This post is a bit longer, but well worth the dive.

Review

The major scale has an ascending pitch pattern of WWHWWWH, that is, 2 whole steps, followed by a half step, followed by 3 whole steps, followed by a half step.  Looking at a piano keyboard, you would play all the white keys from C to the next C, an octave above (or below).

Where is C?  Here.

You may have heard of “middle C” on a piano.  If you sit on the piano bench (or chair, stool, picnic table…) and square yourself so that there are the same number of keys to your right as there are to the left, middle C is slightly to the right, not the exact middle of the keyboard.

If you change the pattern from WWHWWWH, but keep the general sequence intact, you get different sounding scales.  The major scale and the minor scale are the most often used.

Key

Key is the organization of half steps and whole steps.

Remember that a major scale is always WWHWWWH.  Starting on C and following the WWHWWWH pattern, you will notice that you will only be depressing the white keys.  The white key immediately to the left of any C is B.  To the left of that is A.  To the right of C is D, then E, F, G, and then the cycle starts again.

Scales in Sharpland[1]

When you start your major scale on G, the keyboard pitches you’ll use are G, A, B, C, D, E, F#, G.  That F# is a black key.  Notice also that the change from F (natural) to F# occurs on the next to last step.  You should also notice that you’ve only added 1 black key, the rest are still white keys.  I know this is an obvious restatement, but bear with me.

Okay, now let’s create a major scale on D, again remembering WWHWWWH.  The result is D, E, F#, G, A, B, C#, D.  You should notice that all of the pitches of the G major scale are the same, except the next-to-last step has been raised from C to C#.  You should also notice that you’ve only increased the number of black keys by 1 again, but now you have a total of 2 black keys.

The A major scale has these pitches:  A, B, C#, D, E, F#, G#, A.  Again, this scale is the same as the major scale on D, except that the penultimate pitch – G – is raised by a half step to G#.  We now have 3 black keys.

The major scale that begins on E has these pitches:  E, F#, G#, A, B, C#, D#.  This is the same scale as the A major scale, except that the penultimate pitch – D – is raised to D#.  We now have 4 black keys.

The major scale that begins on B has these pitches:  B, C#, D#, E, F#, G#, A#.  This is the same scale as the E major scale, except that the penultimate pitch – A – is raised to A#.  We now have 5 black keys.

The major scale that begins on F# has these pitches:  F#, G#, A#, B, C#, D#, E#.   This is the same scale as the B major scale, except that the penultimate pitch – F – is raised to F#.  We now have 6 sharps, but still only 5 black keys.

Let’s pause a moment to look back at what we did for major keys, so far:

  • The first scale we looked at, C major, has no black keys.
  • The scale with 1 sharp and 1 black key is G major.
  • The scale with 2 sharps and 2 black keys is D major.
  • The scale with 3 sharps and 3 black keys is A major.
  • The scale with 4 sharps and 4 black keys is E major.
  • The scale with 5 sharps and 5 black keys is B major.
  • The scale with 6 sharps and 5 black keys is F# major.
  • The scale with 7 sharps is C# major.

Let’s look at that another way:

C (0 sharps) -> G (1 sharp) -> D (2 sharps) -> A (3 sharps) -> E (4 sharps) -> B (5 sharps) -> F# (6 sharps)

What to remember for flatland[2] keys:

  • The new scale begins on the 4th degree of the previous one (from C go up or down to F).
  • All pitches of the new scale are unaltered except the 4th degree.  It is lowered a half step to a flat (the 4th degree in C major is F.  Starting on F, count up to the 4th degree (again) and lower it a half step (B becomes Bb – “B flat”).
  • The next scale in flatland also begins on this 4th degree (Bb major from F major).

After B, what do you think will be the next scale?  Undoubtedly, and accurately, you’ve pointed at F#.  We can again use the WWHWWWH sequence to create a major scale on F#:  F#, G#, A#, B, C#, D#, E# (yes, E#.  This pitch, on the piano, looks the same as F natural, but because it functions as the penultimate pitch in the F# major scale, it is called E#.  When you play it on your instrument, you can go ahead and play F natural and no one will know), and finally, F#.  This scale is the same as the B major scale, but with E#.  This scale has 6 sharps in it, although it only has 5 black keys.  Look at the piano again.  Do you see unique black keys?

