Lesson #3: Keys/Key Signatures – The Circle of Fifths – Triads/Chords – More Scales – Bass Clef

You can find last lesson here: http://paulfredericksmusic.com/lesson-2-reading-music-rhythm-time-signatures-all-12-major-scales-enharmonics/

Welcome to your 3rd lesson on LearnMusicWithPaul I first wanted to thank you guys for the amount of support I’ve received these past 2 weeks, this subreddit is basically 3 weeks old and we already hit 400 members! So thanks again, as we continue on I’ll try to post some youtube videos that will accompany an entire lesson.

So the last lesson we had we went over reading notes on the treble clef, understanding and reading different rhythmic beats and rests as well as time signatures. We ended the lesson with me going over all 12 main major scales in order of easiest to hardest based on the amount of accidentals as well as the idea of some odd/rare enharmonics.

Today we will be going over what key signatures are and how we can use them, what chords are and how they fit within a key, the circle of fifths, all 21 possible major scales based on all possible enharmonics, as well as reading notes on the bass clef. So let’s jump in FIRST with all 21 possible scales so then I can explain how the enharmonics and key signatures relate to the scales.

So last week we did 12 major scales, because there are 12 different notes on a piano.

A-Bb-B-C-Db-D-Eb-E-F-F#-G, & Ab

But every note can have all 3 types of accidentals, each note can be natural, each note can be sharp, and each note can be flat, as such:

Ab-A-A#, Bb-B-B#, Cb-C-C#, Db-D-D#, Eb-E-E#, Fb-F-F#, Gb-G-G#

Giving us a possibility of 21 different scales, even though some are enharmonics of the other, they still technically exist and you may see some weird ones in the future when learning new songs. Obviously some of the rarer keys and scales aren’t used as much, especially the enharmonics surrounding B-C & E-F. But we will still learn them and understand how they work.

Now since we are using these new/rare/odd enharmonic scales we will actually get some new types of accidentals, but they are decently easy to understand.

We will be gaining 2 new types of accidentals, one is called a double sharp which symbol is an “x”, a double sharp does exactly what you think, it raises the note up 2 half steps aka 1 whole step.

Then we will get a double flat, which symbol is simply two b’s “bb”, this does exactly what you think as well and it lowers the note down 2 half steps aka 1 whole step.

Here is a picture of the symbols.

So why do we have these types of accidentals? It goes back to our first lesson when I mentioned that when we create our scales they must go in alphabetical order such as D-E-F-G-A-B-C-D, so the letters will always be going in the correct order and there will be times where the scale wants us to play a note that is out of order alphabetically, so we need to give that note a name (enharmonically) that fits within the scale. The last example I gave of a situation like that was our F# scale, so here is an example that uses a double sharp enharmonic. Our G# scale would go as such:

G# = 1, up a whole step is A#, up a whole step is B# (C enharmonically),up a half step would be C#, up a whole step is D#, up a whole step is E# (F enharmonically), now we need to go up a whole step from E#(F) which would have to be G but we have to call it some type of F. So since G is a whole step up from F, aka 2 half steps up, we will call this G, Fx (F double sharp)

Now for the rest of the double accidentals I will mention these when we get to them in our scales down below. (This is also why we would use easier enharmonic scales/keys instead of scales/keys with double accidentals,)

So I will be putting these scales in order of the circle of fifths, then after I will explain how that order came about and how it helps us learn the keys and scales faster.

Once again the formula for the scales is: 1,w,w,h,w,w,w,h (We will always start with C as it is the only major scale that has 0 sharps and 0 flats.)

(Ascending the circle of fifths, clockwise)

C Major: C-D-E-F-G-A-B-C – 0 sharps, 0 flats

G Major G-A-B-C-D-E-F#-G – 1 sharp (F#)

D Major: D-E-F#-G-A-B-C#-D – 2 sharps (F# & C#)

A Major: A-B-C#-D-E-F#-G#-A – 3 sharps (F#, C#, & G#)

E Major: E-F#-G#-A-B-C#-D#-E – 4 sharps (F#, C#, G#, & D#)

B Major: B-C#-D#-E-F#-G#-A#-B – 5 sharps (F#, C#, G#, D#, & A#)

F# Major: F#-G#-A#-B-C#-D#-E#-F# – 6 sharps (F#, C#, G#, D#, A#, & E#)

