Some science behind the scenes

Chromatic scale

The chromatic scale is a musical scale with twelve pitches, each a semitone or half step apart. A chromatic scale is a nondiatonic scale consisting entirely of half-step intervals having no tonic due to the symmetry of its equally spaced tones.

The most common conception of the chromatic scale before equal temperament was the Pythagorean chromatic scale, which is essentially a series of eleven 3:2 perfect fifths. The twelve-tone equally tempered scale tempers, or modifies, the Pythagorean chromatic scale by lowering each fifth slightly less than two cents, thus eliminating the Pythagorean comma of approximately 23.5 cents. Various other temperaments have also been proposed and implemented.

The term chromatic derives from the Greek word chroma, meaning colour. A rainbow of notes.

 

This is Your Brain on Music – Professor Daniel Levitin
The twelve notes in our musical system are called the chromatic scale. Any scale is simply a set of musical pitches that have been chosen to be distinguishable from each other and to be used as the basis for constructing melodies…..

 In any Major scale, the pattern of intervals – pitch distances between successive keys is: whole step, whole step, half step, whole step whole step, whole step, half step [the major 7 keys as opposed to all the minor keys as well].

The specific frequencies for notes may be arbitrary, but the distance from one frequency to the next – and hence from one note to the next in our musical system – isn’t at all arbitrary. Each note in our musical system is equally spaced to our ears (but not necessarily to the ears of other species).

Although there is not an equal change in cycles per second (Hz) as we climb from one note to the next, the distance between each note in our system is approximately 6 per cent more than the one before it. Our auditory system is sensitive both to relative changes and to proportional changes in sound. Thus each increase in frequency of 6 per cent gives us the impression that we have increased pitch by the same amount as we did last time.

[In the twelve note musical scale] Every tone is 6 per cent higher than the previous one and when we increase each step by 6 per cent twelve times, we end up having doubled our original frequency

The Indian system is similar. In any seven-tone mode (starting with S), R, G, D, and N can be natural (shuddha, lit. 'pure') or flat (komal, 'soft') but never sharp, and the M can be natural or sharp (tivra) but never flat, making twelve notes as in the Western chromatic scale. If a swara is not natural (shuddha), a line below a letter indicates that it is flat (komal) and an acute accent above indicates that it is sharp (tivra or tivar). R, G, D, and N may be either shuddha or komal; M may be either shuddha or tivra. Sa and Pa are immovable (once Sa is selected), forming a just perfect fifth.