  • The scale with 6 sharps and 6 black keys is F# major.

Small Digression

Enharmonic Notes

So far, I’ve introduced the black keys as pitches that are raised a half step; going from the white-key F to the first black key to its right, F#, for example.  While this is true, these black keys also represent the lowering of a pitch by a half step; going from the white-key G to the first black key to its left, Gb.  The same is true for all the other pitches: If you go to left of a key by a half step, that first pitch will be flattened.

The bottom line is this:  you can refer to a black key in two ways, but it depends on the context.  In the key of E major, the middle black key of the group of three black keys is G#.  In the key of Eb major, this same key is Ab.  Another way to refer to this black key is that G# is enharmonically equivalent to Ab (F# = Gb, etc.).

Likewise, if you go to the half step below C, you get Cb, but it is still a white key.  If you want a half step below F, you get Fb.  Again, a white key.

  • F# is the enharmonic equivalent of Gb.
  • C# is the enharmonic equivalent of Db.
  • G# is the enharmonic equivalent of Ab.
  • D# is the enharmonic equivalent of Eb.

Back to the Show

When we looked at the major keys in sharpland, we added one sharp key at a time – always raising the 7th degree, or 2nd to last pitch, of the scale.  We also started the next scale on the pitch that is 5 diatonic steps up from the previous pitch.

Scales in Flatland

Let’s go in the other direction – going down five steps.  This is the direction of flatland.

Starting again from C (no sharps or flats), count down 5 diatonic steps, as if the C is the fifth degree of the new scale, and you’ll get to F.  Use the first part of the WWHWWWH sequence, the first 4 steps (WWHW), but in reverse (WHWW) so that when you start on C, you will go down a whole step to Bb.  Down from Bb, the half step is A.  Down from A, the whole step is G.  Down from G, the whole step is F.  F is the new tonic of the scale that has one more flat in it than the previous scale (C – no flats).

What to remember for flatland keys:

  • The new scale begins five diatonic steps lower than the previous one.
  • All the pitches of the new scale are the same except the fourth degree of the new scale (the fourth degree of the new scale). The altered pitch is lowered by one-half step.
  • The 7th degree of the new scale is already a half step below the tonic, so no change is needed.

Using this same procedure (counting down five diatonic steps), again in reverse, you’ll get F to Eb = whole step.  Eb to D = half step.  D to C = whole step.  C to Bb = whole step.  The new tonic is Bb.  This new key, Bb major, has two flats in it and two black keys.

Using this same procedure, you’ll get Bb to Ab = whole step.  Ab to G = half step.  G to F = whole step.  F to Eb = whole step.  The new tonic is Eb.  This new key, Bb major, has two flats in it and two black keys.

Let’s look at this with bullet points like we did with the sharpland keys:

  • (The scale with no flats or sharps and no black keys is C major).
  • The scale with 1 flat and 1 black key is F Major.
  • The scale with 2 flats and 2 black keys is Bb Major.
  • The scale with 3 flats and 3 black keys is Eb Major.
  • The scale with 4 flats and 4 black keys is Ab Major.
  • The scale with 5 flats and 5 black keys is Db Major.
  • The scale with 6 flats and 6 black keys is Gb Major.

Let’s return to our small digression

Remembering the discussion on enharmonic pitches, this should be simple:

The major scale that begins on F# has these pitches:  F#, G#, A#, B, C#, D#, E#.   Switch the F# major scale to Gb major and you get Gb, Ab, Bb, Cb (yes, Cb), Db, Eb, F, and Gb.  (For tuning purists, of course I’m walking about equal temperament.  This blog post is for beginners.  Do you think I want to blow their minds even more?)

The major scale that begins on C# has these pitches:  C#, D#, E#, F#, G#, A#, B#.  This is the same scale as the F# major scale, except that the penultimate pitch – C – is raised to C#.  We still have 5 black keys, but we now have seven sharps.

Switch the C# major scale to Db major and you get Db, Eb, F, Gb, Ab, Bb, C, and Db.  This is a scale with five flats and five black keys.

 

Next up:

Our next topic will be the minor scale.  This will be so much easier to understand now that I’ve presented the major scale in all its glory.  Stay tuned…

[1] “Sharpland” is not an officially recognized term in music theory.

[2] “Flatland” is not an officially recognized term in music theory.

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