higher in frequency than the one below. As a part of this definition of
the pitches used to make music, certain intervals were defined. In particular in
the so called major scale, the sequence of intervals TTSTTTS (T=tone,
S=semi-tone) were used to define the various intervals of the musical scale.
The note a tone above the base of the scale (the Do, in the Do-Re-Me
nomenclature) is called the major second, the one two tones above the major
third, the one two tones plus a semi-tone (or 5 semi-tones) is the perfect fourth,
the one 7 semi-tones above is the perfect fifth, etc. But this "explanation" or
rather description of the scale gives one very little idea of why in the world
musicians would have hit on this slightly weird division of the pitches.
In order to get some feeling for why the scale was organized in this way, we will make use of some physical features of any sounds, especially continuous sounds, which make up the experience we call a pitch. A note with a definite pitch tends to be a sound with a definite repetition in time, a definite period. However such notes are almost never pure sinusoids- they have a more or less complex shape when one views the pressure distribution in the note as a function of time. We have learned that such a complex distribution of pressure can always be represented by a sum of pure sinusoidal sounds, a fundamental, which has the same fundamental period as the sound, and its various harmonics (frequencies which are integer multiples of that fundamental frequency).
One of the most astonishing feature of human hearing is that that huge set of disparate frequencies ( and we know that those different frequencies excite different parts of the basilar membrane, and send signals down different nerves to the brain- almost as if the ear were doing a Fourier analysis of the sound, and reporting to the brain about each of the separate sinusoidal frequencies that make up the complex sound) are experienced by us as a single pitch. Those separate components are amalgamated in the brain as a single pitch, with the different amplitudes changing the "tone-colour" of the note, but not the pitch or the unity of the experience of that sound. Ie, it seems that the brain tried to amalgamate frequencies which are integer multiples of each other into a single sound experience.