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The parallel minor of C# minor is C# major. "Enharmonic" means "same pitch, different name." C# and Db are enharmonic equivalents. So instead of writing the central section in C# major with 7 sharps, Chopin writes it enharmonically in Db major with 5 flats. The sound is the same as if he had written it in C# major. The aural relationship between C# minor and C# major is the same as the aural relationship between C# minor and Db major: minor to parallel major.

OK, thanks. Yes, I do recall this now. So any major or minor key will have an enharmonic equivalent and the choice of writing this with flats vs. sharps will be mere convenience.

No, only some keys have enharmonic equivalents, at least if you want to avoid double sharps and flats.

For example, if every key had an enharmonic equivalent, then what would be the enharmonic equivalent of C major? It would be B# major. Hmmm.

C major: C D E F G A B
B# major: B# C## D## E# F## G## A##

Ugh. So we don't normally talk about B# major as a key.

Here is an exploration to find the normal major keys with enharmonic equivalents: work around the circle of fifths in the sharp direction and write down the major keys and their number of sharps: C 0, G 1, D 2, A 3, etc. up to C# 7.

Then work around the circle of fifths in the flat direction and write down the major keys and their number of flats: C 0, F 1, Bb 2, etc. up to Cb 7.

Now compare your lists. Where do you find enharmonic equivalents? You should find three pairs of enharmonic equivalents.

What pairs did you find? How many sharps and flats in each? What is the minimum number of sharps or flats for a major key to have for it to have a normal enharmonic equivalent?

Add the number of sharps and flats in each pair. (For example, C# major 7 sharps and Db major 5 flats adds up to 12.) You should get the same sum for each pair. What is it?

(The number of sharps and flats adding up to 12 is true even for the ridiculous abnormal pairs like C and B# above: count the number of sharps in the B# note list; double sharps count for 2).

There is a similar exploration for minor keys and enharmonic equivalents. Do the major key exploration first, and then I'll give pointers on how to get started with the minor key exploration.

Enharmonic equivalents:

Db (5 flats) = C# (7 sharps)
Gb (6 flats) = F# (6 sharps)
Cb (7 flats) = B (5 sharps)

... if I am following correctly.

Minimum number of sharps or flats thus, for an equivalent is 5.
_________________
My pause in responding was due to an appointment with the red dot. I wish I could say "it went fabulous" instead I will simply say ..."I have a recording".

Correct on the enharmonic equivalents for major keys! Well done.

For minor scales, do the same exploration: write down the minor keys around the sharp side of the circle of fifths, with their number of sharps: Am 0, Em 1, Bm 2, etc. up to A#m 7. Then write down the minor keys around the flat side of the circle of fifths, with their number of flats: Am 0, Dm 1, Gm 2, etc. up to Abm 7.

(You can find these quickly by taking the relative minor of each of the major keys you already wrote down: go down a minor third from the major key to get the relative minor key. Remember that a minor third has to skip a letter in the note names, as well as being three half-steps. For example the note a minor third below B is G#, not Ab.)

Now identify the enharmonic pairs. They should turn out to be the relative minors of the enharmonic pairs you already found for the major keys.

Enharmonic equivalents:

Bbm (5 flats) = A#m (7 sharps)
Ebm (6 flats) = D#m (6 sharps)
Abm (7 flats) = G#m (5 sharps)

So far this explores enharmonic major to major and minor to minor. In our score, we have C# minor moving to the enharmonic major, Db.

I have a feeling it is not going to be as simple as just substituting some of these majors for minors ... hmmm ...

You need a rest, Jeff!

There's nothing more to cover. The waltz moves from C# minor to C# major or it's enharmonic equivalent, Db major.

Well done on the minor pairs, Jeff.

Fabulous idea. Thank you, Richard ...

Just a further thought to what you've just been doing...

D'you remember we talked about the circle/ribbon of fifths earlier? I use a ribbon rather than a circle because I developed it for my chord playing on guitar and it tells me at a glance what notes are used in the scale and what chords are used in the keys.

You might like to write/draw/print it out and keep over your desk/piano/other convenient area.

The first row is the number of sharps/flats in the key/scale:

7b, 6b, 5b ... 5#, 6# 7#

The second row is the name of the Major key with that many flats:

Cb, Gb, Db ... B, F#, C#

The third row is a minor third below, the relative minor:

Ab, Eb, Bb ... G#, D#, G#

The fourth row is another minor third below:

F, C, G ... E#/F, B#/C, Fx/G

You might add a fifth row yet another minor third below:

D, A, E ... Cx/D, Gx/A, Dx/E

You'll notice that the first three columns and the last three are enharmonic equivalents.


Major row: subdominant, tonic, dominant
Minor row: supertonic minor, relative/submediant minor, mediant minor
Third row: leading not (major)/diminished, n/a, n/a
Last row: leading note (minor)/diminished 7th, n/a, n/a

Note the shape of this box:

| F | C | G |
|---|---|---|
| D | A | E |
|---|---|---|
| B |
|---|
| G#|

In a major key, here C major, the tonic is upper middle. The dominant is the right hand man.
The sub-dominant is the sinister side. The leading note is at the bottom left a knight's move away and the notes of the diminished/diminished 7th in the left column. These are added to the dominant note to form the dominant 7th/dominant 7b9. (Note the b9 appears here as the enharmonic #8!)

