The Tromba Marina
A Study in Organology
1978 / 2002 by Dwight Newton
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CHAPTER THREE

ACOUSTICS

It seems odd to be describing the acoustical principles surrounding a sound that is rarely ever heard. Nevertheless, these principles are essential to understanding the existence of such an acoustical oddity as the tromba marina. The subject has been a favorite plaything for writers through the centuries.

The first principle to be dealt with is that of the equal divisions of the string. It has been well known since the time of Pythagoras that a string of a certain mass, when placed under a certain amount of tension, will yield a certain pitch. It is also known that, when caused to vibrate, this string simultaneously produces other pitches called "overtones" or "harmonics" which are equal to the perfect divisions of the whole, ie. 1/2, 1/3, 1/4, 1/5,..., theoretically to infinity. The intensity of the individual overtones varies according to the material used for the string, the type, force, and position of attack; the size, shape and mass of the amplifying resonant chamber; etc. In any case, while the open pitch (1/1) is so much louder than the over tones as seemingly to obscure them altogether, they are always present and in themselves determine the quality of tone in any musical instrument. This is how the ear can determine the difference between, say, a note played on a guitar and the same note played on a harpsichord.

The cause of the overtones lies in the fluid motion of the mass of the string. Because of this it is possible to touch the string at any of the points of equal division and effectively eliminate all of the overtones not equally divisible into that division. For example, if the exact center of the string is touched, the open tone (1/1) is eliminated as are all odd numbered shorter divisions (1/3, l/5, ....). This may best be illustrated as follows:

The points of division are called "nodal points". It can be seen that the 1/4 divisions, since they are equally divisible into 1/2, remain as overtones, while the 1/3 and 1/5 divisions are eliminated because the middle sections are damped by touching the string at the 1/2 node.

In listing the divisions of the string in order, each division in turn becomes the loudest tone resulting in what is called a harmonic progression or harmonic scale. Given a 200 cm open string tuned to A-110, the harmonic scale would go as follows:

Ratio

Frequency

Pitch

Cm node (distance from nut)

Cm Distance from adjacent node

1/1

110

A

200.00

0.00

1/2

220

A

100.00

100.00

1/3

330

E

66.67

33.33

1/4

440

A

50.00

16.67

1/5

550

C#

40.00

10.00

1/6

660

E

33.33

6.67

1/7

770

G

28.57

4.76

1/8

880

A

25.00

3.57

1/9

990

B

22.22

2.78

1/10

1100

C#

20.00

2.22

1/11

1210

D

18.18

1.82

1/12

1320

E

16.67

1.52

1/13

1430

F#

15.38

1.28

1/14

1540

G

14.29

1.10

1/15

1650

G#

13.33

0.95

1/16

1760

A

12.50

0.83

(Click to hear MP3 audio recording of this progression using a sine wave oscillator - 198k)

The tromba marina takes advantage of the fact that from 1/8 to 1/16 a major scale is available, though after about 1/12 the divisions come very close together, making them difficult to finger accurately, and they become progressively weaker. But this and the impracticality of playing in extremely high pitches, are the reasons for the usual great length of the monochord.

The inherent weakness of the high partials would make them virtually inaudible were it not for two factors; (1) the act of bowing imparts a great amount of continuous energy to the vibrating string, and (2) the trembling bridge of the tromba marina adds a percussive effect similar in principle to the snares on a drum, which tends to emphasize the vibration.

Another acoustical phenomenon commonly, though not always, employed on the tromba marina is that of sympathetic vibration. Additional strings that are not actually played are occasionally attached to an instrument in order to add a certain echoing quality to the tone. When a pitch is played corresponding to the pitch of the additional string or one of its overtones, that string will vibrate sympathetically with the played note and tend to reinforce it. The use of sympathetic strings at the time of the first development of the tromba marina, though only rarely employed, was certainly known. They are quite commonly used in the East, especially on such instruments as the Indian sitar and sarangi.

The fully developed tromba marina of the eighteenth century utilized all of these acoustical phenomena to the utmost degree. The instrument had an overall length upwards of seven feet, thereby allowing the nearest divisions of the string. The resonating body was large and rounded to give forth a full tone. The bridge was well designed and could be manipulated to strike the soundboard hard and clean. And it was often fitted with anywhere between eight and thirty (one example has fifty) sympathetic strings made of brass wire and tuned to the great monochord so that the divisions and their overtones would vibrate sympathetically with the overtones of the whole. It was this instrument that was given a place in the orchestras of Vivaldi, Cavalli, and of the Grande Ecurie of Louis XIV.

NOTES

1. The practicality of so limited a compass is discussed in various parts of "Performance Practice."

2. See for example the baryton and later the viola d'amore.