Woodshed Wallpaper ™
Circle of Fifths
This is a concise version of the standard circle of fifths.
The circle has an awful lot of valuable and perfectly valid uses, though it's used primarily to spell key signatures. It gets its' name because it organizes all 12 tones in a series of perfect Fifths, as you progress to the right — clockwise — around the circle. By inversion then: as you move left, the tones progress by perfect Fourths. And that all leads to some more uses.
The circle is viewed as oriented from the top, at C; and wrapping around six degrees in each direction, to the enharmonics at the bottom.
The circle organizes all 12 keys by key signature, since: as you move around the circle by a single position, you add (or remove) a single sharp, or a single flat to the key signature; and arrive at the next adjacent key. (Some circles somewhat redundantly display each key signature, but they are removed here to reduce the clutter.) The numbers just inside the circle indicate how many sharps or flats each key signature has; and, moving right on the circle adds sharps to the key signature, and moving left adds flats.
Starting from C Major with no sharps or flats: G Major has one sharp, D Major has two sharps, etc. F Major has one flat, B♭ Major has two flats, etc. And you can use the indicated notes on the circle to find the order of added sharp and flat names in the key signature. Sharps begin with F and progress to the right: first F♯, then C♯, etc. Flats begin with B and progress to the left: first B♭, then E♭, etc.
And by convention, each relative minor key is indicated by the small letters inside the circle, which obviously share the same key signature.
Theoretical keys are keys that contain double sharps or double flats. These don't appear on the circle. Yet still: you could look further to find them enharmonically.
Another useful key signature feature is that you can find the closely related key modulations according to the next adjacent key. By convention, closely related keys are the ones that share the most tones — or chords — in common. So obviously any major key and its' relative minor share all seven tones in common. One move on the circle, which adds a single sharp or flat to the key, then will share six tones; two moves would share five, and etc. And so: an adjacent key will directly share all the same chords, or triads, that don't include the single added sharp or flat. Note that adjacent keys include modulation from a major or minor to the next minor or major, etc.
Also, modulations can be considered by their interval relation to the starting key. E.G: a modulation from C Major to G Major can be viewed as modulating to the Ⅴ of the home key; and that is a single step on the circle. And so, moving from the home key up a perfect fifth, is on the circle one step to the right.
The circle therefore shows the five most closely related keys in the five adjacent positions.
With a little inspection, the circle also shows standard harmonic progression, by moving left (and retrograde progression by moving right). However, the given notes will not always show the correct sharp or flat in your key — you can just always identify each chord's root letter, with or without the proper modification. Since standard forward progression is by fourths; or, where each chord is preceded by its' Dominant chord, then counter-clockwise movement by fourths will trace the forward progression: Ⅳ, ⅶ, ⅲ, ⅵ, ⅱ, Ⅴ, Ⅰ.
The dominant of any chord is always located directly to it's right (up by the Fifth), and so any single chord would be led by the chord to the right that way — it is the Ⅴ of the chord to it's left.
The Ⅳ - Ⅴ - Ⅰ progression is found with the three chord notes all next to each other (again, that's reliable, because the circle lays out fourths and fifths). For instance, F - G - C — in C Major — are located at the top of the circle. Starting at the root chord, that progression is always in this order: Ⅳ is to the left, and Ⅴ is to the right.
The ⅱ - Ⅴ - Ⅰ is also easy to locate: D - G - C in C Major, again all at the top of the circle. And this time, they all progress forward by fourths; and so they simply move left, from the ⅱ to the Ⅰ.
Obviously the circle shows perfect Fifths by it's design — and so you can use it to find any Fifth by looking right. Any Fourth is also simply found to the left. And, notes directly opposite on the circle form a Tritone (because you'll go through 6 shifts, of a perfect Fifth). These three intervals are always represented accurately.
Notice that any move left is always the inversion of the same move right; and vice-versa.
1 P5 P4 5
2 M2 m7 2
3 M6 m3 3
4 M3 m6 4
5 M7 m2 1
6 +4 ○5 6
Notice that the above intervals are all the expected Perfect, Major, and Minor intervals (which is a product of the 7-tone scale construction; through the series of perfect fifths); except for the Tritone, yet that is also expected, as it occurs naturally after the 6 shifts of the P5. And: the inversions are the expected ones as well (which may not immediately seem obvious; while looking at the circle through the "opposite moves left", yet still is).
You can see the above interval classes at this page. There's even a strong connection between the interval class numbering, and the number of moves on the circle; if you're familiar with that.
You can also discover that many types of scales can be spelled by various combinations of adjacent notes on the circle. This may seem obvious after inspection: as noted above in Intervals, you can envision spelling a scale by starting at the root note, and then moving around by the indicated intervals to find the notes in the scale. The resulting pattern of the adjacent notes will also wind up the same for various scales.
Any pentatonic scale can accurately be found on the circle as five adjacent notes. For example: C Major Pentatonic (and A Minor) is found by starting at that root C note, and taking the next four notes to the right. The scale is spelled C D E G A; which all appear side-by-side on the circle: C G D A E. This will be true starting at any note on the circle, and taking the five adjacent notes, progressing to the right; from the major root note. You can see also that the relative minor is the same one indicated in small letters inside the circle — A Minor for that C Major.
This is in fact also obviously expected for that Pentatonic spelling, since it is a scale that is constructed from the series of Perfect Fifths; and then re-arranged in order. We can also see that we can spell the scale by the intervals in sequence; as charted above. The Pentatonic scale is spelled Root - Whole - Whole - minor Third - Whole (- minor Third back to the Root). So as shown above, two moves right is a Whole step; and three moves left is a minor Third. So in the same way, we can start at C, move two to the right for the whole step to find D, and again to find E, then three moves left for the minor Third to find G, and two right again to find A. All five tones wind up being the ones that are side-by-side on the circle — C G D A E. Any Pentatonic is found that same way: five notes side-by-side, with the Major root note being the first on the left, and the minor being the one indicated inside the circle (and is the second-to-last note on on the right).
Any Diatonic scale can be found in essentially just the same way: the seven notes are all side-by-side on the circle. To spell the scale, the Major root note is the second one from the left. So to find C Major, we take the seven notes side-by-side starting from the F and moving right for six more notes. D♭ Major appears as: G♭ D♭ A♭ E♭ B♭ F C — all seven notes are side-by-side, and the Major root note is the second from the left — and again, the relative Minor is indicated inside the circle as usual.
You can see the same interval spelling as noted above for the Pentatonic also: you could find the same notes by moving around the circle for the intervals in sequence. You can also see that this is just the same as finding the Pentatonic, and then adding in the Four and the Seven: starting with the five pentatonic notes from C, we add in the Seven by moving right one more note; and add in the Four by moving left one note from the root note (and we don't add that in by making another move right, since that leads us to the Tritone instead — which does actually turn out to be a Lydian scale that way).
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