WESTERN MUSIC...

Let us examine the frequency aspect of music first. This is perhaps the most studied aspect as well. We mentioned that all music is produced in the audible frequency range, a range which varies from person to person. Although human ears cannot tell very high 'tones', musical instruments can produce frequencies (overtones) even beyond the threshold of human hearing. Music is sometimes described technically as 'tonal' or 'chromatic', both terms simply mean that we use a whole spectrum of frequencies to produce music.
The audible range is divided into 'octaves'. An octave is really a frequency range from a frequency f1 to f2 such that f2 is twice that of f1 in terms of cycles or hertz. For some physiological reason, the human ear is logarithmic and is sensitive to frequency octaves. The audible frequency is then comprised of many, many octaves. We can choose any number to be our f1 (and f2 of course is 2 times f1) - we can define an octave from 10 Hz to 20 Hz or equally well another one, say from 15 Hz to 30 Hz.
In terms of sound production, a typical human voice can produce several frequencies, although it is usually limited to about three or four octaves - even if we have a drum-like, groggy 'morning voice' at the low end of the range and a shrill, ear-piercing shriek at the high end. Only the exceptionally gifted people can produce a wide spectrum of vocal sounds spanning several octaves. (Of course, there are those female Indian movie playback singers who can produce ultra high frequencies which only dogs can hear clearly !) By the way, here we are only talking about 'primary' frequencies and not overtones associated with the 'quality' of our voices - remember, overtones are higher frequency components, but produced in much lower intensities.
A piano or a keyboard is a typical Western musical instrument. All we see is a bunch of keys, some in black and some in white. However, upon a closer look, we see that there is a periodicity. As we go from the left of the keyboard to the right (and here I am assuming you know how to sit in front of a keyboard) the keys produce higher and higher frequencies. In fact, the key frequencies are arranged in such a manner that they are in a geometric series. That is, the frequency between any key and the key immediately to its left (irrespective of the color of the key) is a constant, the constant being equal to the twelfth root of two or 1.059. For example, typically, there is a white key in the keyboard set to 240 Hz. Then the adjacent key on the right, a black one as a matter of fact, is set to 240 X 1.059 = 254 Hertz.
By the specific choice of this ratio (twelfth root of two) we see that by the time we reached the thirteenth key, we have doubled our frequency and thus spanned a whole octave. In fact, if you look at the keyboard you see that the key pattern repeats every twelve keys. If you chose the white key at 240 Hz, then the thirteenth key will be at 480 Hz and your octave ranged from 240 to 480 Hz. Equally well, you could have started counting from the black key at 254 Hz and twelve keys later you would have still spanned an octave, except that this time your octave ranged from 254 to 508 Hz.
This division of the octave into twelve 'tones' which have specific ratio between adjacent keys (the ratio equalling 1.059) is peculiar to Western music. This geometric arrangement of frequencies of the keys in an octave is called an 'Equally tempered' arrangement. And besides the keyboard, most Western musical instruments are also tuned to such an arrangement.
Even though there is a degree of freedom about what you want to be the range of an octave (whether it is from 240 to 480 Hz or 254 to 508 Hz etc.) the Western music defines a standard octave called the 'Middle C octave' (also called the Middle C scale etc) starting from the white key set to 240 Hz. The entire octave (the twelve key pattern, that is) is shown in Fig. 1. On your keyboard, this octave is located somewhere near the middle. Once you figured out where this octave is, you can quickly identify the first key of this octave (set to 240 Hz). And because we know the ratio of the key frequencies now we can pretty much compute the frequency generated by ANY key. You will also notice that the keyboard has about three to four octaves (between 36 to 48 keys, depending on how much you paid for it) The upper octave, starting from 480 Hz is the Upper C octave and the lower octave starting at 120 Hz is the Lower C octave etc.