Building Major and Minor Scales + The Cycle of Fifths

[seattleblah]

I'm reading a chapter in my music theory book that speaks to the Cycle of Fifths. As part of this chapter they have listed out the set of Major and Natural Minor keys which make up these cycles as listed below:

Major: C, G, D, A, E, B, F#/Gb, Db, Ab, Eb, Bb, F
Minor: Am, Em, Bm, F#m, C#m, G#m, D#m, Bbm, Fm, Cm, Gm, Dm

In the appendix of the book they then list the full set of Major and Natural Minor scales as:

Major: C, Db, D, Eb, E, F, F#/Gb, G, Ab, A, Bb, B
Minor: Am, Bbm, Bm, Cm, C#m, Dm, Ebm, Em, Fm, F#m, Gm, Abm

My question is two fold:

1. Why the discrepency between the natural minor scales defined as part of the cycle of fifths and those in the appendix? Shouldn't they be exactly the same like the major scale is?

2. When defining the set of scales, what is the logic that is used to determine the set of keys to be used? For example, why in the major scale is Db used instead of C# or A# instead of Bb?

[walternewton]

Generally speaking you would choose the key spelling that is simplest - just try spelling out your examples:

Db Eb F Gb Ab Bb C (5 flats)
vs.
C# D# E# F# G# A# B# (7 sharps)

or

Bb C D Eb F G A (2 flats)
vs.
A# B# C## D# E# F## G## (4 sharps and 3 double sharps - theoretically possible, but obviously too unwieldy to be of much practical use)


For completion's sake, I'd suggest getting comfortable with the ability to spell 15 keys from Cb (7 flats) to C# (7 sharps).

[seattleblah]

Thank you!

[Malcolm]

Look at the bottom of the circle, gets a little crowded down there. Why?

It finally hit me one day.
C @ 12:00 O'clock has no sharps or flats.
G @ 1:00 O'clock has 1 sharp.
D @ 2:00 O'clock has 2 sharps, etc, etc. which is a neat cheat sheet in itself, however.............

There are seven sharps so the sharps go past 6:00 O'clock and wrap around. The flats do the same thing, F has 1 flat and Cb has 7 flats, so you have what walternewton was talking about.

I just pulled this chart up a few days ago, to make a point, and something else hit me.
What is to the left of C? F.
What is to the right of C? G. So pick a tonic then look to the left and right and you have the I IV V chords for that tonic. OK knew that years ago. Neat thing that I had not picked up on. Look below each of those and you have the relative minor of each so...... drum roll...... you now know the three major AND three minor chords in the key of C. Where is the diminished? Same spot it always is. It's minor so look on the minor inner circle.

So --- if stacking 3rds is not soaking in show the circle and how it points out the seven chords in any key. I had missed that, which brings up the subject, I wonder what else is in the chart that I've missed.

[corduROY]

.....
What is to the left of C? F.
What is to the right of C? G. So pick a tonic then look to the left and right and you have the I IV V chords for that tonic. OK knew that years ago. Neat thing that I had not picked up on. Look below each of those and you have the relative minor of each so...... drum roll...... you now know the three major AND three minor chords in the key of C. Where is the diminished? Same spot it always is. It's minor so look on the minor inner circle.

So --- if stacking 3rds is not soaking in show the circle and how it points out the seven chords in any key. I had missed that, which brings up the subject, I wonder what else is in the chart that I've missed.

Over 10 years playing and I've missed this too! Thanks Mal.

[JonR]

Where is the diminished? Same spot it always is. It's minor so look on the minor inner circle.

That's a little confusing, IMO. Firstly, the diminished isn't precisely "minor", although it has a minor 3rd.
And if it's on the minor inner circle, where? You need to look clockwise, outside the central block of 6, to find Bm. But of course you don't want Bm, you want Bdim.
So the dim chord isn't actually there, you have to make it up. Which is fine, because (a) the circle isn't supposed to showing chords anyway (we just kind of pervert it to those ends ), and (b) we don't really need the dim chord anyway.
For a "quick fix" guide to the useful chords in one key, that block of 6 (one quarter of the circle) will do just fine.

Incidentally, it might be worth pointing that in the diagram you found, the relative minors of C# and Cb are not shown (A#m and Abm). They obviously didn't have room, and it's not too big a deal, I guess. Just to good to be aware of correct enharmonics.

So --- if stacking 3rds is not soaking in show the circle and how it points out the seven chords in any key. I had missed that, which brings up the subject, I wonder what else is in the chart that I've missed.

