## Scales

Scales are the foundations of music. It is a huge subject and there are many many different types of scale. But here we are just concerned with the basic definition of the kind of scales used in most popular western music.

An octave contains 13 notes each separated by a semitone... so 12 distinct notes. The Major Scale is defined as the 8 notes (including the octave) over these 12 notes such that they are separated by
intervals of a tone or a semitone as follows: Tone Tone Semitone Tone Tone Tone Semitone (ie TTSTTTS). So for C Major we have C D EF G A BC. This is an example of a
*diatonic* as it obeys the general rule that a diatonic scale must have five tone intervals and two semitone intervals that are separated. So that the
Major Scale is a specific example of this rule. It is of no real significance for us at the moment but the word 'diatonic' is often thrown into descriptions, so it
is good to be vaguely aware of what it means!

The Major scale is the basis of the other common scales. By changing some of the intervals we can arrive at the Minor scale and many other exotica.

TBD

### Intervals

### Chords

The basic chord is a triad consisting of the root, the 3rd and the 5th.### Equal Temperament

(need to move this) The formula for the frequencies of the notes of the Equal Tempered scale is just: fn = f0 * (a)n where

- f0 = the frequency of a single fixed note as a reference. This is usually the A above middle C (A4) at f0 = 440 Hz.
- n = the number of half steps away from the fixed note you are. If you are at a higher note, n is positive. If you are on a lower note, n is negative.
- fn = the frequency of the note n half steps away.
- a = (2)1/12 ie. the twelth root of 2 or the number which when multiplied by itself 12 times equals 2