Scan 72
Grove's dictionary of music and musicians: ed. by J. A. Fuller …, Volume 5, 1910
12 lines. Read by computer on 3 September 2026. Printed page 54. See the scan on archive.org.
1Beats, the tuning is then called Just Intonation.
3When a piece of music containing much change of key is executed in just intonation, we find that the number of notes employed in each Octave is considerable, and that the difference of pitch between them is, in many cases, comparatively minute. Yet, however great the number of notes may be, and however small the intervals which separate them, all these notes can be correctly produced by the voice; as they may be derived from a few elementary intervals, namely the Octave, Fifth, Major Third, and Harmonic Seventh.1 Instruments like the violin and the trombone are also suitable for the employment of just intonation; because, in these cases, the player can modify the pitch of each note at pleasure, being guided by his sense of key-relation. But it is otherwise with instruments whose tones are fixed, such as the pianoforte, organ, and harmonium. Here the precise pitch of each note does not depend on the player, but is settled for him beforehand by the tuner. Hence, in these instruments, the number of notes per Octave is limited, and cannot furnish all the varieties of pitch required in just intonation. A few scales may, indeed, be tuned perfectly; but if so, certain notes which belong to other scales will be missing. Compromise then becomes a mechanical necessity; and it is found that by putting most of the consonant intervals, except the Octave, slightly out of tune, the number of notes required in modulation may be considerably reduced, without too much offence to the ear. This mode of tuning is called TEMPERAMENT, and is now usually applied to all instruments with fixed tones. And although voices, violins, and trombones naturally have no need of temperament, they must all conform to the intonation of any tempered instrument which is played in concert with them.
5We shall omit from the present article all reference to the arithmetical treatment of temperament, and simply deal with its physical and audible effects. We shall describe the means by which any student may obtain for himself a practical knowledge of the subject, and point out some of the conclusions to which such knowledge will probably lead him.2 The first and most important thing is to learn by experience the effect of temperament on the quality of musical chords. To carry out this study properly it is necessary to have an instrument which is capable of producing all the combinations of notes used in harmony, of sustaining the sound as long as may be desired, and of distinguishing clearly between just and tempered intonation. These conditions are not fulfilled by the pianoforte; for, owing to the soft quality of its tones, and the quickness with which they die away, it does not make the effects of temperament acutely felt. The organ is more useful for the purpose, since its full and sustained tones, especially in the reed stops, enable the ear to perceive differences of tuning with greater facility. The harmonium is superior even to the organ for illustrating errors of intonation, being less troublesome to tune and less liable to alter in pitch from variation of temperature or lapse of time:
7By playing a few chords on an ordinary harmonium and listening carefully to the effect, the student will perceive that in the usual mode of tuning, called Equal Temperament, only one consonant interval has a smooth and continuous sound, namely the Octave. All the others are interrupted by beats, that is to say, by regularly recurring throbs or pulsations, which mark the deviation from exact consonance. For example, the Fifth and Fourth, as at (x), are each made to give about one beat per second. This error is so slight as to be hardly worth notice, but in the Thirds and Sixths the case is very different. The Major Third, as at (y), gives nearly twelve beats per second: these are rather strong and distinct, and become still harsher if the interval is extended to a Tenth or a Seventeenth. The Major Sixth, as at (z), gives about ten beats per second, which are so violent, that this interval in its tempered form barely escapes being reckoned as a dissonance.
9The Difference-Tones resulting from these tempered chords are also thrown very much out of tune, and, even when too far apart to beat, still produce a disagreeable effect, especially on the organ and the harmonium. [RESULTANT TONES.] The degree of harshness arising from this source varies with the distribution of the notes; the worst results being produced by chords of the following types —
11By playing these examples, the student will obtain some idea of the alteration which chords undergo in equal temperament. To understand it thoroughly, he should try the following simple experiment. 'Take an ordinary harmonium and tune two chords perfect on it. One is scarcely enough for comparison. To tune the triad of C major, first raise the G a very little, by scraping the end of the reed, till
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