My initial thought is that this is a circular alternative to Mr Cato’s Diagram. All it needs is the enharmonic equivalents of Cb & Fb to be added to B & E.
Is this a useful way to look at it?
2 Likes
I would argue that it does more than Mr Cato’s diagram. Much more. 
5 Likes
@Richard_close2u Thanks for being a great teacher and investing so much time and effort in a fascinating topic.
So far, I went through part 1 only and it felt a bit like reading a good crime novel, which will keep me engaged making observations and deductions.
I thought, I had spotted a pattern of scales starting at the fifth note of the previous scale. (“Wait a second, there is something going on here.”) What a nice feeling of accomplishment, when this turned out to be a thing indeed.
Looking forward to reading the other parts in the next days.
2 Likes
Those moments are super good. I’m so glad you’re having fun. Thanks for your comments and keep on going.
1 Like
Wow Richard! That was thread was a dense and useful read. You didn’t use the word “maths” once (which makes us Americans giggle until we’re used to it) and your poetry was top shelf. My brain hasn’t toiled that hard since college physics (1978). I am always working on scales, arpeggios and chord progressions and sometimes looked at the Circle of Fifths chart in my notebook and thought “Oh yes, that is useful for something,” and quickly turned the page. Now, it is poetry to me! 
2 Likes
@mfeeney0110
Michael. I appreciate your comments more than you may have anticipated when you wrote them.
I am always happy to read positive comments about the concepts and how working through this heavy-going topic has opened up a new level of understanding for people.
I am super happy to have you select some of my humble attempts at creative writing (as opposed to plain, text-book factual paragraphs) and describe it as poetry!
Goodness me.
2 Likes
Richard, thanks for posting this. Many years ago, during an earlier attempt to play guitar I bought “The Chord Wheel: The Ultimate Tool for All Musicians” by Jim Fleser (Hal Leonard). It’s a tool with the chord wheel and a rotating template on the cover. The twelve page booklet explains how to tuse the wheel and it’s very skimpy on theory. To be honest, I wasn’t sure how or why it worked or even how to use it. I almost threw it out. I stumbled on this thread and pulled out the old wheel. I learned more about the Wheel in the first few posts then I did trying to read the instructions. I don’t know if the Chord Wheel is still available. There are a few differences with the Wheel and your approach. On the Wheel the inner most ring are the keys. The second ring are the Minors. The abbreviated outer ring are the diminished chords. It wasn’t hard to figure out how to use your information with the Wheel. I looked at the on-line Circle of Fifths posted in the topic but I’m old school enough to use my “paper” wheel instead. Again, thanks for posting.
FWIW - there are 2 typos on page 9 of the booklet. When showing the notes of the C and D scales the vi notes are mislabeld as “iv”.
I had a small lightbulb moment this morning, when I started analyzing “As tears go by”. Key of G with an A chord as an exception or “foreign object”.
Now, where does the A come from, I wondered. It does not seem to be borrowed from G Major’s parallel scale, because then it would be expected to appear as a diminished chord. So I made the hypothesis that the A comes from the key of D, since D is the fifth of G. A in turn is the fifth of the key of D.
Checked the Circle of Fifths - and it’s all right there, plain to see.
Tested my hypothesis by playing the first two chords of the song in different keys, referring to the Circle of Fifths, and found that my hypothesis holds true.
EDIT:
Maybe there is a more likely explanation still, seeing that in the song the A will then be followed by the fourth of the key of G. Accordingly the A could also be taken from the key of E, where it is fourth. Maybe not as beautiful an explanation, but also clearly visible in the Circle of Fifths.
Still haven’t had time to read and understand everything you have compiled, but I just got to say that I am starting to fall in love with the Circle of Fifths (though Mr. Cato’s has its use as well…)
2 Likes
Good example of a Secondary Dominant.
The A Major here is functioning as what is called a Secondary Dominant. Like you said the fifth of the fifth. It provides that movement and resolution from the G through the A, to the D, which sort if acts like a temporary root.
Of course Stones threw in that C just before the the D, to add even more movement and colour. Cool sound.
