# Measuring key-relatedness of chords on the circle of fifths

Is there an easy way to visualise scale-degree triads for a given key, based on the circle of fifths? And to also use the circle to 'measure' how distant a given out-of-key chord is to our home key? I thought that the answer to both these questions amounts to steps one needs to take on the circle of fifths, but clearly I've misunderstood this.

Assume a piece is in the key of C major. The most related chords to the tonic would then be d, e, F, G, a, and b0. Clearly, even if one puts aside the minor mode of the 2nd, 3rd and 6th scale degrees, it is not the case that these chords are nearest to C on the circle. For instance, B-flat is only 2 steps away from C, whereas the in-key chord E is 4 steps away.

CoFs below, for easier visualisation.

• How are these relatedness and distance things utilized? What do you do if the distance is long or if it is short? Or would you want to use this chart for finding a chord like, "I want a short-distance chord here"? Commented Nov 8, 2019 at 12:46
• It is to figure out how expected/unexpected a given chord should sound, as a function of how much it fits int he current key or not Commented Nov 8, 2019 at 14:03
• I think there is a lot more to expectations than the circle of fifths. Like for example, anything that has happened before. Play any random sequence of sounds a few dozen times and the listener will start to expect whatever there is in the sequence. :) Commented Nov 8, 2019 at 18:41
• You are completely right! Here however I was just trying to understand the relationship between inter-chord distance on the circle, and their relation as triads based on scale degrees of a given key. Commented Nov 9, 2019 at 13:06

I thought that the answer to both these questions amounts to steps one needs to take on the circle of fifths...

You are conflating the two circle of fifths.

Root progression by descending fifth is a common harmonic progression, it is commonly called a circle of fifths, but that isn't the circle of fifth of key signatures.

Circle of fifths progression is visually represented like this:

Circle of fifth key signatures is visually represented like this:

Is there an easy way to visualise... And to also use the circle to 'measure' how distant a given out-of-key chord is to our home key? For instance, B-flat is only 2 steps away from C, whereas the in-key chord E is 4 steps away.

Roman numerals are used to label chords in relation to the key signature not the circle of fifths.

In `C` major the `E` minor is the diatonic triad build on the third scale degree. It's labelled like this:

`C: iii`

In that case the tonic is `C`, but you can make a sort of temporary or secondary reference using one of `C` major's diatonic chords using a slash notation. If we are in `C` major and then use a `D` major chord, we can say `D` major is the dominant of `G` major which is the dominant of `C` major, and then label it like this:

`C: V/V`

If you compare that to the circle of fifths of keys, it is two steps away.

You can have other secondary chords. An `A` major chord is the dominant of `D` minor. `D` minor is the `ii` chord. The secondary label is then:

`C: V/ii ii`

You would say that out loud as "five of two" resolving to the "two chord."

That `A` major chord is three steps away on the circle of fifths of keys, but that is more or less coincidental. The important thing is the secondary dominant relationship, and that is an immediate relationship to the `ii` chord.

You can look at two elements in the case of `C: V/ii ii` or `A` major to `D` minor in the key of `C` major.

• the `A` major chord can be associated with the key `A` major which as 3 sharps and is three steps away from `C` major on the circle of fifths of keys.
• `A` major is the dominant of `D` minor, it is a chord from the key of `D` minor. It is the `V` chord of `D` minor. The key of `D` minor has one flat and on the circle of fifths of keys it is only one step away from `C` major.

In harmonic analysis the second point is the important one!

Relate chord to the keys to which they belong. Don't relate chord to their coincidental place on the circle of fifths of keys.

The chord `B` flat major in the key `C` major presents an interesting and different kind of relationship which can be looked at two ways: a secondary chord or a borrowed chord.

You can view that as a secondary subdominant chord. In `C` major the subdominant is `F` major. In `F` major the subdominant is `B` flat major. So, `B` flat is the subdominant of the subdominant in `C` major. You can label it as:

`C: IV/IV`

...the "four of four."

Borrowed chord are chord that can be found in the parallel key. `C` minor is the parallel minor of `C` major. In `C` minor `B` flat major is the `VII` chord build on the lowered seventh scale degree. In Roman numerals we use upper case to show the chord is major and add a flat sign to show the chord root has been lowered from the major mode:

`C: bVII`

In terms of measuring distance the secondary subdominant comes from a key which is one step away on the circle of fifth: `B` flat comes from the key of `F` which is one flat different from `C` major.

When thinking of the measure of the borrowed chord, I suppose you could say there is no distance because the tonic doesn't change from `C` major to `C` minor. Or you could say it is fairly distant, because `C` minor is three flats different from `C` major and that is three steps along the circle of fifths of keys. Probably many think of the borrowed chords as colorful because of their chromatic nature, but they aren't distant because the tonic isn't changed.

