By The Numbers

[David L]

David, I didn't intend to call the V7 the most stable chord, but rather the V chord, which is probably not right either. The V is the dominant chord. I'll have to re-read what I wrote there. This is the type of problem that occurs when a non-expert like me gets in over his head a bit with terminology. Thanks for pointing out the problem.

It isn't just the 7 in the V7 which makes it unstable, V chords also want to resolve to the tonic, which is why they are called the dominant, even without the 7. "Stable" means that a chord doesn't want to go anyplace else, like the tonic.

[sblock]

Mark, thanks for the corrected link to your Circle of Fifths article. I just had a quick peek at it.

I commend you on the public service you do by preparing and sharing these instructional materials with your fellow musicians. Even though you requested our comments and feedback -- a brave request to make, I must say! -- I'm still a bit reluctant to criticize anything, because it's been my experience that whatever I offer (and however well-intentioned and carefully phrased), someone on the Mandolin Cafe will write in to tell me that I'm either wrong or unfair. Fools rush in...

Anyway, I noticed one minor error. On page 9, where you show a Circle of Fifths, you display arrows at the top of the diagram indicating clockwise and counterclockwise rotational directions around the circle. The clockwise arrow is labelled "up by fifth". That's true: each clockwise step around this Circle takes us up by a musical fifth interval. But the counterclockwise arrow is labelled "down by fifth." Actually, taking a step in that direction represents a musical fourth interval, not a fifth. For example, going clockwise from C to G is going up a fifth. But going counterclockwise from C to F is down by a fourth.

A couple of minor tweaks to the diagram would help, IMO. Here are two suggestions, but of course, you don't have to take them.

1) I would find it easier if you indicated the relative minors key (the inner circle) as either (1) "Am, Bm, Cm, etc.", or (2) in lower case, as "a, b, c, etc." I find the use of all caps for both the major and minor to be unconventional and confusing.

2) I would highly recommend that you add a Circle of Fifths diagram (or augment an existing one) that illustrates how the Nashville Numbering system maps so nicely into the this circle. Pick any home key, like C. This is the I chord. The chord that's clockwise by one step is the V chord. The chord that's counterclockwise one step is the IV chord. Go clockwise by two steps and you have the II chord. Go counterclockwise by two steps and you have the VII chord. For most folk and bluegrass tunes, all the most common chords used are found within a step or two of the home chord on this circle. This ties in very well with your Nashvile Numbering document.

[Mark Gunter]

Again, many thanks for all the great thought and suggestions. Eventually, I'll be making some minor revisions and maybe expanding a bit on these articles.

Even though you requested our comments and feedback -- a brave request to make, I must say! -- I'm still a bit reluctant to criticize anything, because it's been my experience that whatever I offer (and however well-intentioned and carefully phrased), someone on the Mandolin Cafe will write in to tell me that I'm either wrong or unfair. Fools rush in...

Anyway, I noticed one minor error. On page 9, where you show a Circle of Fifths, you display arrows at the top of the diagram indicating clockwise and counterclockwise rotational directions around the circle. The clockwise arrow is labelled "up by fifth". That's true: each clockwise step around this Circle takes us up by a musical fifth interval. But the counterclockwise arrow is labelled "down by fifth." Actually, taking a step in that direction represents a musical fourth interval, not a fifth. For example, going clockwise from C to G is going up a fifth. But going counterclockwise from C to F is down by a fourth.

The thing is that requesting feedback is a great way to lean something, and in discussing feedback there are also opportunites to teach as well as to learn.

I would disagree with your second paragraph, but it is merely a technical point. You have a circle there. Measure between two points of a circle (example, between F and C on this circle) with a compass, and you get a value x. Now, flip the compass and measure the distance between the same two points (from C to F) you get the same value, x.

A perfect fifth is a musical value of seven semitones. From a root F to the note C in the scale of F is seven semitones. From an octave C down a scale of C to F is seven semitones. The inversion of a perfect fifth yields the fourth of the scale. Research interval inversions for more information, and see my primer, bottom of page 4.

