" 1F? " 2C? fifth above.

" 2C? " 2G? fifth above.

" 2G? " 1G? octave below.

By 2C tune 1F fifth below. Temper sharp.

" 1F " 2F octave above.

" 2F " 1B? fifth below. Temper sharp.

" 1B? " 2B? octave above.

" 2B? " 2E? fifth below. Temper sharp.

Now by 2E? try 1A? (G?) fifth below for the "wolf."

Note that this last trial brings you back to the last tone tuned before the break.

This system is used by a great number of very successful tuners, and it has but one appreciable disadvantage, which is that involved in changing from fifths upward to fifths downward. This difficulty is easily overcome, if it were all there is to encounter; but in practice, we find that after tuning the intervals in the above succession down to the last step in the first series, middle C will often have changed pitch somewhat, and the last five tones with their octaves tuned from it will not be in true harmony with the intervals tuned in the first series. For this reason it is better to go on through, as in our system, tuning by fifths upward, and if there is any change of pitch in the first tones tuned, they may be more easily corrected by going over them in the same way as at the start; also, the amount of difficulty in locating discrepancies is greatly lessened.

SYSTEM C.

The following system is one that is followed by many good tuners of the present day and has many advantages. To use this system successfully, however, one must be familiar with the number of beats necessary in each interval used.

Take 1F as a standard.

By 1F, tune 2C, fifth above.

By 1F, tune 1B?, fourth above.

By 1F, tune 1A, major third above.

By 1F, tune 2D, sixth above.

By 1F, tune 1A?, minor third above.

By 1F, tune 2F, octave above.

By 2C or 2D, tune 1G, fourth or fifth below.

By 1G, 1A or 2C, tune 2E, sixth, fifth or third above.

By 1G or 2E, tune 1B, third above or fourth below.

By 1A or A?, tune 2C?, major or minor third above.

By 1A?, 1B? or 1B, tune 2E?, fifth, fourth or major third above.

By 1B?, 1B, 2C? or 2E?, tune 1F?, major third, fourth, fifth or sixth below.

As each step is taken in this system, the tone tuned is tested with any or all of the tones previously tuned.

You will notice that six tones are tuned by the first standard, F.

Therefore, if any error is left in any one of the intervals it exists in this only and is not transmitted to other tones, if corrected before such other tones are used to tune by.

The numerous tests possible, early in the system, and the small compa.s.s used, one octave, may be said to be the chief advantages of the system.

The intervals used are the minor and major third, perfect fourth and fifth, and major sixth. The thirds and sixths beat from about 7 to nearly 12 per second. The exact number of beats for each step in the system may be calculated from the "Table of Vibration Numbers" in Lesson XIII. For instance, take middle C (2C) at 256, and its major third, 2E. The exact third, determined by multiplying 256 by 5/4, is found to be 320. By reference to the table, we find the tempered third vibrates 322.54. The difference then is 2.54 vibrations per second, and, knowing that a difference of one vibration from the exact major third produces 4 beats, we simply multiply 2.54 by 4 and we have 10.16, the number of beats we should hear per second when this third is tempered correctly. Other intervals may be figured out in like manner by reference to the various tables given.

It is very doubtful if a beginner could succeed with this system. He should tune by an easier system until he can hear the beats very distinctly and judge quite accurately the rapidity of them. Having acquired this ability, he may try this system and follow it in preference to others.

In any system used it is well to test your work in the following manner:

Begin with your lowest major third and strike each third in succession, ascending chromatically. Of course, each third should beat slightly faster than the one below it. For instance, in our system of two octaves, take 1C-E; this third should beat about 5 per second.

Next, take 1C?-F, which should beat about 5-1/2 per second. The beats should increase each test nearly a half beat, or the amount of 5 beats in this octave; hence, 2C-E will beat about 10 per second; or, using the exact figures, 10.16. After arriving at the last-named test, 2C-E, you may test the remainder of the two octaves by tenths, beginning with 1C-2E. The tenth is similar to the third mathematically, and its beats are even more distinct.

We may remark here that our system may be reduced to the compa.s.s of an octave and a half by simply not tuning the octaves upward which reach beyond 2F?; and if anything were to be gained and nothing lost by shortening the compa.s.s of the temperament, we would advise using only the octave and a half. But in many years of experience in tuning all imaginable types, styles and kinds of pianos, and by all systems, we have found good reasons for adopting the two-octave temperament as laid down in Lesson VIII, for universal application. Its advantages may be summed up as follows:

~Simplicity.~--But two kinds of intervals are employed: the fifth and the octave. The fifth is always tuned to a fundamental below and hence always flattened, which relieves the tuner of any mental operation to determine which way he is to temper. Being a regular succession of fifths and octaves, without a break, the system is easily learned, and can be followed with little mental strain.

~Uniformity.~--After the tuner has become well trained in tempering his fifths, there is little danger of an uneven temperament, as the various intervals used in trials will prove a false member in some chord in time to correct it before he has gotten so far from it as to make the correction difficult. When a correction is necessary, the offending point is most easily found.

