4. Some fifths sharper instead of flatter than perfect; a condition that must be watched with vigilance.

5. Some or all of the strings tuned fall from the pitch at which they were left.

From a little reflection upon these causes, it is seen that the last trial may prove a correct fifth and yet the temperament be imperfect.

If this is the case, it will be necessary to go all over the temperament again. Generally, however, after you have had a little experience, you will find the trouble in one of the first two causes above, unless it be a piano wherein, the strings fall as in Cause 5.

This latter cause can be ascertained in cases only where you have started from a tuning pipe or fork. Sometimes you may find that the temperament may be corrected by the alteration of but two or three tones; so it is always well to stop and examine carefully before attempting the correction. A haphazard attempt might cause much extra work.

In temperament setting by our system, if the fifths are properly tempered and the octaves are left perfect, the other intervals will need no attention, and will be found beautifully correct when used in testing.

The mistuned or tempered intervals are as follows:--

INTERVALS FLATTENED. INTERVALS SHARPENED.

The Fifth, slightly. The Fourth, slightly.

The Minor Third, The Major Third, considerably. greatly.

The Minor Sixth, The Major Sixth, considerably. greatly.

~Tuning the Treble.~--In tuning the treble, which is always tuned by exact octaves, from their corresponding tones within the temperament, the ear will often accept an octave as true before its pitch has been sufficiently raised. Especially is this true in the upper octaves.

After tuning a string in the treble by its octave in the temperament, test it as a fifth. For instance, after tuning your first string beyond the temperament, 3C?, test it as a fifth to 2F?. If you are yet uncertain, try it as a major third in the chord of A. The beats will serve you as a guide in testing by fifths, up to about an octave and a half above the highest tone of the temperament; but beyond this point they become so rapid as to be only discernible as degrees of roughness. The beats will serve as a guide in tuning _octaves_ higher in the treble than the point at which the beats of the _fifth_ become unavailable; and in tuning _unisons_, the beats are discernible almost to the last tone.

The best method to follow in tuning the treble may be summed up as follows: Tune the first octave with the beats as guides both in the octave and in testing it by the fifth. If yet uncertain, test by chords. Above this octave, rely somewhat upon the beats in the octave, still use the fifth for testing, but listen for the pitch in the extreme upper tones and not so much for the beats except in bringing up unisons, in which the beats are more prominent.

In the extreme upper tones, the musical ear of the tuner is tried to the utmost. Here, his judgment of correct harmonic relation is the princ.i.p.al or only guide, while in the middle octaves the beats serve him so faithfully, his musical qualifications being brought into requisition only as a rough guide in determining pitch of the various intervals. To tune by the beats requires a sharp ear and mental discernment; to tune by pitch requires a fine musical ear and knowledge of the simpler laws of harmony.

As stated above, the tuner will fail in many cases to tune his high octaves sharp enough. Rarely, if ever, will a tuner with a good ear leave the upper tones too sharp. Now, there is one more fact which is of the utmost importance in tuning the treble: it is the fact that the extreme upper octave and a half must be tuned slightly sharper than perfect; if the octaves are tuned perfect, the upper tones of the instrument will sound flat when used in scale and arpeggio pa.s.sages covering a large portion of the key-board. Begin to sharpen your octaves slightly from about the seventeenth key from the last; counting both black and white. In other words, begin to sharpen from the last A? but one, in the standard scale of seven and a third octaves of which the last key is C. Sharpen but slightly, and increase the degree of sharpening but little as you proceed.

~Tuning the Ba.s.s.~--In tuning the ba.s.s, listen for the beats only, in bringing up the octaves. It is sometimes well to try the string tuned, with its fifth, but the octave in the ba.s.s should suffice, as the vibrations are so much slower here that if you listen acutely the octave beats will guide you.

It is not necessary to pull the strings higher than the pitch at which they are to stand. Learn to pull them up gradually and in a way that will "render" the string over the bridges, which is an easy thing to do, the strings being so much heavier here than elsewhere. Never leave a ba.s.s string the slightest amount too sharp. As flatness is so obnoxious in the treble, just so is sharpness in the ba.s.s, so if there must be any variation in any ba.s.s tone let it be flat; but aim at perfect octaves throughout the ba.s.s.

~False Waves.~--We say "false waves" for want of a better name. You will find a string occasionally that will give forth waves or beats so similar to the real ones that it takes a practiced ear to distinguish the difference. Where a unison contains a string of this kind, select some other string by which to tune the interval, and leave the bad string until the last; you may then find difficulty in being able to tell when you have it in unison. The cause may be a twisted string, a fault in the string by imperfect drawing of the wire, or in the construction of the sound-board.