Cheers, Shane
2 Likes
Seems I will have to do some research on secondary dominants and their functions. Thanks 
1 Like
These sorts of questions are fantastic when you come across them. And exploring ways to a solution can be very satisfying.
Yes and no.
The parent major scale is D. More soon.
The visual of the Circle of Fifths will help you find matching progressions in all keys. Hurray!
You have gone a little off track here.
Yes.
I’m afraid it isn’t that either Shane.
It is the 5th of the 5th. But …
It does not precede the 5th so it is not functioning as a secondary dominant.
Something else is happening.
The G major scale
G → A → B → C → D → E → F#
The diatonic chords
G → Am → Bm → C → D → Em → F#dim
The chord progression
| G | A | C | D |
As Roman numerals
| I | II | IV | V |
The A major chord is non-diatonic. It would be Am if only chords from the key were used.
A major = 1, 3, 5 = A, C#, E
A minor = 1, b3, 5 = A, C, E
It is the note C# that makes the difference.
C is the 4th scale degree in the G major scale. To play the A major, the chord built off the 2nd scale degree, the 4th scale degree has been raised - sharpened from C to C#.
There is one and only one place we need look for something with a raised 4th. It is to the Lydian mode.
The Lydian mode (or scale) is the same as the major (Ionian) scale except for one difference, it has a #4.
The G major scale
G → A → B → C → D → E → F#
The diatonic chords
G → Am → Bm → C → D → Em → F#dim
The G Lydian scale
G → A → B → C# → D → E → F#
The diatonic chords
G → A → Bm → C#dim → D → Em → F#m
I mentioned that D is the parent major scale. And here we can see that. Look at G Lydian. It has two sharps - C# and F#. That is an exact match for the D major scale. Look at the diatonic chords of G Lydian - they are the same as those in the key of D major. G Lydian is a mode of the D major scale.
Aha.
The A major chord is a Major II chord in the key of G.
It is a borrowed chord.
The term ‘borrowing chords’ is an easy means of describing something that music theory allows us to analyse. A term with an equivalent meaning, perhaps a more formal term, is ‘modal interchange’.
Modal interchange applies when one or more chords are taken from a mode of the same root note (a parallel mode). This need not be limited to the parallel minor key but can be any of the seven modes.
This song borrows a chord from the G Lydian mode.
If the progression was
| G | C | A | D |
or
| G | A | D | C |
then it would rightly be seen as a secondary dominant. Because it directly precedes the V chord of D major.
For more about borrowed chords and using the Circle of Fifths: Using borrowed chords - introduction + examples
For more about modes (including some Circle of Fifths also): Modes Parts 1 - 9
All of which reminds me …
I had promised long ago to extend my series and write a full topic about secondary dominant chords.
One day, when time allows.
4 Likes
I don’t even know what to say except for: Thank you so much for your exhaustive answer.
It hadn’t even crossed my mind to think about the difference between the A major and A minor triads and to use this as a starting point for asking questions. I saw modes mentioned, but hadn’t really spent time on them yet.
What would usually happen and why doesn’t it happen here? Questions I will remember to ask.
Looking forward to studying your links when I will have a bit more time next month.
1 Like
Interesting discussion. So, @Richard_close2u, you are not saying the chord progression is in G Lydian (since it has a C major chord), but rather the A major in the progression is borrowed from the G Lydian mode?
Yes, that’s exactly right.
The G → A → C chord move can create a voice leading opportunity of notes D → C# → C (as intervals within the chords, the 5th of G to the 3rd of A to the root of C).
Hi Richard,
I just have to reiterate this again. We are so very fortunate to have someone like you here mate. You just can’t get this experience anywhere else. I trust everyone really appreciates that.
Right. Now to it. I follow your basic reasoning here Richard. Fascinating, and somewhat out of left field for me re the Lydian connection. I will have to delve a bit more to absorb it more fully, so my Sunday morning is now gone.
One question however; about function vs form.
Why is the fact the A not immediately preceding the D disqualify it from functioning as a secondary dominant?
I’m going to argue that the intervening C chord functions as an additional ‘colour’ or movement in this subdominant cadence.
