Background to the musical scale

Music theory in Western music is a mixture of 'rules' with religious, psychological, traditional, and acoustical origins. The religious, psychological and traditional aspects have 'evolved' over the period of development of Western music. What has not changed -  what does not change -  are the natural laws of acoustical phenomena that lie at the foundation of the theory of harmony.

Roughly speaking, the Western musical scales used today are part of a line of 'evolution' that can be represented as:

It is within this line of evolution that arises the 12 note division of the octave we call the chromatic scale. Other cultural lineages have produced different divisions of the octave, for example, the 7 or 5 note divisions of the Pelog or Slendro scales used by the Javanese gamelan. In the West, the attempt to utilise divisions of the octave greater than 12, is not merely an avant garde or contemporary approach - this was explored during the renaissance, motivated by the desire to reproduce Justly Intoned musical intervals on fixed pitch instruments, i.e. fretted instruments (viols, lutes, and other members of the 'guitar' family) and keyboard instruments.

Pitch

It has been theorised that the use of 'musical intervals' by human beings arose from the natural behaviour of the human voice - because roughly 'musical' intervals occur naturally as a result of the different levels of vocal effort employed, in order to communicate at a distance. This would have happened in an early 'survival situation'. Roughly 'musical' intervals may also be associated with the vocal expression of emotion, which is also associated by some, with evolutionary development. 

Whether this is true or false, the aural starting point for the development of scales is the perception of musical pitch. A good deal of research has been done on pitch perception, and research continues. It is clear that the perception of pitch is much more dependent on subjective psychological factors and 'hidden' acoustical influences, than most listeners would probably guess. 

Our ability to accurately determine pitch depends to a large degree on the acoustical structure of the tone we are hearing - the acoustical 'elements' from which it is made, and their relationship to each other. This acoustical structure is usually constrained by natural laws governing the vibrational movement of the object producing the tone, but by using modern electronics, we could 'manufacture' any acoustical structure for an 'artificial' tone, and create pitch illusions.

The octave

The next steps towards the scale, after the general perception of musical pitch, are the perceptions of specific pitch, and the 'octave'.

The word 'octave' implies 8 notes, but the musical interval itself is not defined by any number of notes in any particular scale. It exists in it its own right simply as part of our aural perception, before we start making any analysis in terms of notes, numbers, wavelengths or frequencies. If we hear a note with a specific pitch, we can name that pitch, and apply that name for as long as we can recognise the pitch. The relationship between one note and another an 'octave' higher or lower, is so strong that in Western music and in other cultures too, both notes usually share the same name. For example, the relationship of identity between a note "A" and another note an octave above or below it in pitch, is such that we usually call this other note by the same name "A", even though it is of a different pitch.

There are many 'explanations' and theories for why this should be, perhaps the best known being the chroma or two component theory. Whatever the 'explanation', there is associated with this 'interval' that we now call the 'octave', an important  feature of natural phenomena . . .