• Excellent response, I think I am clear on it now, thanks so much Michael. Commented Nov 8, 2019 at 15:03
• I think that tonic change is not an on/off toggle, it is more elastic and can be ambiguous. It would be interesting to see a visualization tool that could be used for even describing feelings regarding key changes. The circle is not such a tool IMO. Something like C - F - G - C - Bb - F - Ab - Db - ... what could come next? What happened with the rhythm and other things? It's more like a fuzzy potential field. Once you step outside a single dumb key, theory guys' tools get inadequate very quickly, and they use paragraphs and pages of text to try and describe their feelings. :) Commented Nov 9, 2019 at 14:33
• @piiperi, `Gb` would come next. I don't understand the point. `F` would be the tonic, and `Ab Db Gb` is just a tritone substitution of a bunch of secondary dominants. Actually the whole progression fits easily into `F`. Relating chords to a key isn't a problem even when the key changes. You wouldn't be able to describe a classical sonata if that were the case. If the harmony becomes non-functional, then drop the functional analysis. The OP asked about keys so there wasn't a reason to bring that up. Commented Nov 12, 2019 at 14:05
• I said what could come next. What is the set of possibilities and how unexpected would each of them feel. My point was that the OP may have assumed that tonic is a matter of declaration, not a matter of feelings and opinion. If that wasn't the case, and if the tonic is really set in stone, why would you need the circle of fifths or distance calculations. Commented Nov 12, 2019 at 14:32
• What does a set of possibilities have to do with this question? But, yes, there is no need to compare to the circle of fifth. I tried to explain that in my answer: "Relate chord to the keys to which they belong. Don't relate chord to their coincidental place on the circle of fifths of keys." Commented Nov 12, 2019 at 15:33

Using the circle of fourths/fifths, not everything can be simply a couple of steps away. Looking at it, anywhere you like will have the I, with its IV on one side and its V on the other side. That's pretty straightforward. But there's no reason why the other 'related' cords - the three minors and the diminished - should be anywhere near.

However, if you move three steps to the 'relative minor' note name (from for instance C round to A, or B♭ round to G), you'll have the three minors clustered together. So, from C, move three steps to A, and either side of that is the D and E - all minors in key C.

The diminished you can come up with your own formula! And I don't understand the last part of the question.

• So of all scale-degree chords, it's just the IV and the V that are found on the circle of fifths in close vicinity to (namely, to the left and to the right of) the tonic chord of the key; while for the others, the spatial positioning on the circle, relative to the tonic, is less straightforward. Am I right? Commented Nov 8, 2019 at 14:02
• It's just that. Moving three steps to find the others isn't onerous. I thought I'd answered the exact question from a circle of 4ths/5ths point of view. What isn't understood? No need to go into any specified keys - they all follow exactly what I've stated.
– Tim
Commented Nov 8, 2019 at 16:51

You already accepted an answer, but I'll just add an edited version of the circle of fifths picture. I've added groups of 3+3 basic chords for each key signature. In this sense, if you're in the key of C, an E major chord is not much of a step at all. It's in the same group of six basic chords, just on the other side of the line that separates the three basic chords of the major key and the three chords of the relative minor key. You need to know where the tonic is. That's your home base, and it's shown in the circle picture as the central chord in each key. When you know where that is, all other six chords are in the same "room". As long as you stay in the same room, you don't have to take any steps to grab any of the six chords, they're all within reach, within arm's length!

This is for vanilla pop song harmony, no special modes or anything. . In e.g. A dorian, you would have D major instead of D minor. Major chords are assumed as dominants on the minor side.

What comes to half-diminished seventh chord of the seventh scale degree, you can think of it as a slightly different ii chord. For example in C/Am, Bm7-5 can be thought of as a Dm6/B, so it's accounted for inside the "d" in the lower left corner. And we don't have to add a seventh letter for each key in the picture. :)

In this next picture the corresponding scale/chord degrees within each key are shown on top of the chords. The picture gets too messy already, but I guess you get the idea. I showed the dominants for the minor side just as the relative major key's "III" to keep things simpler and not have to talk about "i and V" for the minor side.

Maybe this helps you understand what a B or B7 chord does in a song that's in A minor of C major. That's none of the six chords in C/Am, so you can look at it as "borrowed" from the neighboring key.

Another example is Bb chord in the key of C. In the circle of fifths, it's just one step away if you think of it as being the IV of F major.

Myself, I never understood the use of the circle of fifths picture and the whole hype about the circle. I learned to know keys by playing songs, and each group of chords is a known thing in itself for me. I recommend trying to eventually get past the circle picture so that you just know all the keys like you know your home. This is best done by playing songs by ear in all keys. (IMO)

One more thing. Visualizing a "fifths" chord progression like "Fly Me to the Moon" happening inside a key could look like this:

It's a compromise from the "looks like a circle" point of view, because C/Am, F/Dm and G/E are shown vertically as pairs.

• That's very useful as an explanation, thank you so much. Two things I don't get though: (i) you always write E as the III of C, which it is, but for it to fit in the key, that triad should surely be 'e', since the third scale-degree triad is naturally a minor not a major?; (ii) in the final figure, the arrows seem to represent fourths- as opposed to fifths-jumps, leaving asside the fact that in Fly Me To The Moon I hear only a first fifths drop, but not further ones so as to say that its chord progression runs by fifths. Commented Nov 10, 2019 at 17:52
• @z8080 (i) in Am you have E major very often, maybe more often than E minor. (ii) a fifth up is a fourth down. It's the same thing. Circle of fifths, circle of fourths, same thing. Commented Nov 10, 2019 at 18:07
• (ii) of course.. so the figure still works if one simply reverses the direction of the arrows Commented Nov 10, 2019 at 19:39