In the low ba.s.s tones, a kind of false waves are always present, and will annoy the tuner long after he has been in regular practice. They are, however, of a different nature from the true waves in that they are of a metallic timbre and of much greater rapidity than the latter.

Close attention will generally enable the tuner to distinguish between them. They are caused by what is known as "harmonics" or "over-tones"; the string vibrating in fractional segments.

False waves will occur in an annoying degree when the tuner sets a mute on a nodal point in the string; it will cause the muted string to sound a real harmonic tone. This does not happen in the upright, as the mutes are set so near the end of the string as to preclude this possibility. In the square, however, it very frequently happens, as there are so many nodes between the dampers and the bridge, where the tuner sets his mutes. If, for instance, he is tuning an octave and has his mute set precisely in the middle of the vibrating segment, in place of muting the string it sounds its own octave, which will disturb the ear in listening for the tone from the one free string.

Move the mute either way until it is found to mute the string entirely.

QUESTIONS ON LESSON XIV.

1. Explain the cause of the beats.

2. How many _beats_ per second in a unison of two strings, one tuned to 100, the other to 101 vibrations per second?

3. How many beats per second in an octave, the lower tone of which is tuned to 100, the upper to 201 vibrations per second?

4. How many beats per second in a fifth, the fundamental of which is tuned to 100, the fifth to 151?

5. The fifth, 2F-3C, when properly tempered, should beat 1-3/4 times per second. How often should a fifth, an octave higher, beat?

LESSON XV.

~MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF TUNING, REGULATING, AND REPAIRING.~

~Comparison of the Different Systems.~--Up to this time, we have given no account of any system of tuning except the one recommended. For the purpose of making the student more thoroughly informed we detail here several different systems which have been devised and practiced by other tuners. It is a matter of history that artisans in this profession and leaders in musical science have endeavored to devise a system of temperament having all the desirable qualifications.

The aims of many have been to invent a system which uses the fewest number of tones; working under the impression that the fewer the tones used in the temperament, the easier the tuner's work. These have reduced the compa.s.s of the temperament to the twelve semi-tones from middle C to B above; or from F below, to E above middle C. This system requires the tuner to make use of both fourths and fifths. Not only does he have to use these two kinds of intervals in tuning, but he has to tune by fourths up and fourths down, and, likewise, by fifths up and fifths down. When tuning a fifth upward, he flattens it; and when tuning a fifth downward he sharpens the lower tone; when tuning a fourth upward, he sharpens it; when tuning a fourth downward, he flattens the lower tone.

It is readily seen that by a system of this kind the tuner's mind is constantly on a strain to know how to temper the interval he is tuning, and how much to temper it, as fourths require a different degree of tempering from the fifths; and he is constantly changing from an interval upward to one downward; so, this system must be stamped as tedious and complicated, to say the least. Yet this system is much followed in factories for rough tuning, and also by many old professional tuners.

The table on the following page gives the succession of intervals generally taken by tuners employing this system using the tones within the F octave mentioned above. Middle C is obtained in the usual way, from the tuning fork.

SYSTEM A.

By middle C tune F fifth below. Temper sharp.

By F " B? (A?) fourth above. " "

" C " G fourth below. " flat " G " D fifth above. " "

" D " A fourth below. " "

" A " E fifth above. " "

" E " B fourth below. " "

" B " F? fourth below. " "

" F? " C? fifth above. " "

" C? " G? fourth below. " "

" G? " D? fifth above. " "

Then try D? with A? previously tuned for "wolves."

We think a little study and trial of this system will produce the conviction that it is a very difficult and precarious one, and that it has every disadvantage but one, namely, that it uses the smallest possible number of tones, which is really of little value, and does not compensate for the difficulty encountered and the uncertainty of the results.

Another system which has many advantages over the above, is one which employs fifths only and covers a compa.s.s of an octave and a half. This system is similar to ours in that it employs fifths in the same succession as far as G?, the most of them, however, being an octave higher. From this G? there is a break in the succession, and the tuner goes back to middle C from which he started and tunes by fifths downward until he reaches the G? at which he left off. This system employs the tones from F below middle C to C, octave above. Below is the succession, starting upon 3C, whose pitch is determined as usual.

SYSTEM B.

By 3C tune 2C octave below.

" 2C " 2G fifth above.

" 2G " 1G octave below.

" 1G " 2D fifth above.

" 2D " 2A fifth above.

" 2A " 1A octave below.

" 1A " 2E fifth above.

" 2E " 2B fifth above.

" 2B " 1B octave below.

" 1B " 2F? fifth above.

" 2F? " 1F? octave below.