The "circle of fifths" is built so that there are seven semitones between each of the twelve notes around the circle. This means either fifths going up, or fifths going down. Fifths going down (inverted fifths) yield the 4th degree of the scale in question.

This is a technical matter, and not important in practice, but maybe of some import to the technically minded, and important in theory.

This is the way I see it and the reason I don't consider that to be an error, but I have benefited greatly from all your feedback and have learned from it.

Editing to say that the value of the COF as a chart to instantly know what the 4th and the 5th is in any key is inestimable, and I do emphasize that usage both in my video on COF and in my primer. The "up in fifths, down in fifths" is merely a technicality, and accurate from a music theory vantage point.

[David L]

Mark, thanks for the corrected link to your Circle of Fifths article. I just had a quick peek at it.


Anyway, I noticed one minor error. On page 9, where you show a Circle of Fifths, you display arrows at the top of the diagram indicating clockwise and counterclockwise rotational directions around the circle. The clockwise arrow is labelled "up by fifth". That's true: each clockwise step around this Circle takes us up by a musical fifth interval. But the counterclockwise arrow is labelled "down by fifth." Actually, taking a step in that direction represents a musical fourth interval, not a fifth. For example, going clockwise from C to G is going up a fifth. But going counterclockwise from C to F is down by a fourth.

This is not true. Going DOWN from C to F IS a fifth, not a fourth. Going UP from C to F is a fourth.

[sblock]

Actually, I think there is substantial agreement here about the theory, but perhaps a disagreement about the proper emphasis.

The interval from C to F (in the key of C) is a rising fourth or a falling fifth. Look at the numbering below to see why.

1 2 3 4 5 6 7 (8)
C D E F G A B (C)

To get from C to F, you go up by a count of 4 letters (starting with 1), or down 5 by a count of 5 letters.

Similarly, the interval from C to G is a rising 5th or a falling 4th.

Anyway, going clockwise around the Circle of Fifths by 1 step gives you the V. And going counterclockwise around the Circle of Fifths by 1 step gives you the IV.

So what you choose to call it depends on whether you're going up or down. Note that the Circle of Fifths does not specify musically "up" or "down." Personally, I find it confusing to think F as being musically a fifth away from C (it is, but only by going down!). To my mind, G is the fifth of C: it is the note that is musically a fifth away from C (a fifth up, that is). And F is the fourth in the key of C.

Going counterclockwise around the Circle of Fifths generates a "Circle of Fourths", e.g., E-A-D-G etc., just as a guitar is tuned (except for the pesky B string), or a bass! Going clockwise around the Circle of Fifths gives true fifths, G-D-A-E, just as a mandolin is tuned.

Furthermore, I think this is worth pointing out to students. When you drop down by a fifth, you get the musical fourth tone. That was my point, however inartfully expressed.

[Dale Ludewig]

If you check out Edly's Music Theory for Practical People (NFI and a great book), he has what is about the best Circle of Fifths diagram I've seen. It shows the key relationships, key signatures, relative minors, and other explanations. No criticisms for anything here, but no need to reinvent the wheel (or the circle).

[sblock]

If you check out Edly's Music Theory for Practical People (NFI and a great book), he has what is about the best Circle of Fifths diagram I've seen. It shows the key relationships, key signatures, relative minors, and other explanations. No criticisms for anything here, but no need to reinvent the wheel (or the circle).

Dale, Sounds intriguing. Can you post a copy of the diagram here so we can all see it, or provide a link? There are oodles and oodles of Circle of Fifths diagrams out there, so I'm wondering what makes this one so remarkable.

[Tom Haywood]

I think this is a great effort given its purpose - to help the new or average player participate more effectively in routine music group communication. I don't see anything "wrong" in it, and I do see a good bit more than a lot of players want or need. Good job, Mark!

[Mark Gunter]

Again I'll repeat how much I appreciate the discussions on these topics. I feel I need to clarify a couple things.

