Musical Theory I

The basics about scales and key signatures:

A scale is a sequence of notes based on the idea of semitones and tones. A tone is a way of measuring the difference in pitch between two notes. A semitone is half a tone. A scale is a sequence of 8 notes (the first and the last being the same note) which are a set interval apart from one another. These set intervals are:

I -tone- ii -tone- iii -semitone- IV -tone- V -tone- vi -tone- vii -semitone- VIII (I)
For a major scale (e.g. C D E F G A B C)

I -semitone- ii -tone- iii -tone- IV -tone- V -semitone- vi -tone- vii -tone- VIII (I)
For a (natural) minor scale (e.g. A B C D E F G A)

This can be best seen on a piano keyboard:
As you can see by looking at the examples for the two given scales above, tones occur where there is a black key inbetween two white keys, and semitones occur where this black key is missing. A semitone by definition on a keyboard would be two notes that are directly next to eachother (i.e. not seperated by another key). Therefore, from C to C# on this keyboard would be a semitone, as would B to C. On a guitar, the distance between two adjacent frets is a semitone. If you skip a fret, that interval is a tone.

These intervals work out fine for a major scale using the white keys from C to C (the C major scale), but what if we wanted to play a major scale from the notes D to D (the D major scale)? Our semitones and tones would be misalligned if we just used white keys. This is why sharps (#) and flats (b) exist. [Note: A flat usually has a more pointed bottom on it, but it does closely resemble a lower case "b", so for our purposes here we will use "b"]

A sharp is defined as a semitone above the given note. For example, D# would be the next key to the right of D, which would be the black key we can call D#. In a similar respect, E# would be the next key to the right of E, which is a white key already named F. Thus F = E#. A flat is defined as a semitone below the given note. For example Db would be the next key to the left of D, which would be the black key we can call Db. You will also notice that in the above diagram this key is labelled C#. That is because every key is to the right and to the left of another key, so every note is a sharp and a flat. Db = C#. Similarly, Cb would be the key to the immediate left of C, which is a white key already named B. Thus, Cb = B.

These sharps and flats, also referred to as "accidentals", can be used to adjust our scale from D to D so that it is a proper major scale by definition. We would raise the third and seventh notes (F and C, respectively) by a semitone in order to obtain our D major scale. Thus the "key of D major" has F# and C# in it. A key signature indicates which notes need to be sharped or flatted to make sure the scale has the correct intervals between each of it's notes. A piece of music is in a particular key when that piece uses (only) notes from the scale which shares a name with the key.

But, let's face it, to figure out all of this semitone and tone stuff every time we want to play a certain scale would be a hassle. There is an easy way to remember which major scales have which key signatures.

"Father Charles Goes Down And Ends Battle"

When read from left to right, the first letter of each word indicates a sharp. This is the order in which sharps occur (FCGDAEB). When read from right to left, the first letter of each word indicates a flat. This is the order in which the flats occur (BEADGCF). Then you only need remember how many flats or sharps each major key has.

Sharp Key------# of Accidentals------Flat Key
C---------------------none------------C
G----------------------1--------------F
D----------------------2--------------Bb
E----------------------3--------------Eb
A----------------------4--------------Ab
B----------------------5--------------Db
F#---------------------6--------------Gb
C#---------------------7--------------Cb

Minor keys derive their key signatures from a relative major. Minor keys and their respective key signatures will be covered next week.