, in Music, a half tone or half note, one of the degrees or intervals of concords.

There are three degrees, or less intervals, by which a sound can move upwards and downwards, successively from one extreme of any concord to the other, and yet produce true melody. These degrees are the greater tone, the less tone, and the semitone. The ratios defining these intervals are these, viz, the greater tone 8 to 9, the less tone 9 to 10, and the Semitone 15 to 16. Its compass is 5 commas, and it has its name from being nearly half a whole, though it is really somewhat more.

There are several species of Semitones; but those that usually occur in practice are of two kinds, distinguished by the addition of greater and less. The first is expressed by the ratio of 16 to 15, or 16/15; and the second by 25 to 24, or 25/24. The octave contains 10 Semitones major, and 2 dieses, nearly, or 17 Semitones minor, nearly; for the measure of the octave

being expressed by the logarithm1,00000,
the Semitone major will be measured by0,09311,
and the Semitone minor by0,05889.
These two differ by a whole enharmonic diesis; which is an interval practicable by the voice. It was much in use among the Ancients, and is not unknown among modern practitioners. Euler Tent. Nov. Theor. Mus. pa. 107. See Interval.

These Semitones are called fictitious notes; and, with respect to the natural ones, they are expressed by characters called slats and sharps. The use of them is to remedy the defects of instruments, which, having their sounds fixed, cannot always be made to answer to the diatonic scale. By means of these, we have a new kind of scale, called the

SEMITONIC Scale, or the Scale of Semitones, which is a scale or system of music, consisting of 12 degrees, or 13 notes, in the octave, being an improvement on the natural or diatonic scale, by inserting between each two notes of it, another note, which divides the interval or tone into two unequal parts, called Semitones.

The use of this scale is for instruments that have fixed sounds, as the organ, harpsichord, &c, which are exceedingly defective on the foot of the natural or diatonic scale. For the degrees of the scale being unequal, from every note to its octave there is a different order of degrees; so that from any note we cannot find every interval in a series of fixed sounds; which yet is necessary, that all the notes of a piece of music, carried through several keys, may be found in their just tune, or that the same song may be begun indifferently at any note, as may be necessary for accommodating some instrument to others, or to the voice, when they are to accompany each other in unison.

The diatonic scale, beginning at the lowest note, being first settled on an instrument, and the notes of it distinguished by their names a, b, c, d, e, f, g; the inserted notes, or Semitones, are called fictitious notes, and take the name or letter below with a , as c called c sharp; signifying that it is a semitone higher than the sound of c in the natural series; or this mark , called a flat, with the name of the note above signifying it to be a Semitone lower.

Now 15/16 and 128/135 being the two Semitones the greater tone is divided into, and 15/16 and 24/25, the Semitones the less tone is divided into, the whole octave will stand as in the following scheme, where the ratios of each term to the next are written fraction-wise between them below.

Scale of Semitones.
for the names of the intervals in this scale, it may be considered, that as the notes added to the natural scale are not designed to alter the species of melody, but leave it still diatonic, and only correct certain defects arising from something foreign to the office of the scale of music, viz, the sixing and limiting the sounds; we see the reason why the names of the natural scale are continued, only making a distinction of each into a greater and less. Thus an interval of one Semitone, is called a less second; of two Semitones, a greater second; of three Semitones, a less third; of four, a greater third, &c.

A second kind of Semitonie scale we have from another division of the octave into Semitones, which is performed by taking an harmonical mean between the extremes of the greater and less tone of the natural scale, which divides it into two Semitones nearly equal. Thus, the greater tone 8 to 9 is divided into two Semitones, which are 16 to 17, and 17 to 18; where 16, 17, 18, is an arithmetical division, the numbers representing the lengths of the chords; but if they represent the vibration, the lengths of the chords are reciprocal; viz as 1, 16/17, 8/9; which puts the greater Se- | mitone 16/17 next the lower part of the tone, and the lesser 17/18 next the upper, which is the property of the harmonical division. And after the same manner the less tone 9 to 10 is divided into two Semitones, 18 to 19, and 19 to 20; and the whole octave stands thus:


This scale, Mr. Salmon tells us, in the Philosophical Transactions, he made an experiment of before the Royal Society, on chords, exactly in these proportions, which yielded a perfect concert with other instruments, touched by the best hands. Mr. Malcolm adds, that, having calculated the ratios of them, for his own satisfaction, he found more of them false than in the preceding scale, but then their errors were considerably less, which made amends. Malcolm's Music, chap. 10. § 2.

SENSIBLE Horizon, or Point, or Quality, &c. See the substantives.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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