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Acoustics

A musical note is produced by a continued cibration of regular frequency. A complete vibration is a whole to and fro movement. Musical notes are measured in terms of vibrations per second. The pitch or frequency of a note is its number of complete vibrations per second.

If the frequencies of two notes bear the ratio 2:1 the former note will be found to be the octave note of the latter. This relationship is called dvigunatva. The octave notes bear the dvigunatva relationship.

In other words, if the pitch of a note, say like the madhya sthayi antara gandhara is equal to 300 vibrations per second, the pitch of the antara gandhara of the tarasthayl will be equal to 600 vibrations per second and so on.

A 9/8 interval is called a major tone and is a Chatussruti interval

A 10/9 interval is called a minor tone and is a tisruti interval

A 16/13 interval is called a semi tone and is a dvisruti interval

The chatussruti rishaba is a major tone above the shadja: 1 * 9/8 = 9/8; the antara gandhara is a minor tone above the chatussruti rishabha: 9/8 * 10/9 = 5/4; the suddha madhyama is a semi-tone above the antara gandhara: 5/4 * 16/15 = 4/3.

The major tone and the minor tone differ by an interval called comma 81/80 (pramana sruti) (9/8)/(10/9) = 81/80.

If a streched string like that of a tambura or a vina is plucked or bowed, the string vibrates as a whole. The amplitude of vibration is greatest at the centre, and this part of the string is called the antinode. The two ends on either side of the vibrating length of the string are at rest and are called the nodes: A node is place where there is no motion.

Every performer on a stringed instrument like the vina or the violin knows that:

When he plays on open strings, the entire length of the string vibrates.

When he stops a string by pressing his finger against the finger-board, he makes only a portion of its length ie., the length between the bridge and the finger to vibrate.

With the shortening of this vibrating length of the string, the pitch increases.

With the increase in the tension of the string, the pitch increases.

Also that thicker strings give notes of lesser pitch.

These truths are summed up in the following laws relating to the transverse vibration of strings:

The pitch of a string is inversely proportional to its length.

The pitch of a string is inversely proportional to its thickness.

The pitch of a string is directly proportional to the square root of its tension.

Thus in a stringed instrument, the three factors that affect and determine the pitch of a note are the length, tension and thickness of the streched string.

Inverse law and Direct law

Inverse law is a case, wherein of two factors, when one is increased, the other decreases in consequence.

Thus of the two factors, pitch and length of a streched string, when the vibrating length of the string is shortened, the pitch is increased and vice versa.

In the flute, the pitch is inversely proportional to its length of the vibrating column of air.

Thus when the vibrating column of air is lengthened by closing more finger-holes from the mouth hole end, the pitch is decreased and vice-versa.

In the mridangam, shorter the area of the drum-head, higher the pitch.

In the human voice, greater the length of the vocal cords, less the pitch. Men's voices are of a lower pitch compared to women's voices, because of the greater length of the vocal cords in men's voices.

Direct law is a case wherein of two factors, if one is increased, the other also increases.

Thus of the two factors, pitch and tension, when the tension is increased, the pitch also increases and vice versa.

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