes D E F G A Bb B C# C. It might have IVm or IV, Vm or V, bVII or VIIdim. Among other possibilities. And I'm usually combining a lot of information, more than just one chord, to determine key, or tonicization.

I like those kinds of exercises too, about what scale a chord might occur in. And I might approach the solution in various ways, depending on the chord quality and even the exact notes. There are larger, more contextual questions to ask, so it might be easy to dismiss the exam-type questions as irrelevant theoretical busy-work. But I think the exam-type microscope-vision questions are trying to foster the learning of skills that can be components of answering the larger, more interesting questions. But that's me; I'm a hopeless optimist about exams, and I think easily in terms of rules and symbols. There are probably ways to build someone's skills at the larger questions, by a different route.

Look at what I've been laying out. A lot of detail about roman numerals, a lot of repetitive exercises in building a restricted set of chords (triads and types of sevenths) from restricted sets of notes, suggestions to practice with yet more repetitive exercises on order to learn certain patterns that occur over and over. And all this is premised on knowing scales and chords, which if I had laid that out would have included a whole nother set of detail and repetitive exercises to get the patterns ingrained.

And all of this is merely prep work to set the stage for a few simple principles that help orient me in harmonic analysis of music that is not too chromatically complex.

Could I have laid it out differently? Perhaps. Although, since I'm trying to lead up to how *I* think about dim7 chords, I think I get at least half a pass on laying it out in this way, because I think this is the underpinnings of how I think about harmonic analysis. It's not a complete story even now; I suspect there are lots of things I use in harmonic analysis that I haven't mentioned yet.

There are other kinds of approaches -- aural, kinesthetic, inductive rather than deductive, etc. -- to reach the same endpoint of being able to understand music in the way we're trying to learn on this thread. And maybe (probably?) some of those approaches are better for some (most?) people, and sidestep or avoid or reach in a more intuitive way how to understand and talk about harmony. But unless we want to completely ditch any connection between chords and keys, what interests me about a question with an answer like "F7 could be IV7 in C melodic minor" (*) is "what underlying skills is it trying to foster, where do we use those skills, and are there alternate ways to teach and evaluate those skills, and perhaps even how to answer this kind of question, other than what might seem tempting, to teach a memorized meaningless routine?"

(*) rats, I left out a place where a 7 chord can appear: as IV7 in a minor key.  So F7 above might be IV7 in C minor.  I think that's the last of the possibilities, but I'm not sure: that will teach me to leave unfinished the cataloguing of chords in harmonic and melodic minor!

OK, what I have been leading up to: among all the chords we have seen as we named types of triads and seventh chords formed from notes in various conventional scales, where have we seen dim7?

Answer: in exactly one place. As VIIdim7 in a minor key. For example, C#dim7 only appears (in our restricted set of chords) as VIIdim7 of D minor.

OK. That's really it about dim7 chords. But let me expand:

This is the first way I learned about dim7 chords. I have learned other things, like how a dim7 chord can slip and slide in many directions (perhaps notated with enharmonic spellings), and that there are essentially only three dim7 chords, and that on lead sheets dim7 chords are named by their lowliest note, and that the spelling can be a clue for where a dim7 chord is going.

But when I see a dim7 chord, I start with what were my first fundamentals. I rearrange the notes so it stacks up as an official series of actual skip-a-letter minor thirds, I name it by the bottom of the stack of thirds, (and specify inversion) and then I start expecting to see the minor key or minor chord a half-step up.

For example, if I see the notes (from lowest to highest) F G# D B, I shuffle them around until I have a stack of formally named minor thirds: G# B D F. (This is actually what I do with every chord I see; there are some patterns I've learned that help me do this faster than when I first learned it, and there's a whole nother art to working things out when notes are missing, but this is how I started: with examples of complete four-note chords.). Anyway, I've stacked my chord up in thirds. Then I figure out what type of chord it is. This is when I first discover that I have a dim7 chord on my hands. G#dim7, or G#dim7/F if I'm keeping track of inversions, which I didn't use to much care about, but come to find out they're interesting and have important patterns for analysis. So what is G# the leading tone of? Half-step up: A. So I expect to find the key of A minor, or maybe just an Am chord, or maybe other important chords from the key of A minor -- perhaps E7 -- or maybe this is just part of a big continuous circle-of-fifths style progression, and I'm going to find Am but already jazzed up with a seventh to lead somewhere else as Am7.