So the sound, the movement, the intention
perhaps? is this subdominant feel.
Is there a ‘rule’, or some sort of accepted practice or agreement that this subdominant cadence can only be exist when the relevant chords are immediately adjacent? What if, as I’m trying to argue here, one wants to ‘colour’ that cadence a little?
Is this amateur still in the debate?
Cheers, Shane
3 Likes
@sclay Thank you for your kind words Shane.
In terms of everything else, I’m just a regular fella, wih a bit of an obsession on this music study stuff, doing what I can to impart what I have learned the best I can in the hopes that it is helpful.
And, do you know what, I have had cause to dive deeper and learn more based on your questions. So thank you for that.
This question …
My first comment - I was a little harsh to dismiss your claim of A being a secondary dominant. I did so because it was a plain major triad, not even an A7 chord. And because it does not move to the V chord. But somewhere in the back of my mind I had a vague memory of music theory and harmonic analysis that describes situations in which secondary dominants do not lead directly tot he chord that they have ‘tonicised’.
Quick introductory
In any chord progression, a non-diatonic chord can introduced with the express purpose of making the movement to a diatonic chord happen with great impact, with flashing lights, fireworks exploding and a great big hurrah. That impact is achieved by inserting a secondary dominant, and usually played as a dominant 7. Not just any dominant 7. It has to be the dominant 7 of the chord you are moving to. Which means it has to be the 5th of the chord you are moving to. Because the 5th chord in any key is the one that takes dominant function.
So, in the key of G, if you want to move to the D chord with a whole lot of razzamatazz, you would play the dominant 7 of the D chord immediately before it.
A7 → D
When that is played during a progression in G major, A7 is a secondary dominant.
It just happens that D is the dominant V chord in the actual G major key. So the secondary dominant (A7) is the 5th of the fifth in the key. It can be labelled V / V (the five of the five chord).
Other diatonic chords in the key can also have their own secondary dominant placed in front of them. If the progression was moving to Em say, and you wanted to herald its arrival in dominant style, you would place the dominant 7 of Em in front.
B7 → Em is secondary dominant to diatonic vi chord in the key of G. The B7 chord can be labelled as V / vi. The five of the six chord.
We have seen two examples. A secondary dominant going to the V chord and secondary dominant going to the vi chord. For each, respectively, we can say that the V chord and the vi chord have been ‘tonicised’.
D major, for a very brief, passing moment, has been made to have the feel of a tonic chord. Similarly, Em, for a very brief, passing moment, has been made to have the feel of a tonic chord. Because, for both, their dominant 7 was placed directly in front, and dominant 7 to tonic is a move we can describe, is a sound we recognise and expect.
V / V → V (the V chord is tonicised)
and
V / vi → vi (the vi chord is tonicised)
Let’s go back to As Tears Go By.
Chord progression (chord names and roman numerals
| G | A | C | D |
| I | V / V | IV | V |
If A is going to be classified as a secondary dominant then it must still be labelled as V / V (the five of the five). But A does not come immediately before the D. Something else is happening. We are not hearing the expected resolution of:
V / V → V
We have what might be called an unexpected resolution. In some theory texts and studies this might be termed a deceptive resolution or an irregular resolution.
V / V → IV
Deceptive / irregular resolutions
My understanding is that any non-diatonic chord within a progression, no matter where it is placed, if analysed and found to be a secondary dominant to a diatonic chord, can be labelled as a secondary dominant. Even if it leads to a different chord (perhaps even another non-diatonic chord) rather than the chord that it ‘should’ precede in its secondary dominant role. When this happens, it must still be labelled using the secondary dominant conventions.
The V / V that does not lead to the V is still labelled V / V
The V / ii that does not lead to ii is still labelled V / ii
etc. etc.
When these anomalies happen - and they can be found in classical and contemporary music, they can be viewed and described and thought about as deceptive or irregular resolutions of a secondary dominant.
V / V → IV is one such that can be found.
I be- lieve in yes- terday
| vi V/V | IV I |
And who am I to argue against professors and experts and musicologists?