C# Major: C#-D#-E#-F#-G#-A#-B#-C# – 7 sharps (F#, C#, G#, D#, A#, E#, B#)

(all these below will have double sharps in them)

G# Major: G-A-B-C-D-E-F#-G – 8 sharps, *1 double sharp*, (Fx, C#, G#, D#, A#, E#, & B#)

D# MAjor: D-E-F#-G-A-B-C#-D – 9 sharps, *2 double sharps*, (Fx, Cx, G#, D#, A#, E#, & B#)

A# Major: A-B-C#-D-E-F#-G#-A – 10 sharps, *3 double sharps*, (Fx, Cx, Gx, D#, A#, E#, & B#)

E# Major: E-F#-G#-A-B-C#-D#-E – 11 sharps, *4 double sharps*, (Fx, Cx, Gx, Dx, A#, E#, & B#)

B# Major: B-C#-D#-E-F#-G#-A#-B, 12 sharps, *5 double sharps*, (Fx, Cx, Gx, Dx, Ax, E#, & B#)

So this is the circle of fifths ascending, going clockwise/up/to the right. This gives us the sharps.

Now if we use the circle of fifths, descending, counter-clockwise/down/to the left. That will give us flats.


(Descending the circle of fifths, counter-clockwise)

C Major: C-D-E-F-G-A-B-C – 0 sharps, 0 flats

F Major: F-G-A-Bb-C-D-E-F – 1 flat (Bb)

Bb Major: Bb-C-D-Eb-F-G-A-Bb – 2 flats (Bb & Eb)

Eb Major: Eb-F-G-Ab-Bb-C-D-Eb – 3 flats (Bb, Eb, & Ab)

Ab Major: Ab-Bb-C-Db-Eb-F-G-Ab – 4 flats (Bb, Eb, Ab, & Db)

Db Major: Db-Eb-F-Gb-Ab-Bb-C-Db – 5 flats (Bb, Eb, Ab, Db, & Gb)

Gb Major: Gb-Ab-Bb-Cb-Db-Eb-F-Gb – 6 flats (Bb, Eb, Ab, Db, Gb, & Cb)

Cb Major: Cb-Db-Eb-Fb-Gb-Ab-Bb-Cb – 7 flats (Bb, Eb, Ab, Db, Gb, Cb, & Fb)

(this scale below will have a double flat in it)

Fb Major: Fb-Gb-Ab-Bbb-Cb-Db-Eb-Fb – 8 flats, *1 double flat*, (Bbb, Eb, Ab, Db, Gb, Cb, & Fb)

Ok now I know there’s a lot of scales here to wrap your mind around, so let’s jump into the easiest way to figure these out and to start understanding our next concept. The Circle of Fifths.


So the circle of fifths is a much faster and easier way of memorizing our scales, and what notes fit within said scales. The above way forces us to use our formula and build a scale every time over and over. The Circle of Fifths cuts this thinking and building process in half.

So the way the Circle of fifths works, is that we have a literal circle, with C at the top at the 12’oclock position. As we move up/right/clockwise/ascending in our circle of fifths we will be gaining scales that have sharps in them, each time we move up another scale we will gain another sharp in the scale.

So how do we move up/right/clockwise? What is the process?

So just as the name implies, we will move up, 5 letters/scale degrees within the scale.

So let’s take a look at what that means:

So our first position at the top is C Major:


1- 2-3-4- 5- 6-7-8

If we go up 5 letters/scale degrees using C as our 1, we get to G.

So That means G would be the second position, 1’oclock. And this also means that G would be the first scale, to have a sharp, and it would only have 1 sharp.

So every time we move upwards 5 notes/scale degrees within the scale, we will get our next scale that has another sharp.

Now just like the circle of fifths has a specific order, there is also a specific order for the order of sharps and how they come about in our scales.

This is the order of sharps:

F#, C#, G#, D#, A#, E#, B#

1, 2, 3, 4, 5, 6, 7

A little mnemonic for this would be Fat, Cats, Get, Down, At, Every, Ball

As you can see as well once we get past our C# scale the order of sharps starts over but with double sharps, so after the 7th sharp we go back to the 1st sharp, but sharp it again, therefore it becomes a double sharp. (Fx, Cx, Gx, Dx, Ax) We won’t go past the 5th double sharp as we would then need to start a scale on a double accidental which is super rare to do.