Or maybe, I'm told VIIdim7 can go to I as well as Im (I haven't actually noticed any examples of this yet to register them consciously, but I'm keeping an eye peeled) so maybe A major chord is coming instead of A minor. But my basic expectation is A minor, or something related to that key.

Now, this might not always be what a dim7 chord does. But I think that in the music we've analyzed, this is what has happened, a lot. Not to say that we're always IN that minor key, so dragging out the roman numeral notation VIIdim7 may not be appropriate. And there are other ways to get to the same final result, and over time I may get more comfortable using those other ways first. And in particular, learning other ways to think about dim7 chords might help with my sight-reading of them (and I do mean sight-reading, not just plain reading).

But essentially, once I find a stack of thirds that I can name dim7, I'm expecting "minor, a half-step up".

And this is one of the reasons why I love dim7 chords.

Another reason I love dim7 chords -- actually dim triads -- is that I like underdogs. And I see dim chords as underdogs. "Learn all the triads in a key, but, ick, don't bother with the last chord, it's wierd. Ignore it for now.". "Modes are interesting, but, ick, don't write in Locrian, because it's nasty."

And another reason is that I find the sound interesting.

I know, it's completely backwards. First theory, then foolish personification, and only last, sound.

Heck, first time I heard the "melodic minor scale" the way it is officially taught, I instantly saw a character that had a personality disorder. I saw this rather literally. Going up: "I'm minor, you can hear that, right?" Half ways up he changes his mind (it's a he, and he wears a straw hat), "As I said, I'm as major as I can be." Then he tilts his straw hat, descends, and says "I never said such a thing. I am a very natural minor, and always was."

Ooh, there's been a lot written since I finished last night!

Now let me throw a spanner into the works while heads are still spinning.

The natural minor shares the same key signature as the relative major but the leading note being a tone down no longer functions as a leading note. For the music to function at a cadence the seventh note must be sharpened. The harmonic minor scale uses the sharpened seventh (nat min key sig, 7 sharpened by accidental).

The interval between the sixth and seventh then becomes an augmented second. It's uncomfortable to sing so when the melody is rising to tonic the sixth is also sharpened to make the melody smoother. When the melody is descending it no longer needs the leading note for the 7-8 effect so both sixth and seventh notes revert to their natural (minor) pitches. This is the reason for the melodic minor scale; flatted third rising, flatted third, sixth and seventh falling (nat min key sig, 6 & 7 sharpened by accidentals).

For harmonic analysis (where harmony needs to be functional) I use the harmonic minor scale plus a bit of natural. Natural minor key signature plus sharpened seventh. I don't follow PS88's convention with Roman Numerals. If you're defining a cadence or a simple harmonic progression, RN's work nicely to show function but if you're modulating and changing keys RN's are a minefield.

C minor: B nat, Eb, Ab [+ Bb].

I C Eb G: C minor

II D F Ab: D diminished

III Eb G Bb: Eb major or
III Eb G B: Eb augmented

IV F Ab C: F minor

V G Bb D: G minor or
V G B D: G major

VI Ab C Eb: Ab major

bVII Bb D F: Bb major or
VII B D F: B diminished

The augmented chord on III was seldom used before the late nineteenth century (Liszt and Debussy) - the minor III is seldom used in major keys either. The chord on the seventh degree was mostly used, as in the major scale, as a rootless dominant seventh or a transpositional device.

How does it fit on the circle of fifths? Recall the major scale for C major:

Major ring: F maj C maj G maj/7
Minor ring: D min A min E min
Dim/7 ring: B dim(G7)

The minor scale for it's relative minor, A minor:

Major ring: F maj C maj/aug
Minor ring: D min A min E min/maj/7
Dim/7 ring: B dim ----- ----- G# dim(E7)

It's not as nice a fit to the circle of fifths but it's workable.

Richard, are you leaving out the possibility of the melodic minor? For the melodic minor, where the 6th is raised from Ab to Anat, you'd also get:
IV: FAC major
VI: ACEb dim

Btw, in England do you say "parallel minor key" or "tonic minor key"?

In England we say tonic minor most of the time but I have heard parallel minor as well.

I'm not intentionally leaving out the melodic minor I was just focussing on the harmonic which is most commonly appropriate for harmonic analysis.

I see I left F major and D minor on the circle of fifths so it's there indirectly. F minor isn't in the neighborhood but all the diminished's are in the vicinity of course, depending on spelling.