The thread was started in order to get feedback on my article, By The Numbers, which was only recently completed. The topic shifted to the COF when sblock suggested that I include the COF and relate it to the NNS - I simply was offering that I had writen a prior article on the COF last year.

The purpose of my writing on these topics is not to "re-invent the wheel" as it were ... these articles have context. I began leading a study group last year; not as a teacher, but as a fellow student. The group chose Mandolin Master Class by Bradley Laird as the first study text. That text is heavy on theory rather than technique. In the course of study, I and others have made videos and handouts to supplement the text. I wanted to supplement the material Brad has given us in order to go deeper into some concepts and to give my own perspective. I'm not an expert, just an amateur musician who has played music since childhood and in the past five years delved more into understanding theory.

The article, By The Numbers, is not meant to teach the Nashville Number System. I wrote it to help understand how numbers are used in different musical contexts, including instrument anatomy, scale degrees, musical intervals and diatonic harmony (chords). I have my reasons for believing that all these numbers referring to different things can cause confusion to Newbies, won't bore you with that story. At any rate, the article introduces a lot of material, but doesn't go too deeply into any of it, including the NNS, which I know only a small bit about.

The article, Circle of Fifths Primer, was written to go with our lesson five, where I encouraged participants to play arpeggios to a backing track around the circle. To do that, you have to learn the circle, and I decided to write a primer explaining things about the circle. It is not meant to be all-encompassing, and is not meant to teach the NNS, but to explain and help understand the concepts behind the COF. I wanted to introduce the idea of a musical helix, flattened into a circle. The idea of the inverted fifth and fourth interval. The understanding of what scales lie behind the circle. To explain why the left side has keys with flat notes. To underscore that mandolin tuning, being in fifths, will help a mandolinist in memorizing it. To show how to calculate key signatures with the Circle. To emphasize its value as a chart that readily gives the IV and V chord of any key, as well as the relative minor and the key signature. The primary way of accomplishing most of that was to make a video, and the Primer was written to delve a bit more into a couple of the concepts.

I know that there are wonderful books, articles, lessons, charts etc. out there, but this is written from my perspective for the Woodshed Group - and wasn't originally intended to even be posted here; in the beginning, I started the thread about By The Numbers.

With those clarifications, I'd like to know where I've erred and how, and what if anything seems unclear and could be confusing to the interested reader, in either of these articles. Many of the comments have given me some direction, and any that don't are still appreciated for the participation alone. I'll be updating these articles to reflect any new understanding I get from this thread, and maybe to supplement them based on suggestions.
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Here is a link to one Interactive Circle of Fifths that I found a couple years ago, can't post the diagram here because it's interactive: https://randscullard.com/CircleOfFifths/

[Dale Ludewig]

sblock, here's a copy of the Edly Circle page. I think it's a good one. Helpful enough for me that I copied the page from the book several times and had them laminated. I have one in my briefcase, one on my desk at home, one on the music stand, one on the night stand. I'm not saying it's the ultimate but it's been helpful. Pardon my notes about the order of sharps: Good Dogs Always Eat Beef.
Great work Mark, by the way!

[sblock]

sblock, here's a copy of the Edly Circle page. I think it's a good one. Helpful enough for me that I copied the page from the book several times and had them laminated. I have one in my briefcase, one on my desk at home, one on the music stand, one on the night stand. I'm not saying it's the ultimate but it's been helpful. Pardon my notes about the order of sharps: Good Dogs Always Eat Beef.
Great work Mark, by the way!

Dale -- Yes, I like this particular version a lot! I'd also point out that the directional arrows around the Circle say the following:

In the clockwise direction, the arrow is labeled with the words "Sharp Keys" and "fifths."
In the counterclockwise direction, the arrow is labeled with the words "Flat Keys" and "fourths."

This is the essence of my suggestion to Mark all along. You go in musical fifths by proceeding clockwise around the circle; you go in musical fourths by proceeding counterclockwise around the circle. In fact, note the title of the diagram: It's called the "Circle of Fifths (and Fourths)." Just so!!

And yes, a fifth down is a fourth up and vice versa.