But, honestly, if it were up to me, I would much rather keep things simple and use the perspective of modal interchange.
Non-diatonic chord in a progression?
Yes.
Is it the 5th of the chord immediately after?
Yes.
Okay, it is a secondary dominant.
No.
Okay, it is a borrowed chord, most likely taken from the parallel minor (from where a vast majority of borrowed chords are taken) or one of the other parallel modes.
For me, that is just simpler and more satisfying. Especially for simple pop, rock and modern music. Perhaps in harmonic analysis of complex jazz or fusion or classical compositions, the deeper approach is the best approach. I don’t know. I don’t tread those paths.
My keep-it-simple approach may break down if the non-diatonic chord / chords is / are played as 7 chords, not just triad chords.
But no examples of that come to mind just now.
Thanks for the inspiration and perhaps another nudge to continue / extend my borrowed chords topic to cover secondary dominant chords.
5 Likes
Hear, hear! 
I remember when I would have read the above treatise and filed it carefully into the ‘gobbledygook’ file…
Now I can follow much of what is being discussed, nodding sagely to the arguments (and then the counterpoints 
)
Thank you both
2 Likes
Follow up reflections …
Why call something a V / V if it is not followed by the V? That makes no sense to me in every day, basic musical thinking.
Why call something a secondary dominant if it is not functioning as a dominant pushing to a tonic (by which I mean the chord it has tonicised, not the actual tonic of the key)? If that is not its function, why call it by that name?
Several thoughts have passed through my mind since yesterday.
Robert M. Pirsig - Zen and the Art of Motorcycle Maintenance.
I am paraphrasing -
A friend of the book’s protagonist had a slight mechanical issue with his brand new BMW motorcyle. The protagonist picked up an empty coke can and proceeded to cut a small piece from it in order to effect a repair. The friend was outraged. He saw a piece of junk that would degrade his motorcycle. The protagonist saw a supply of thin aluminium perfect for cutting and shaping some shim which was exactly what the repair needed.
What is that small piece of metal? Junk or shim?
Is it what it is or is it what it does?
Before I add this next visual part, I need to please beg for all forgiveness for the graphic as it sits wholly and firmly in the realm of sexism. I’m so, so sorry. 
Such nonsense is not my usual style at all. I use it simply to raise a question, to reinforce a point.
Shoe or hammer?
Knife or screwdriver?
1 Like
Hello Richard,
Appreciate the detailed response. This discussion has certainly expanded my practical knowledge in this area.
The ‘modal interchange’ talking point in particular has certainly made some things clearer in regards to more quickly ascertaining where some of these borrowed chords come from when it is apparent the paralle key is not the answer.
And importantly, how they, and associated borrowed chords from these sources can be used; and now, more like a palette to choose from, rather than ‘stabbing in the dark’ to find that sound that’s in my head.
That Lydian reference has opened that up for me, so thank you again.
I suppose I’m still at the point where I can lock into one structural/functional perspective of a progression etc, and then fail to perhaps pan back out and see it anew.
I really enjoy what these discussions continue to reveal; and not just as an intellectual joy ride, but, more importantly, how knowledge of them can serve me with my fingers on fretboard.
So, again I’m edging forward a bit more Richard, after engaging with you. Thanks again for your great insight.
Cheers, Shane
1 Like
Both. It depends on what is available when you need it. Obviously the main purpose of a shoe is being a shoe, similarly a knife will always strive to be just that. Yet, there may be a time of need when a certain kind of shoe will serve well as a hammer and a certain type of knife will work fine as a screwdriver. It’s an entirely different question how durable knife and shoe are in their non-intended functions. Their lifespans may be cut short … thus it’s usually preferrable to use hammer and screwdriver, if they are available.
Notably, however, a hammer cannot be used as a shoe, and most screwdrivers are too small to even be considered as an alternative for a knife.
I love what this is becoming and have read @sclay and your posts with sparkling eyes.
Time for me to admit that there is absolutely no harm for me in progressing faster with music theory than with actual guitar skills. Strangely, this insight makes me very happy. But I’m weird like that, I also like immersing myself in the grammar of languages.
1 Like