Why the need for Sharps and Flats?

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Occasionally a bright student will ask this question:

Why do we have to have both sharps(#s) and flats(bs)?"

It's an innocent enough question, but the answer lies buried quite deep in the traditions established during the evolution of musical notation.

The simplest answer is that in any one key you must include just one of each of the letter names (from A-G).

One way to derive the notes in any key is to apply the major scale formula: Tone, Tone, Semi-tone, Tone, Tone, Tone, Semi-tone to the chromatic scale starting on the key note. Suppose we do this starting on D:

Chromatic scale: D D# E F F# G G# A A# B C C# D

Major Scale: D (T) E (T) F# (s/t) G (T) A (T) B (T) C# (s/t) D

Telling us that the key of D major has 2 #s: F# & C#

Note: There is one of each letter name used in this scale.

No problem.

But now try it in the key of F:

Chromatic scale: F F# G G# A A# B C C# D D# E F

Major Scale: F (T) G (T) A (s/t) A# (T) C (T) D (T) E (s/t) F

We have violated the rule that in any one key you must include just one of each of the letter names (from A-G).We have both A and A# in the same key and we are missing a B. So to satisfy this rule we call the note that sounds like A# by it's enharmonic name of Bb (B flat). ('enharmonic' is a fancy way of saying: 'sounds the same as'):

Chromatic scale: F Gb G Ab A Bb B C Db D Eb E F

Major Scale: F (T) G (T) A (s/t) Bb (T) C (T) D (T) E (s/t) F

Now we have one of each letter name. I should stress that there are other perfectly valid answers to this question, but this is probably as far as you need go in answering your student's question unless you have already taken them through the whole subject of key signatures, circles of fourths and fifths, relative major and minor keys, naming of intervals etc. etc.

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