Well, you can extend the principle of "chords close together in the circle sound good together", by reaching out either side of that set of 6.
So, on the clockwise side (in the major circle), we have the secondary dominants, 4 of them in a row. Working from key of C, that's D (V/V), A (V/ii), E (V/vi) and B (v/iii).
This is the "sharp" direction round the circle of course, and each of these chords involves raising one note in the C major scale to provide a leading tone to the root of the "target" diatonic chord. (B gives us 2 raised notes, of course.)
Going anticlockwise (in the flat, or "darker" direction), the first 3 majors we see are those commonly "borrowed from the parallel minor" in rock music. Bb (bVII), Eb (bIII) and Ab (bVI). As with the secondary dominants,the nearer ones are more common than the further ones.

For any one major chord, its tritone sub is on the opposite side of the circle. (We need to assume both as dom7s.) Eg, anywhere D7 will resolve, Ab7 will probably resolve just as well - and maybe in cooler fashion.

Thirdly, I've seen people use the circle to make pictures, graphic symbols, for chord types, by treating the outer circle as notes only, and "joining the dots". I'm not sure what practical use this is, but it's a fun game.
Eg, a major triad is a lop-sided triangle, pointing across the circle in the clockwise (sharp) direction (try it by drawing straight lines between C, G and E). A minor triad is the same shape in reverse, pointing the other way (in the flat direction). The diminished triad is an isosceles triangle - 2 equal sides, the longer one exactly dividing the circle; and the dim7 chord is an exact square, usefully demonstrating its symmetry. An augmented triad is likewise a symmetrical triangle.
Weird things happen when you add 7ths.
As I say, this is of debatable practical value - unless you are someone with a highly developed visual sense who likes using (meaningless) shapes as memory aids. And you might (might...) get more meaningful diagrams if you arrange the circle of notes in chromatic order, rather than in 5ths. (The dim7 and aug chords are the same shapes, but other triads are different.)

Actually, having tried both, I think the shapes are a little more meaningful if taken from the circle of 5ths. One thing I've spotted from all the pretty shapes is that you can quickly spot when a large chord (a 7th or extended or altered dominant) contains other chords within it. Eg, the shape for an m(maj7) makes explicit the augmented triad it contains (between 3rd 5th and 7th); the shape for a 7b9 clearly shows the dim triad within, and hints at the full dim7 square too (depending on how many of the connecting lines you draw in).

I'll see if I draw them all up on the computer and attach them here for your delectation... (may be a few hours as I have some WORK to do. Ah, work.... the curse of the drinking classes... )
In the meantime, of course, you could do it yourself .

[JonR]

I had missed that, which brings up the subject, I wonder what else is in the chart that I've missed.

Just thought, the other thing is that "circle progressions" - the typical moves in jazz harmony - travel anticlockwise round the circle. (Add 7ths to all the chords, and this gains momentum.)

In a sense you can think of the clockwise direction as ramping up tension, "brightening", or "pushing onward" (against resistance); anticlockwise is then "relaxing", "darkening", or "returning home". (Obviously "returning home" stops when you reach your tonic; going beyond there would then be "darkening".)
Anticlockwise can also be "warmer", "softer", while clockwise can be "colder" - obviously "sharper" .

[corduROY]

Blimey Jon, 1 post from you will keep me busy for a month experimenting.

[corduROY]

Im going to stick this here because it came up while looking at the circle of 5ths things this afternoon.

Looking at the Beatles "And I love her" in conjunction with Alan Pollack's Beatles notes, after the 3rd verse Pollack states that
"...the music neatly modulates up one half step; if the original key pair was E/c#, we're now in F/d; from the world of four sharps to one of one flat."

So we have verse F#m - C#m - A - B - E
Going to solo section Gm - Dm - Bb - C - F
Now before reading anyone elses comments about a piece I like to figure it out myself and compare my results.

My interpretation of this was that the Tritone substitution for E is Bb, move that Bb to the relative minor and we get Gm.

Pollack is saying this is F/d I'm saying Gm, so...
1. Have I missed something or is stuff like this subjective? Never having studied or listend to much jazz is my brain just recoiling from the E > Gm switch?
2. If this can be explained in two ways, anyone else think of similar tritone/relative minor kinky substitutions in songs?

Thanks guys.

[walternewton]

Honestly I think you're overthinking what's basically just a shift of the entire progression a half step higher.

Yes the effect is jarring - which is why this site, which lists a number of examples, calls it the "Truck Driver's Gear Change" modulation.

[corduROY]

You are probably correct Walter, I do have that tendancy, its always nice to be able to explain things in different ways though. If not for Jon's post pointing out interesting things with the circle of 5ths I wouldn't have got anywhere near using it for tritones etc.

Great website "Truck Drivers Gear Shift" The key shifts in Living on a Prayer by Bon Jovi have got to be the worst thing I've ever heard!