Thanks for your vigilance!

Perhaps they just wanted to confuse the heck out of Greener.



Among my biggest challenge at this point are the minor scales. Since every major scale has it's relative minor and share the same key signature, only a natural minor applies in terms of the key signature. Is this correct so far?

Melodic, harmonic -- and understand many others -- are of help in further understanding cadences. Is this also correct.

There is a lot to digest from the overnight posts, so hope no quizzes forthcoming today. So far have just read through everything. It is all great but will be sinking in I think over time.

So, just want to further inquire on a few things at a time as we move along. There will be more ...

I was holding out a bit as I wasn't quite done reading. So some of my previous questions, already confirmed.

Just an additional point. The melodic minor scale, as it is often taught (see Hanon) assumes 6 and 7 ascending as it is in a major scale but lowered when descending.

From this it is easy to assume that “melodic” can not go “down” the same way. But a melodic minor scale, as I am defining it here, with the same degrees used both ways, is VERY common when a dominant is used, and you find it all over the place in Bach, for instance, this way:

LH plays G or G7 in key of C minor. RH plays D C B A G F Eb D C...

A good piece to examine this in would be CPE Bach Solfeggio, obviously not by THE Bach, but CPE Bach was trained by “Dad”.

Relative minor shares the same key signature. In the harmonic minor the 7th is raised, which creates a leading note, and gives us a real dominant seven chord (G7 instead of Gm7). Example of relative minor: C major, A minor.

Tonic or Parallel minor has the same tonic note. Example: C major, key of C minor. You can still figure out the key signature as per above. C minor has the key signature of Eb major. This also tells you which notes are lowered when comparing C major and C minor. C minor has Eb, and Ab, but the "Ab" of Eb major tends to stay B because of the harmonic minor. You can go back and forth either way.

I just wanted to chime in and mention that this so-called VIIdim7 chord is just as likely to show up in a major key. And because even somewhat sophisticated music does not stay strictly in major or minor, I use a different system from the traditional one, but we should define it:

Traditional, major:

Using upper and lower case: I ii iii IV V iv vii I. Some people write vii°, but that is not necessary.

Traditional, minor:

i ii (ii°) III iv v OR V, VI VII

For me this is system is NUTS because of minor, which is not a dependable concept but rather a set of pitches that is in continuous flux.

And that is why I drive traditionalists nuts, always using major as my default, then referring to chords within a major scale framework. For me in the key of Cm we can have a I chord, since obvious C may move to Fm. In traditional thinking we have to name C as V or IV, and although that is logical, it always short-circuits my brain.

I am mentioning this because if we call Eb bIII in the key of C minor, many people are going to be confused. I wanted to bring this out before we run into problems. I use my own system, which is really very close to at least one jazz system, but it could throw people here directly to Mars!!!

Gary, I was trying to present the roman numerals as you use them, because I have come to think of them as the most powerful and flexible system I know for music that may borrow notes from outside the scale of the key. If you think we should use another system on this thread, let me know and I'll correct what I've written. The qualities of the chords stay the same (the part after the roman numeral). What changes is whether the roman numeral has a flat, sharp, or nothing in front of it. At least, if we're at least agreed on all upper-case roman numerals.

In the system I originally learned, in Dminor, C7 is VII7 and C#dim7 is vii°7. Fine for certain kinds of music, but there are weaknesses in this system.

Richard, keystring, any thoughts on roman numeral system to use?

I like that Gary's system allows me to say Cdim is VIIdim in C major, and it is also VIIdim in C minor. I don't have to say something like "it's #VIIdim in D minor" or "it's VIIdim in D harmonic minor".

The main reason I introduced the roman numerals was two-fold:

1. So I could point out the general pattern of chords in a minor key. There are other ways I could have pointed out the patterns, but for me roman numerals are the perfect shorthand for exhibiting a pattern, and I hoped that their role as pattern shorthand would be comprehensible to others.