So F# is our first sharp, and we would see ONLY this sharp in our first scale that has 1 sharp.

Now every other scale after G will always have more than 1 sharp, and the sharps will always carry over into the next scale.

So let’s move up 5 notes/scale degrees within our G scale now.


1- 2-3-4- 5- 6- 7- 8

So D is our 5th note, so D would be our 3rd position, at 2’oclock. This means D has 2 sharps, F# (which carries over) and then it adds our second sharp in the order, C#.

So the circle of fifths ascending/clockwise order would be:

C-G-D-A-E-B-F#-C#-G#-D#-A#-E#(The easier version which only goes up to 7 accidentals would only be: C-G-D-A-E-B-F#-C#)

*Scales with double accidentals don’t usually show up on standard circle of fifths as we mentioned before they aren’t used as much, nearly at all, and we can use a different, and easier, enharmonic scale/key.*


Now if we applied that same logic to the circle of fifths descending/down/to the left.

We would get our flats.

So if we take C and we go DOWN 5 letters/scale degrees it would look as such:


8- 7-6-5- 4- 3- 2-1

C is our 1, 5 down from C is our F, so our F Major scale will have 1 flat, and would be our second position, in the 11’oclock position in the circle of fifths, now the first flat would be in the F Major Scale, and would be Bb.

Just like the order of sharps we have an order of flats, and easily enough it is the order of sharps, BACKWARDS.

B, E, A, D, G, C, F

1, 2, 3, 4, 5, 6, 7.

I think of this as BEAD Get Coffee Fast or you can think of it as literally backwards “Ball, Every, At, Down, Get, Cats, Fat”

Whatever works for you best.

(Once again after we get past our Cb major scale the order of flats starts over but with a double flat on B)

Now every other scale after F will always have more than 1 flat, and the flats will always carry over into the next scale.

So let’s move down 5 notes/scale degrees within our F Scale now:


8- 7-6- 5- 4- 3-2-1

So Bb is our 5th note, so Bb would be our 3rd position in the 10’oclock position in the circle of fifths. This means Bb has 2 flats, Bb (which carries over) and then it adds our second flat in the order, which would be Eb.

So the circle of fifths descending/counter-clockwise order would be:

C-F-Bb-Eb-Ab-Db-Gb-Cb-Fb(The easier version which only goes up to 7 accidentals would only be: C-F-Bb-Eb-Ab-Db-Gb-Cb)

Once again *Scales with double accidentals don’t usually show up on standard circle of fifths as we mentioned before they aren’t used as much, nearly at all, and we can use a different, and easier, enharmonic scale/key.*

Now when we make the actual image of the circle of fifths, some of the enharmonic scales can overlap.

So for example in our 6’oclock position we can have both F# and Gb as they are the same enharmonic note, and both will have 6 accidentals.

F# has 6 sharps, Gb has 6 flats.

It seems no circle of fifth image has all enharmonics only the most common so I had to edit some of them in, so it may look a bit weird lol

I’ll also post a version without the extra odd/rare enharmonics (only 7 accidentals max)

So that’s how the circle of fifths work, it basically helps us understand what scales have sharps, and what scales have flats in an easy to remember way. Instead of having to build every scale using the formula we can memorize the order of sharps, the order of flats, and the circle of fifths to give us a work around to memorize what scales have what accidentals in them. (Obviously the odd/rarer scales aren’t used as much and people won’t memorize them within the order since they won’t be using them unless in some odd scenarios/songs).


Now we get to the idea of “keys/key signatures”.

A Key and key signature, are very similar to the idea of the circle of fifths, as well as the idea of a time signature. A Time signature told us before the music started what rhythmic note gets the beat, and how many of those beats will fit within a measure.

A Key signature tells us what notes, in our piece/song, get accidentals added to them, therefore telling us what scale, “key”, to use when playing a song. The way they do this is by adding sharps or flats on the designated line or space.

So if we see a key signature with 1 sharp, that 1 sharp will usually be F#, and using the circle of fifths we know the major scale that uses 1 sharp, is G Major.

Here are all sharp major scale key signatures.

Here are all flat major scale key signatures.

So if you hear someone say “this song I wrote is in the Key of A Major, that means the song most likely uses only the notes from the A Major scale, which means we have 3 sharps, F#, C#, & G#. All other notes (A,B,D,& E) are natural.

