Italian form of the word, Notturno, is employed by Mozart to denote a piece in three movements for strings in two horns (K. 286). It is also used by Mendelssohn for the title of the lovely entr'acte in the Midsummer Night's Dream Music, which represents the sleep of the lovers. More recently the name has been used to cover a multitude of sins in more than one branch of art.
[ J. A. F. M. ]
NOCTURNS (Lat. Nocturni, Nocturnæ Orationes. The Night Hours). Portions of the Office of Matins, consisting of Psalms, Antiphons, and Lessons, of which three divisions are usually sung, on Sundays and Festivals, and one only on Ferial Days. [See Matins.]
[ W. S. R. ]
NODE (Latin nodus, a knot). The vibration of a string may assume many different forms. In Fig. 1 the string is shewn vibrating as a whole; in Fig. 2 it divides into two equal segments; in Fig. 3 into three equal segments. These segments, where the amplitude of vibration is greatest, are called Loops (l, Figs. 2 and 3), and the points of rest between them are called Nodes (n).
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But when a string is plucked, as in the harp and guitar, or bowed as in the violin, it does not vibrate in any one of the simple forms just described, but in several of them at once. The motion of the whole string combined with that of its halves would be represented by Fig. 4. Here the node is no longer a point of complete rest but a point where the amplitude of vibration is least.
If the string while vibrating be touched at ½, ⅓, ¼, etc. of its length, as in playing harmonics on the harp or violin, all forms of vibration which have loops at these points vanish, and all forms which have nodes there become more marked. Thus it is possible to damp the vibrations of the whole string, of its third parts, of its fifth parts, etc., leaving the vibrations of its halves, of its fourth parts, of its sixth parts, etc., unimpeded.
The column of air in an open pipe vibrating as a whole has a node in the centre, towards which the particles of air press and from which they again draw back (see Fig. 5, n).
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Thus at the node the air does not move but undergoes the greatest changes of density. At the loop (l) there is no change of density but great amplitude of vibration. The open ends of the pipe are always loops, for the density at these points being the same as that of the outer air, does not change. This remains true whether the pipe have two, three, or more nodes, as shewn in Figs. 6 and 7.
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In a stopped pipe the closed end is always a node, and the open end a loop, whether the column of air vibrate as a whole (see Fig. 8), or divide into segments as shown in Figs 9 and 10.
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In practice both an open and a stopped pipe vibrate not in any one of the ways just described, but in several of them at once. Here, too, as in the case of strings, the node is not a point of complete rest but of least motion.
Chladni showed that sand strewn on vibrating plates or membranes collects along the lines where the motion is least. These are called nodal lines, and may assume a variety of symmetric forms.
[ J. L. ]
NODUS SALOMONIS (Solomon's knot). A celebrated Canon, composed by Pietro Valentini, and described by Fr. Kircher, in his Musurgia. It was originally intended to be sung by ninety-six Voices, disposed in twenty-four Choirs: but Kircher afterward ascertained, that, provided the distribution into four-part Choirs was properly carried out, the number of Voices might be increased to five hundred and twelve, or even to twelve millions two hundred thousand. The Guida—in which four notes only are used—stands as follows:—
The First Choir leads; the Bass and Tenor entering together; the former, with the Guida, and the latter, with its Inversion, beginning on the Twelfth above. After a Semibreve Rest, the Alto sings the Guida, and the Treble its Inversion in the Twelfth above, both beginning together, as before. All the other Choirs enter in the same way, each pair of voices beginning one Semibreve later than the preceding pair. But, when the