2. So I could refer specifically to VIIdim7.

~~~~~~

I don't recall meeting a dim7 chord in a major key, unless it was heading towards the expected minor chord, but I haven't been paying close attention for this. I'lll keep my eyes peeled. Gary, I did expect that you would mention it.

Having laid out all the patterns, I'm going to walk through the first movement of the Clementi Sonatina #4 showing how the dim7 orients me.

Imagine me identifying the chords throughout.  I don't trust my ear enough to tell me all the interesting places to look at harmonies.  Plus, I enjoy identifying dead-simple patterns like F F F or G7 C G7 C G7 C.  Again, this is because my ear doesn't always identify these, at least not with an associated name for the quality of what is going on.  So making the names is part of a long-term project for me to understand what I hear better, and also in the short-term allows me to, say, talk about whether a piece is harmonically simple or complex at any given point: again, because I don't trust my ear to give me full answers on that.

But for this post, I'm going to focus on just the parts where I spot a diminished, half-diminished, or fully diminished chord.

m. 3, Em7b5.  Remember from our chord types that this shows up in only a few places.  It shows up as VIIm7b5 in a major key, and as IIm7b5 in a minor key.  I think I'm more used to seeing it in a major key, but maybe I haven't been paying close enough attention.  It also turns out it shows up as VIm7b5 and VIIm7b5 in a harmonic minor scale, but I really don't remember seeing that in music before.  I'll be on the lookout now, though.  So, in letters Em7b5 might signal F major, D minor, or F minor.  But since we're in F major already, and I'm (perhaps sloppily) used to expecting half diminished chords in a major key pretty much all the time, in fact I just think: "Em7b5, expect F major, oh yes we're IN F major, and the next chord is F, nice familiar pattern."

m. 6, Bdim.  The next chord is C.  Another nice familiar pattern, from VII dim to I in a major key.  I'm not saying we're actually IN C major here, but what I'm basically thinking is "dim triad, therefore major or minor chord a half-step up will be familiar.".  (Diminished triads show up in other places in the types of chords -- IIdim in natural minor, VIdim and VIIdim in melodic minor -- but I'm not so used to those.). Actually, omitting the Bdim for a moment, the progression from m.7 to m.9 is Gm/Bb C F.  This is a IIm V I progression in our home key of F major.  The brief Bdim before C serves to "tonicize" C: to make it seem inevitable.  But then we  perhaps don't really change keys to this inevitable C; we continue back to F.  This is a very interesting progression because it crosses the division between phrases, or maybe it glues two phrases together by overlapping them on F in m.9.

m.32, Bdim/C.  The C is a pedal, appearing in each of mm.31-33.  Bdim makes me expect C major or C minor, and it's true that m.31 is C major; indeed here we are at the start of the exposition appearing, perfectly normally, to be in C major, just where the exposition left us.  But wait, m.33 is C7, which, while it is a type of C chord, is unexpected.  And the tritone F-B of Bdim doesn't resolve outward as expected to E-C.  It resolves inward to G-Bb.  And starting in m.34 we get a flurry of A, A7, and inverted Dm chords.  Since A is a fifth above D, something D minor-ish is going on, although the lack of a cadence on a root position Dm chord might lead some to deny that we're actually in D minor.  Not me, though, I like having a key to give me moorings.

Thinking Dm, I recall from melodic minor that Bdim might be VIdim (and there I just said I haven't seen these!), where the root, B, appears in the melodic minor scale.  And then C7 can be bVII7, using notes from the natural minor scale.  So from m.32 to the first beat of m.35, I have VIdim bVII7 V Im (with some inversions, which I'm ignoring).  Hmm.  Six, five, and one are familiar to me when associated in a six-two-five-one progression.  Aha!  If I rewrite m.33 as Edim/C, and treat C as a pedal point, I now have a sort of 6-2-5-1, even if the dim chords are unusual qualities for the 6-2.  VIdim IIdim V Im (ignoring inversions).

I'm not sure if this is actually what it sounds like to people who can hear these things instead of just juggle symbols on paper.  Indeed, way back at the Bdim, who would think we're in D minor?  Nobody!  We expect to still be in C major.  The Bb in m.33 signals that it's not C major any more.  The next most likely expectation might be that we're going back to our real home, F major, with a C7 F (V7 I) progression.  Although if we realize we're starting a development section, we would be disappointed by returning home so soon, and Clementi doesn't disappoint, by taking us to the relative minor of F major, D minor.

m.38, F#dim7.  I expect G minor.  Sure enough, we get D7 (reduced to the bare minimum C D) and then in m.39 Gm.  A lovely familiar two-five-one, in minor: IIdim7-V7-Im.