Now when someone mentions a key, they most likely also mean all the chords used in the song fit within the A Major scale.

So a key isn’t just the scale, notes, and accidentals being used, but also chords that are being used that FIT WITHIN that scale/key.


So now we need to learn a bit about chords.

A chord is when we play 3 or more notes at the same time/simultaneously. So, yes, any 3 notes played at once is a chord. Technically if I played C, Db, & D all at once, it would technically be some type of chord. But usually chords will come in a few specific varieties/qualities. There is also a very common pattern for chords just like the pattern/formula for the major scale.

The most common chord is called a “triad”. In music, a triad is a set of three notes that can be stacked vertically in thirds. So what does this mean?

What exactly is a “third” and how do we know what type of thirds can stack on top of one another? A third is a type of interval, we won’t get too much into intervals at the moment, so I will try to explain thirds, triads, and chords in an easy way until we can explain more in the next lesson.

So when we stack thirds, this basically means we are stacking notes that are 2 letters away from one another. So for example A up 2 letters would be C, and if we go 2 more letters up from C we get E. So we can have a triad that consists of A, C, & E.A-B-C, C-D-E1- 2-3, 1- 2-3

So if you were to play A, C, & E at once on your piano or any instrument, you would be playing a type of A Chord.

So when we are talking about triads we have 3 main types/qualities of triads/chords that will fit within a given major scale/ major key.

We will have a “Major Triad/Chord”

A “Minor Triad/Chord”

And finally a “Diminished Triad/Chord”.

Each of these types of triads and chords are built using different formulas/patterns/and types of thirds.

Let us first look at our Major Triad.

So a Major triad is based on a root note (1) any note of your choice basically.

Then we will go up a “major third” (once again this is a type of interval) a major third consists of 2 whole steps.

So if we were to choose C as our 1/root, we would go 2 whole steps up from C.

Which would be E.

Then we will stack another third on top of our E. This time we will be going up a minor third (type of interval) which consists of 1 whole step + 1 half step.

So one whole + one half step up from E would be G.

So our C Major triad has 3 notes: C, E, & G.

Now let us look at our minor triad.

A Minor triad is also based on a root note (1), and instead of going up a major third to begin, we will go up a minor third from the root.

So once again if C is our root, we will go up 1 whole step + 1 half step, which would bring us to D#/Eb. Now since we are going two letters/notes up from C we will call it an Eb since C-E is 2 letters up, but C-D is technically 1 letter up.

Then we would stack a major third on top of our Eb, so we go up 2 whole steps to G.

So our C Minor triad has 3 notes: C, Eb, & G.

Finally we get to our Diminished triad.

A Diminished triad is based on a root note, and then we will stack 2 minor thirds in a row on top.

So C up a minor third we already know is Eb, then if we go another minor third up from Eb we would end up on Gb.

So a C Diminished Triad is C, Eb, & Gb.

Here are pictures of these 3 chords, C major, C minor, & C diminished in sheet music & on a piano.

(Green = C Maj, Red = C Min, Pink = C Dim.)

This is a very brief introduction to types of triads, types of intervals, we will talk more about triads, chords, and intervals next lesson. So let us continue on with our understanding of “keys/key signatures”.


So our major scale has 7 notes within it, this means we can build triads on all 7 of our notes within one major scale.

Now since we are only using 7 letters, that means we can also ONLY use those 7 letters when building our triads. So for example we won’t build a major, minor, and diminished triad on each letter as that may give us notes that are not within the scale/key.

So let us look at the easiest scale and it’s key, the C Major Scale.

The C Major scale is all 7 natural letters, no sharps, no flats. So all 7 of our chords will have no sharps, and no flats.

What we can do is simply stack 3rds on top of all 7 notes.

Let me show you what I mean.

Here is our C Major Scale:


1-2- 3-4- 5- 6-7-8

We can 7 different chords, each chord will be built on each note within the scale.

So we will have a C chord, a D chord, an E chord, an F chord and so on.

Now instead of building all the different types of triads, we can simply just stack letters that are within the scale on top of one another.

So our C chord would use C as its root, then we would stack a third on top of it, now the only 3rd we can stack on top of it would be a major 3rd since E is a major third away from C. There is no Eb or E# in the key of C so we wouldn’t use those letters when stacking our triad. Then we’d stack another third on top of E, we know there is no Gb or G# so our final third stacked ontop would be a minor third from E.

