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Musical Principles
Resonance
A given body is a made to vibrate with a frequency, which may (or may not) be different from its natural frequency. This can be done by imposing the vibrating energy from some vibrating body to the given body. This case of vibrations is called as Forced Vibrations.
If it so happens that the frequency of the two bodies match, when one body begins to vibrate the other starts vibrating automatically and the amplitude of the vibrations become large. The result is that the intensity of sound heard increases considerably. This phenomenon is called as ‘Resonance’.
Thus, we can say that Resonance is a particular case of Forced Vibrations where the two frequencies are equal.
This phenomenon is used in instruments like sitar, santoor to get richer tonal quality. The sitar has strings called as ‘taraf’ strings placed under the main strings to be played. They are tuned to the notes of the particular raagas to be played. When the note is played on the main string the ‘taraf’ string of that particular frequency starts vibrating automatically giving a richer quality of sound.
The basic principles of Sound and Music therapy are 'Forced Vibrations' and 'Resonance'.
Beats
Let A and B be two bodies giving sound notes of unequal frequencies n1 and n2 respectively. When either A or B is struck we hear sound note of that particular frequency i.e. n1 or n2. The intensity remains constant and then fades smoothly.
If now, both A and B are struck simultaneously or just one after the other the resulting sound that we hear is not of the same and smooth intensity. It is observed that its intensity goes on increasing and decreasing, alternately. This happens for a definite number of times. This waxing and waning of sound is known as the phenomenon of beats.
From one waxing to the next waxing is one beat. The number of beats heard per. sec. = the difference between the two frequencies.
Human ear is able to hear these beats when the number is less than 10. This principle of beats is used in tuning string instruments.
Harmonics and their significance
A pure note can be represented by a sine curve. It has no musical significance. Except the sound produced by a tuning fork (pure tone) all other sounds are complex. A pure note consists of only one fundamental frequency. Whereas a complex note consists along with the fundamental frequency, a number of other frequencies which are integral multiples of the fundamental. These are called as Harmonics.
The harmonic content of any particular sounding body has its own particular pattern. Every harmonic has its own significance and contribution. The intensity of every harmonic differs. So also the distance between the sounding of every harmonic differs. Or in other words the tempo of the harmonic content also differs. It is the content of these harmonics and their relative intensity which gives a particular quality to a sound. The harmonic content of a sound decides its musical significance. The relative intensity of harmonics in a good, musical voice is under control. When the harmonic pattern remains constant and regular the sound is termed as musical. On the other hand when there is no repetition it, the pattern of harmonics and their relative intensities and it constantly keeps on changing the sound is termed as noise. Graphically pure tone, musical tone and noise can be shown (approx.) like this:
Pure tone
Musical tone
Noise tone
The ups and downs in the curves represent the harmonic content of the sound.
Difference in the harmonic production when the same note is produced on 1) flute 2) Bansuri 3) Sarangi 4) Sitar and 5) Tabla.
The method of initiating sound of a musical instrument plays a major role on the quality of the sound, content of harmonics and its audibility.
Blowing: In the flute the sound is generated by blowing. A flute is open at one end and closed at the other by a reed or a mouthpiece used for blowing. The air column inside the flute is made to vibrate to produce sound. The pitch is controlled by changing the length of the holes. In a flute only the odd numbers of harmonics are generated i.e. the 1st, 3rd, 5th and so on. The even number of harmonics is missing.
In a bansuri, which is also a type of flute, but with a difference, sound is generated by blowing. Whereas a flute is open only at one end, a bansuri is open at both the ends, this being the specialty of the instrument. This difference enhances the tonal quality, making it richer. In the beginning the odd harmonics are produced but along with it the even harmonics, which the flute lacks are produced.
Bowing: In a Sarangi the sound is initiated by bowing. Bowing helps to produce a large number of harmonics. Bowing faster helps to control the harmonics or the overtones, which are not pleasant. Slower bowing need skill to control the harmonics.
Plucking: In a Sitar the sound is generated by plucking. Compared to the bowing in Sarangi the plucking in sitar produces fewer harmonics. But, still the number of harmonics is good enough to give it a favourable acoustical value. To produce the maximum number of harmonics and to make them stay longer (or fade slowly) a small area should be plucked. In a sitar, the plucking is done by a ‘mijrab’ and not by hand for this reason.
Thomas Young had discovered that when a string, 100 cms. long, is plucked at a distance 100/n the harmonic numbering ‘n’ will be missing. This is called as the Thomas Young rule. He also stated that it is better to pluck at the length of 1/5 or 1/6 of the total length. To overcome this missing harmonic the bridge of the Sitar is specially designed with a curve of a parabola. Also we make use of the ‘jawhari’ to control the harmonics.
Striking: In the drum family of musical instruments, sound is produced by striking.eg. tabla, dholak, etc. Other instruments like the Santoor, Jaltarang, Piano, etc. also come under this category. Here, many harmonics are produces. But, along with it many inharmonics and unwanted overtones are also produced. To overcome these unwanted frequencies or control these frequencies, is the job of a good craftsman. It is a skilled job. Acoustically, striking is the least qualitative method of producing sound.
Musical Intervals
The ratio of the frequencies between the notes of an octave is called as musical intervals. The frequency of C = 240 and D = 288 since the musical interval between D and C = 288/240 = 9/8.
The musical intervals have been given particular names. The musical interval of 9/8 is called as major tone, 10/9 is called as minor tone and 16/15 as semitone.
To get the ratios or intervals between C and E of an octave multiply D/C = 9/8 and E/D = 10/9. Similarly to get the musical interval of C and C’ we multiply all the ratios of the octave to get 2:1.
If the interval gives a pleasing effect it is called as a consonant interval.
The simpler the ratio or the interval, more is the pleasing effect.
|
Intervals |
Notes |
Hindustani equivalent notes |
Name |
|
2:1 |
C’ : C |
Sa(octave): Sa |
Octave |
|
3:2 |
G : C |
Pa: Sa |
Fifth |
|
4:3 |
F : C |
Ma: Sa |
Forth |
|
5:4 |
E : C |
Ga: Sa |
Major Third |
|
6:5 |
E flat : C |
Ga (komal): Sa |
Minor Third |
We can observe that as the intervals become more complex, the pleasing effect goes on lessening.