mm.40-41, Edim7.  Expect F minor.  Sure enough, we get (almost) the same thing as mm.38-39, a whole step lower: Edim7, a minimal pair of notes Bb and C to represent C7, and then... oh wait a second, the A naturals (instead of Ab) at the end of m.41 tell us that we're in F major.  This to me is a surprise, because the Db of Edim7 belongs to F minor, not F major.  On the other hand, C7 can quite respectably go to F instead of Fm.  Plus Gary has been telling me that VIIdim7 can lead to either Im or I.  So I'll chalk this one up to experience. And right after the previous post where I said I didn't remember meeting one of these!

Written out like this, I'm afraid it makes my process look long and tedious. But it doesn't feel long and tedious to me. To me it feels comfortable and fun and like making sense out of random strings of notes and turning up occasional jewels to surprise and delight.

You know why I prefer this system. I’ll continue to use it, but I am also used to “translating” to other systems that people know better. As you perfectly summed up, there are severe limits to the traditional RN system. In fact, there are limits to any numbering system, and that is why sometimes an “it is what it is system” is most handy. For me usually that means using letters!

This whole subject drives me nuts as a teacher. I’ve never known how to teach it.

The REAL story is that our key signature conventions are based on a very pure set of pitches or notes. Minor is simply major, starting on a different degree of the scale. So C major, C D E F G A B C

Becomes A minor, A B C D E F G A

Same key signature, and what could be easier?

Except as we ALL know, it has not been that simple for several centuries, and at any point in a piece in A minor it is just as likely that we will see a G# as a Gnat. The second most common chord in A minor will be the V chord, E G# B. So the key of A minor could be just as easily one sharp, G#, or two sharps, F# and G#. In other words, the key signature we have inherited is logical and works best for natural minor, but in the Baroque, Classical and Romantic periods, that form of minor no longer was the default.

I continue to teach that minor is major with “toggles”. We can depend on 3 being lowered most of the time, since it is on the tonic chord, but 6 and 7 are like little switches that continually flip up and down.

Way back when, I had a flute book which tried to teach the three firms if minor scales. Natural, harmonic, and melodic. It illustrated with C minor, and maybe a few other keys, and talked about forming these scales by lowering third sixth and seventh degrees.

I hated it.

I thought it was the most dad-blasted useless thing I'd ever met. I refused to learn them.

I'm not sure when I finally learned about minor keys, but eventually I did, via the key signature as relative minor, and look at the last note to figure out which key is, the major or the minor. The accidentals didn't bother me. I was used to having accidentals in music and never wondered why they were there, just took them as instructions for what to play.

A long time later, I got Edly's Music Theory For Practical People and was introduced to the explanations for natural minor (Aeolian mode, so it's a logical choice to lower three six and seven, it's not just randomly made up for the heck of it), harmonic minor (to provide a leading tone), and melodic minor (to fix up the melodically jagged augmented second).

Lights went on!

What had been a complete mystery before, now made sense.

Several years later, I took a college course in harmonic analysis and when we learned about secondary dominants and changes of tonality and key, even more lights went on. Those apparently random accidentals all had a purpose!

I should say that I somehow managed to avoid a possible pitfall in learning about natural, harmonic, and melodic minor scales: I never expected that minor key music was somehow supposed to only use notes from one of the scales. And at some point I observed that the raised sixth and seventh from melodic minor were sometimes used descending, and that didn't bother me either.

That sounds like a cookbook. Music Theory for Dummies. To me it sounds anti-intuitive, non-playful, and it reminds me of almost everything I experience in public school.

I think that the flaw I any such approach is that it separates scales from harmony, and even the word “harmony” does not convey the idea that I love most, “playing with chords”.

I also don’t know why we do not see it suggested more often that scales, any of them, are suggested BY chord structure. This is not the only factor, but it is huge.

I'm not sure when I finally learned about minor keys, but eventually I did, via the key signature as relative minor, and look at the last note to figure out which key is, the major or the minor. The accidentals didn't bother me. I was used to having accidentals in music and never wondered why they were there, just took them as instructions for what to play.

I know you wrote more, but for me this begins to bring it together. Secondary dominance is a start at seeing how much we can move, seeming to go everywhere, yet we still retain the feeling of “home”, and “home” is the key we are in, with all its complexities.

Clearly F7 in M39

The Recapitulation M51-M84 very closely matches Exposition M1-M34, so no question of where coming from and ALL is accounted for.

Development starts out very similar to M1-M4, the next three measures are a melodic variation of M5-M7, then I think new material up to M48. M49 could be coming from M16.