~Precision.~--In our experience, we have never known another system by which we could attain the absolute precision gained by this.

~Stability.~--Stability is the feature wherein rests the paramount reason for employing two octaves. From what has been said in previous lessons concerning the liability of some strings to flatten or sharpen by reason of altering the tension of other strings, the student will readily see that the temperament should cover a sufficient portion of the instrument, if possible, to insure that it will stand while the remaining portion is being tuned. Our two octaves cover nearly all the strings between the over-strung ba.s.s and the brace in the metal plate.

This being the case, any reasonable alteration of the strings beyond, or outside, the braces from the temperament, will rarely, if ever, affect it noticeably.

~Final Inspection.~--Always test every key on the piano, or especially those of the middle five octaves, for bad unisons. Upon finding one, search for the string that has stood in tune, by testing each string of the unison with its octave. This being done, simply bring the other to it. Go over the whole key-board, striking octaves, and correct any that might offend. One extremely bad tone or octave may disparage your reputation, when in reality your work merits commendation.

~Loose Pins.~--You will occasionally find pianos in which the tuning pins have become so loose that they will not resist the pull of the strings. If many of them are in this condition it is better, before you begin to tune, to take a hammer of considerable weight and drive them a little. Commence at one end of the row of pins and aim to strike all the pins with the same force. Those which are tight enough will not yield to the blow, while those which are loose may require two or three blows to tighten them sufficiently. This defect is generally found in very old squares or cheap uprights wherein the pin-block is of poor material or defective in manufacture or in pianos which have been abused.

~Split Bridges.~--Even in pianos of the highest grade, we sometimes find a string sounding as if there was a pin or some metallic substance bearing against it. In such cases, find the string and examine the place where it crosses the bridge. You will often find the bridge split at that point or the bridge-pin, having yielded to the pressure of the string, vibrates against the next pin, giving rise to the singing effect. You can do little if anything toward repairing a split bridge. You may, however, stop the singing by inserting the point of your screw-driver between the close pins and pressing them apart. This will generally stop the difficulty for the time being at least.

Strings crossing the bridge near a split will not stand in tune well, and will, perhaps, have to be gone over two or three times. The same may be said of a broken metal plate. Many old squares have broken plates; generally found near the overstrung ba.s.s, or within the first octave of the treble. All the tuner can do is to apprise the owner of the defect and inform her that it will not stand well at this point, as the intense strain is thrown largely upon the wooden frame, which will have a tendency to yield gradually to it.

~Stringing.~--Strings break while the tuner is drawing them up, sometimes because he does not pull them gradually, gives them an abrupt turn or draws them too far above the pitch at which they are intended to stand. More often, however, they break from being rusty at the point where they pa.s.s over the bridge or around the tuning pin.

The best instruction concerning putting on new strings is, follow appearances. Make the string you put on look just like those on the instrument. In most modern pianos the string is wound with three coils around the pin.

You will, of course, have to take out the action; not the key-board, however, unless it be one of those rare cases where the key-board and upper action are built to come out together. In the square it is only necessary to remove the shade over the dampers, and the dampers, which are all removed easily by taking out the screw at the left. This allows the whole set of dampers with their support to come out together.

Treble strings are nearly always pa.s.sed around the hitch-pin, one wire thus forming two strings. Take out the old string, noticing how it pa.s.ses over and under the felt at the dead end. After removing the string always give the pin about three turns backward to draw it out sufficiently so that when a new string is put on, the pin will turn into the block as far as it did originally. Run one end of the string barely through the hole in the tuning pin and turn it about twice around, taking pains that the coils lie closely; then unwind enough wire (of the same size of course) from your supply to reach down to the hitch pin and back. Place the string on the bridge pins properly, draw it as tight as you can by hand and cut it off about three fingers' width beyond the pin upon which it is to be wound. This will make about three coils around the pin. Place the end in the hole and turn up gradually, watching that the string is clear down on hitch pin and properly laid on the bridge. New strings will require drawing up two or three times before they will stand in tune, and even then they will run down in a short time. It is well on this account to leave them slightly sharp, calling the owner's attention to the fact.

[Ill.u.s.tration: KNOT FOR SPLICING WIRE.]

When a ba.s.s string breaks at the point where it starts around the tuning pin, it can nearly always be spliced and the trouble of sending it away to have a new one made be avoided. Take a piece of new wire as large or larger than the old string and splice it to the broken end by a good secure knot. A knot called the square or ruft knot is the best for this purpose. When a ba.s.s string breaks too far from the pin to permit of a splice, the only resort will be to send the broken string to some factory and have a new one made from it.

QUESTIONS ON LESSON XV.

1. Name the advantages and disadvantages of system A.

2. Name the advantages and disadvantages of system B.

3. What are the important points to be desired in any system of setting temperament?

4. State three or four items of importance in the operation of putting on a new string.

5. Why do pianos get out of tune?

LESSON XVI.