In a minor key, here A minor, dominant will frequently be a major chord using the sharped seventh, the note a knight's move away, the bottom of the left column.

You'll get used to the way this grad is traversed in tonal music and how the switch from major to minor or vice versa allows a jump of three columns.

If you are/get into rock, if you find the major keys in the minor row then the top row gives you the bVI, bIII and bVII chords (also the parallel minor key signature on the flat side. It's down and left on the sharp side).

Yes, agree. This will be an excellent resource.

I've documented it and hopefully it is close. Could you kindly review and advise of any corrections that may be needed.

Ribbon of 5ths

That's pretty much it, Jeff. My only qualm is the flats in the bottom middle where I'd prefer to see sharps. The seventh of G minor is F# not Gb!

You might add a bold line between 5b and 4b and between 4# and 5# so you can see more quickly where the ends overlap.

COMPLETE

I've made the corrections and uploaded again. Previous link has been updated. But is listed again here ...

Ribbon of 5ths

A great resource for anyone that wants to make use of it.

Good job, Jeff.

Thanks. And Thank you for the idea and content, Richard.

... back to the Bahamas now ...

Chopin Nocturne in E flat, Op. 9 No. 2

I am starting to work on the coda and can see that this is going to be some fun. For one thing I'm having a hard time just reading the notes. So much for the chords here. I'm writing in the notes and going back and listening to make sure I am getting it right.

Everything to this point has been straight forward as it is really just variations of the same two themes. It all still needs a ton of work of course, and perhaps that is where I should stay for the time being. This last section I will work on in chunks. This is clearly going to be the most challenging section.

Chopin Nocturne in E flat, Op. 9 No. 2

Here is a final set of chords that will complete the coda. I'm not able to play this section yet. Knowing the chords though will hopefully assist in learning it. I am finding it a tricky section to read.

M25
1 - Abm
2 - "
3 - "
4 - "
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - "
11 - "
12 - "

M26
1 - Abm
2 - "
3 - "
4 - "
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - "
11 - "
12 - "

M27
1 - Bb11
2 - "
3 - "
4 - "
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - F7
11 - "
12 - "

M28
1 - Bb11
2 - "
3 - "
4 - Bb
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - "
11 - "
12 - "

M29
1 - Abm
2 - "
3 - "
4 - "
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - "
11 - "
12 - "

M30
1 - Abm
2 - "
3 - "
4 - "
5 - "
6 - "
7 - Eb
8 - "
9 - "
10 - F7
11 - "
12 - "

M31
1 - Bb11
2 - "
3 - "
4 - G7
5 - "
6 - "
7 - Cm
8 - "
9 - "
10 - F7
11 - "
12 - "

M32 - Bb7
M33 - Eb
M34 - Eb

Chopin Nocturne in E flat, Op. 9 No. 2

I've not looked at your chords closely, Jeff. They look fine, and I wouldn't be expecting harmonic fireworks in the coda; technical dazzle perhaps, but nothing harmonically unsettling.

Look again at M1-4 and look at the chord progression he's using.

I don't use Roman's very often but look at the relationships we have here. From chord I classical music moves most readily to IV or V. I-vi is a common move. But not I-VI, the submediant major. This may be fine nowadays, (Sittin' On) The Dock of the Bay comes to mind, but it's unsettling tonally, setting up the expectation of a move to ii (major or minor). Here we go to the minor via Bb minor, the dominant as a minor chord in a major key (!), then diminished.
The dominant Bb major appears only briefly at the beginning of M3 as we wander to G major (that's another non-diatonic chord where we'd normally expect G minor) the tension is increasing as we're far from home (and we've only just started).

Finally in M4 the dominant returns (as a tense eleventh chord) with a crescendo that comes crashing down on a forte tonic chord with a 6-7-8 resolution. And after having wiped the floor with our emotions he proceeds to do it all again with bells on as he decorates the melody line and look at that crescendo in M6 pointing the appoggiaturas as they fall on the C major arpeggio.

How calm does the dominant measure M9 feel now?

This is very interesting. I had no idea there was this much going on, or the uniqueness of it. The move to VI is the C major at the beginning of M2? If I am understanding this right, in the second iteration of this measure (M6), the melody passes b9, 11, b13 and b9 again. Is this what you mean by "pointing the appoggiaturas" back to the C major?

Yes, agree. M9 is a very soothing contrast to everything up to this point. I've really liked the sound of this transition all along, but had no idea of why it had such an impactful effect. The every beat chord changes at the end of this section in M12, ending on the dominant and starting all over again, I also really like (and enjoy playing) in this section.

I've also observed how M4 (the crashing back to tonic) gets more interesting with each iteration. There is not much difference in M8, but clearly more colour and feeling of suspense in M16. And, very slick off beats in M24.

Do you suppose Chopin actually had in mind the harmonic fireworks he was developing (in contrast to other works of his time) and was striving for this as he was composing? Or, was it more like "this sounds nice, I think I'll put this here".