| The ratio 3:2 signifies
that the second harmonic of the higher frequency tone coincides the third
harmonic of the lower frequency tone and such a relationship is very easily detected by the human ear. Two
tones related through a ratio 91:85 are not perceived as being very harmonious because the
common harmonics are the 91st and 85th. Such high harmonics typically have very low
intensity and may even be beyond the frequency range of the human ear.
The principle of integral ratios is
inherent in our perception of sound. A tune is identified by the ratio of
frequencies that appear in succession to produce it and only special training develops the
ability to perceive the absolute pitch (frequency) of sounds. Next we
observe that there are a total of twelve keys in the repeating pattern
(or twelve swara sthanas in an octave).
This division of an octave
into twelve swara sthanas has evolved over a period of millennia. This is
evident from the fact that while some ancient forms of music use fewer swara sthanas, the current
forms of many styles of classical music which evolved independently (including Western, Hindustani and
Carnatic) use only twelve swara sthanas to an octave.
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