The musical term scale, having nothing to do with fish, or lime scale, derives from the Italian word scala, meaning ladder. There are many different types of scale, but the majority of western music uses only two forms, the major and minor scale.

Major and Minor Scales

Major Scale

The major scale is the same as the Ionian mode (see below). After a while in mainstream western music (circa 1500) most of the modal scales dropped out of use, leaving the Ionian as our present day major scale, and the Aeolian as our minor scale. (See A Brief History of Western Music.)

Each note in a scale has a name, the equivalent note in C major is shown in brackets.

• Tonic (C)
• Supertonic (D)
• Mediant (E)
• Subdominant (F)
• Dominant (G)
• Submediant (A)
• Leading-note (B)
• Tonic (C again)

The tonic is the most important in the scale. The second most important is the dominant. This gives rise to related keys; for a piece written in the key of C major, it is classically (that is classical in the sense of traditional- "classical" music, as in non pop music, often breaks classical rules), allowed to have a change of key to G major, since that is the dominant in the key of C. It would not be allowed to have a modulation (key change) to Db¹ major, for example, because that is in no way related to the original key of C.

The pattern of tones and semitones² in a major scale is this: (T=tone, S=semitone)
T T S T T T S

- There is a tone (in C major) from C to D, a tone from D to E, a semitone from E to F and so on.

Minor Scale

The minor scale is based around the Aeolian mode. However, in the Aeolian mode there is a tone between the leading note and the tonic, so the leading note doesn't lead to the tonic like it does in a major scale. To get around that there are two versions of the minor scale, the harmonic minor, which is modified so that it does have a semitone, and the melodic minor, which is different depending on whether the scale is ascending or decending.

This is the pattern of tones and semitones in a harmonic minor scale: (T=tone, S=semitone 3/2= 3 semitones)
T S T T S 3/2 S

- In A minor, the notes are A B C D E F G# A.

The pattern of tones and semitones in a melodic minor scale is this: (T=tone, S=semitone)

Ascending: T S T T T T S Descending: T T S T T S T

- In A minor, the notes are ascending: A B C D E F# G# A, and descending: A G F E D C B A.

Chromatic Scale

The term chromatic comes from the Italian for colourful. There are twelve notes in a chromatic scale:

• C
• C#/Db (These are the same note on a piano³.)
• D
• D#/Eb
• E
• F
• F#/Gb
• G
• G#/Ab
• A
• A#/Bb
• B

There is a semitone step between each note in this scale, making none of the notes more important than any of the others.

Modal Scales

The earliest types of scale to be used were the modal scales, used in renaissance music. These were derived from very early ancient Greek scales. There are eight modes:

• Ionian -can be played from C to C on the white notes of a piano. This scale is the same as the Major scale. (see above)
• Dorian -can be played from D to D on a piano
• Phrygian -can be played from E to E
• Lydian -can be played from F to F. This mode sounds like a major scale but with a wrong note in.
• Mixolydian -can be played from G to G. This mode also sounds quite like a major scale.
• Aeolian - can be played from A to A. This is the same as the Minor scale.
• Lochrian -can be played from B to B. This mode is was (and is) very uncommon.

The names for these modes were supposed to be the same names that the Greeks gave them. However, they aren't the same.

Pentatonic Scale

Much traditional folk music is based around a pentatonic, or five note scale. This is also quite widely used in popular music and anything relating to blues. The E minor pentatonic scale is particularly easy to play on the guitar. For a pentanotic scale based on the key of C major, the five notes would be C, D, E, G and A.

Whole Tone Scale

The whole tone scale is perhaps the newest of these scales. It was used by composers such as Debussy. The whole tone scale is similar to the chromatic scale inasmuch as there is a constant gap between every note. In the case of the whole tone scale, this gap is a tone. The notes of a whole tone scale starting on C would be: C, D, E, F#, G# and A#.

The Science Bit

As music is sound, there is physics underlying the way the scale works. You pluck a string (or blow into a pipe) of length X, and you get a particular note (the fundamental). You also get small percentages of other notes (the harmonics).

The first harmonic is one octave above the fundamental; the second is 1.5 octaves above. These are heard (usually subconsciously), and so the brain thinks they sound right. That's why all modes and scales have a tonic, a dominant (the second harmonic, but an octave low) and the next tonic (the first harmonic). From here, the various modes part company (depending on who cut the string or chopped the pipes), but they do have a note (the median) to go in the gap between tonic and dominant. The other notes just fill in the gaps (or not much, in pentatonic).

In any single key, you can generate all the notes in the scale by starting with a long enough string\pipe and continuing to cut it in half. That accounts for the ideal intervals between all the notes.

Unfortunately, if you start from a different fundamental (like from G instead of C, for example), the seconds, fourths and sevenths that you generate fall at slightly different frequencies from what should be 'the same' notes obtained from different keys. The difference, is called a "comma", and it was what drove harpsichord tuners nuts. The "equal temperament" tuning, the reason Bach wrote his famous Well Tempered Clavier, a collection of Preludes and Fugues in every key, was a compromise which equalled out all the "commas" over the whole range of the keyboard. Bach wrote the 48, as these have become known, to prove that this method of tuning worked well for every single key.

Kes wrote the science bit.