When to B Sharp

A Friend asked me a question about the following piece of music:

This song has 3 flats….E B A. Why do they have a C flat and F flat and not use B and use natural sign? or E and use natural sign.

The answer has to do with the relationship between the major and minor scales. Lets start there.

In the middle ages, when musicians were standardizing musical notation, music was often performed in a minor key. Thus, if you play all the white keys on a piano, they start on a really low A, and you play up a minor scale.

This is called the Natural minor scale, to distinguish it from many other minor sounding scales. This is the same set of notes as the C Major scale.

We call these two scales the “Relative major” and “relative minor” to each due to the fact that they are sharing a set of notes.

Lets look at the keys we are not playing now. There are black keys on the piano that appear in a group of two followed by a group of three. None of these notes appear in the A natural minor or C major scale.

We use these grouping of black keys to keep track of our location on the keyboard. If we look at the Key all the way to the left, we know it is a C because it is followed by a group of two black Keys. This diagram has four Cs on it, 3 of them right before the pattern, and one all the way at the right.

We need a way to name these black keys. The white keys have letter names that are in sequence, A through G. The black keys are usually named in relationship to the nearest white keys. If we go up to a black key from a white key, we use the same name as that white key, but add the term Sharp. If we go down from a White key, we append the term flat. The generic term for sharps and flats is “accidentals.”

You might be tempted to call the first black key all the way to the left C sharp (C#) and the last black key on the right B flat (B♭) and people would know what you are talking about. However, you would be equally correct to call these two notes D♭ and A# respectively. There is no one canonical name for these two notes…or any note on the key board. More on that in a bit.

Because we skip these black keys as we play up the white keys, the difference in frequencies between two successive notes changes. When we go from C to D, we skip the left most of a pair of two notes. By skipping a key, we say we are progressing in a “Whole step.” When we go from E to F, we do not have a black key to skip. We call this a “Half step.”

I’ll abbreviate W for Whole and H for Half.

The pattern for the Major scale is W W H W W W H.

The pattern for the Natural Minor Scale is W H W W H W W.

We usually talk about the pattern of the notes from low to high, but the pattern holds equally from high to low. Thus we can take these patterns and start on any note of the piano and build a scale. If we start too far to the right, where we would run out of keyboard, we can build the scale downwards. Thus, we say there are 12 distinct major scales and 12 distinct natural minor scales.

We can start on the A and make a major scale. From A we Go to B, just like we did in the natural minor scale. But instead of the Half step to C, we go a whole step to the black key after it. We call this C#….more on that in a bit. The pattern continues with D E F# G# and finally returning to A.

This has the same major quality as the C major scale I posted above, but starts lower. This pattern can be moved all around the keyboard.

The same thing can be done using the minor pattern starting on C. The end result of that is:

Instead of adding 3 sharps, we have added three flats.

When we compare A major to A minor, or C major to C minor, we call these parallel scales.

  • We call A minor the parallel minor to A major
  • We call C major the parallel major to C minor.
  • E flat Major is the Relative Major to C minor
  • F sharp minor is the relative minor to A major

Music often switches between the major and parallel minor for dramatic effect.

My friend tells me that the music has 3 flats it the key signature. This is the key of E flat major. In order to play the relative minor, we would have to add 3 flats. But there are only 5 black keys on the piano. How can we get 6 flats? Lets first talk about the order in which we add sharps and flats to a scale.

We use the term “interval” to define the distance between two notes, based on the major scale. The distance from C to E is a third, as E is the third note in the C scale. The distance from C to G is a fifth. The fifth is a really important interval.

The image below demonstrates a concept called the cycle of fifths.

If you start at C, you can play up an interval of a fifth to G. Repeat this pattern to D, and so on. Eventually you will return to C. You get all 12 distinct notes of the chromatic scale this way.

One thing that this cycle of fifths diagram shows is the relationship between a scale and the accidentals. As we take one step around the circle clockwise, we add a sharp. If we take one step around the circle clockwise we remove a sharp. The key of C has no sharps. The key of G has one sharp (F#), the Key of B has 5 sharps. The key of C has no flats, the key of F one flat (B♭) and the key of A♭ has four flats.

Look at the pattern of the sharps and flats we add. First we add F#, then C#, Then G#. Each of these notes is a fifth away from the one prior to it. Adding flats, we add B♭, then E♭, then A♭. These are also a fifth away from each other (just in the other direction). When you think of it, it makes sense: the scales are a fifth apart, so the changes to the scales are also a fifth apart. Math is fun!

What about those two scales at the bottom that have two names: D♭/C# and G♭/F#? They have both notations? This gets back to what I was talking about when I said there is no one canonical name for a black key, or any note on the keyboard. The sequence of Black Keys can be thought of as: C# D# F# G# A#. They can also be D♭ E♭ G♭ A♭ B♭. Once we get above 5 accidentals, one of the white keys will also get labeled with an accidental. The C note can be thought of as B#. The B note can be names C♭. F♭ is the same key as E, and F is the same key as E#.

So that key of B with 5 sharps could be rewritten as the key of C♭ with 7 flats. C♭D♭E♭F♭G♭A♭B♭C♭. That would balance off the D♭/C# scale posted above.

While the circle of fifth above is posted with the major scales, we can use it to determine the notes of the parallel natural minor scale. We know that A natural minor has the same set of notes as C major. This makes sense: we said we add a sharp each time we go clockwise, and add a flat when we go to counter-clockwise. It turns out that adding a flat is the same as subtracting a flat. To go from A major to minor, we want to subtract 3 sharps. Thus, we look three spaces counter-clockwise around the circle of fifths. We would do this by noting the “borrowed” notes as natural ising the sign: F♮, C♮ and G♮.

If we are writing in the key of C major, and we want to write in the key of C minor, we would add 3 flats.

At this point, we have enough theory to understand why the notation at the top of this article uses a C♭ to indicate a note that could be as clearly marked as a B. It is because we are in the key of E♭ and we are borrowing the C flat from the relative minor scale. Compare the two passages below:

The second one is much simpler.

Musical notation is an aid to communication of musical intent. The same thing can be written multiple ways. The writer should chose the notation that makes it easiest to communicate their intent.

Let me close by adding that musical notation editors like Musescore will transpose parts and keep them in key. If this part had originally been written in C, with the minor notes using added flats, it would translate to E♭ by adding the C♭. Notation like we see in this example if very common with the musical tools used today.

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