So our first chord we can build in our C Major scale is a C Major Chord.

C,E, & G.

Now another, and possibly, more simple way of building chords within a key/key signature/scale is to use scale degrees to specify the exact notes we want stacked on top.

So C is our 1st note of our scale, E is our 3rd note, and G is our 5th note.

So we can build a chord by playing the 1st, 3rd, and 5th note of a scale together to build our first chord on the first scale degree/note.

1-3-5 = C Major = C-E-G

So now what we can do is simplify our building of triads by using this same idea on all 7 notes.

So if we started with our 2nd note which is D we would then stack our F on top, aka our 4, and then finally our A, aka your 6th note.

2-4-6 = D Minor = D-F-A

Here is a 2 octave C Major Scale so you can see how we are doing this:


1-2- 3-4- 5-6- 7- 8-2- 3-4-5- 6-7-8

1-3-5 = C-E-G = C Major

2-4-6 = D-F-A = D Minor

3-5-7 = E-G-B = E Minor

4-6-8 = F-A-C = F Major

5-7-2 = G-B-D = G Major

6-8-3 = A-C-E = A Minor

7-2-4 = B-D-F = B Diminished

And the formulas before we talked about with the different types of stacked thirds give us these names of our triads within the key.

Here is an image on sheet music and piano of all of these chords (the image on piano will be split in multiple octaves as I cannot overlay on the same notes)

(Green = C Maj, Red = D Min, Blue = E min, Yellow = F Maj, Purple – G Maj, Orange = A Min, Pink = B Dim.)

So this pattern will always be the same for all the major scales.

Triad built on 1st degree will always be a Major Triad

Triad build on 2nd degree will always be a Minor Triad


1 = Major

2 = Minor

3 = Minor

4 = Major

5 = Major

6 = Minor

7 = Diminished

So if we were building triads/chords in our A Major scale this means:

1= A = Major

2= B = Minor

3 = C# = Minor

4 = D = Major

5 = E = Major

6 = F# = Minor

7 = G# = Diminished

I know some of you will have many questions when it comes to chord/triad types, and how chords fit within a key so please ask as many questions as needed to help you understand this concept, and next lesson we will talk more about chords/triads and intervals.


So we’ve looked at our 21 major scales, we’ve seen how the circle of fifths can help us understand and memorize the notes within a given major scale. We’ve also seen how the circle of fifths helps us understand what accidentals each major scale uses, and the order of said accidentals.

We then talked about our key signatures/keys and how that “basically” means the given scale used in a song, and the chords we can use that also use the notes of said given scale. How ever many notes in a scale = how ever many triads can be built on those same notes.

Finally we can look at the Bass Clef.

The Bass clef will have the same idea as the treble clef, a specific symbol which means specific lines and spaces will have specific notes.

So it’s just another clef to learn and memorize the positions of the notes.

Just like before we have 5 lines, 4 spaces, top and bottom notes, and ledger lines. Here’s an image that has from our bottom ledger line up to our top ledger line.

Now you will notice something interesting here, the top ledger line is our C ledger line, this is THE SAME EXACT C that is our bottom ledger line on treble clef. This ledger line C is in THE MIDDLE of these 2 staffs, this is called “Middle C” not only is it in the middle of these 2 staffs, but it is also IN THE MIDDLE of the piano.

Here is a “grand staff” which is just both treble and bass put together, with all the notes from bottom ledger of bass up to top ledger of treble.

So now we have gone over how to read a key signature, (figure out how many sharps or flats, then figure out what major scale those sharps/flats are in *using the circle of fifths*) how playing within a key means using it’s specific major scale and specific 7 chords/triads that fit within it, and finally how to read bass clef.

(Obviously when playing in a key we have many more chords and notes we can use but this will be a bit more advanced in understanding how to choose said chords and notes).


Next lesson we will be going over the minor scale, how those scales and keys of those scales relate directly to the circle of fifths, and major scales, and how the chords within those minor keys directly relate to the same chords we went over today. And then we will go over the idea of inversions. I’m also going to post ANOTHER lesson next week with the beginning of understanding and playing the guitar and using some of this theory we’ve used on piano, and applying it to the guitar.