_The Fischer System_ or method of "setting the temperament" has these advantages: It uses but two kinds of intervals: the fifth and octave; by employing two whole octaves in place of one or one and a half, nearly all of the middle section of strings is brought up in pitch which insures that the temperament will stand better while the remaining strings are being tuned; and the alternate tuning of the fifth and octave makes the system exceedingly easy to learn, enabling the tuner to work with less mental strain. Also the two-octave system gives a greater compa.s.s for testing, thus insuring greater accuracy.

If you have access to a piano, it will now be well for you to begin training the ear to perceive the pulsations. If you cannot use a piano, you can train very well by the use of a mandolin, guitar, violin, zither, or any stringed instrument. An instrument with metal strings, however, is better, as the vibrations are more perfect.

You will, of course, know that the front top panel of the case has to be removed to give access to the tuning pins, and that you should have a regular tuning hammer and set of mutes to begin with. The panel is held in place in various ways: sometimes with b.u.t.tons, sometimes with pins set in slots, and sometimes with patent fastenings; but a little examination will reveal how it may be removed.

To produce a tone of a certain pitch, the string must be of the right thickness and length. These items are decided by the scale draughtsman in the factory; if incorrect, the tuner can do nothing to improve them.

To produce the correct pitch, the string must be of the right tension, which is brought about by winding one end of the string around the tuning pin until the proper degree of tension is reached. This must be decided by the ear of the tuner. Two strings of equal thickness and equal length produce the same tone when brought to the same tension; the result being known as "unison." A defect in the unison being the easiest way in which to detect the beats, we advise that the student practice on it first.

After taking out the panel, the first thing to do is to place your rubber mute between two trios of strings (if the piano is an upright which usually has three strings to a note) so that only two strings sound when the key is struck. Select some key near the middle of the keyboard. Strike the key strongly and hold it down. If the two sounding strings give forth a smooth, unwavering tone--a tone that sounds as if it came from one string, the unison is perfect. If you find it so, remove the mute and place it on the other side of the trio of strings. If the piano has been tuned recently by an expert, you may have to continue your search over several keys before you find an imperfect unison; but you will rarely find a piano in such perfect tune that it will not contain some defective unisons. However, if you do not succeed in finding a defective unison, select a key near the middle of the key-board, place your mute so that but two strings sound, and with your tuning hammer loosen one of the strings very slightly. Now you will notice a throbbing, beating sound, very unlike the tone produced when the strings were in exact unison. See if you can count the beats. If you have lowered the tension too much, the beats will be too rapid to permit counting. Now with a steady and gradual pull, with the heel of the hand against some stationary part, bring the string up slowly. You will notice these waves become slower and slower. When they become quite slow, stop and count, or wave the hand in time with the pulsations. After practicing this until you are sure your ear has become accustomed to the beats and will recognize them again, you may proceed to perfect the unison. Bring the string up gradually as before, and when the unison is reached you will hear one single, simple, musical tone, as though it were from a single string.

Never have more than two strings sounding at once. You might go over the entire key-board now and correct all the unisons if the scale is yet fairly good. See which string is, in your opinion, the nearest to correctness with respect to the scale, and tune the other one, or two, as the case may be, to it. If the scale is badly out of symmetry, you will not get very good results without setting a temperament; but the tones will sound better individually. This experiment is more for practice than for improving the piano.

_The cause_ of the waves in a defective unison is the alternate recurring of the periods when the condensations and rarefactions correspond in the two strings and then antagonize. This is known in physics as "interference of sound-waves."

~The Octave.~--When perfectly tuned, the upper tone of the octave has exactly double the number of vibrations of the lower. If the lower tone vibrates 1000 per second, the upper will vibrate 2000. Of course, the ear cannot ascertain in any way the number of vibrations per second; we use these figures for scientific demonstration only.

However, there is an instrument called the Siren which is constructed for the purpose of ascertaining the number of vibrations per second of any given tone, and which is delicately accurate in its work. By its a.s.sistance we know, definitely, a great many things regarding our musical scale of which we would otherwise be ignorant. But, while we cannot, by the ear, ascertain these numbers, we can, by the "interference of sound-waves" above referred to, ascertain, to the most delicate point, when the relative vibration of two strings is mathematically exact, if they are tuned to a unison, octave, fifth, etc.

Practice now on tuning the octave. Find an octave in which the upper tone is flat. Mute all but one string in the lower tone to make sure of getting a pure tone, then select one string (the middle one if a piano has three strings) of the upper octave and proceed to pull it up gradually until all beats disappear. This being done, bring up the unisons.

~The Fifth.~--In our system, when we speak of a fifth, we mean a fifth upward. The fifth to C is G, to G is D, and so on.

The vibration of the fifth is one and a half times that of its fundamental. If a certain F vibrates 100, the C, a fifth above, will vibrate 150, if tuned so that no waves are heard; but for reasons which will be fully explained later, the fifth cannot be tuned with mathematical precision. On account of certain peculiarities in our tempered scale, the fifth must always be left somewhat flatter than perfect. This fact is always learned with some astonishment by beginners.

In your practice on tuning the fifth, first tune it perfectly, so that no waves are perceptible; then flat it so that there are very slow waves; less than one per second. Some authorities say there should be three beats in five seconds; but the tuner must learn to determine this by his own judgment. The tempering of the fifth will be treated exhaustively in subsequent lessons.

We advise that you confine your practice to the unison until you are sure you have a clear conception of its peculiarities in all portions of the key-board, except the extreme lower and upper octaves; do not try these yet. Do not begin to practice on the octave until you are very familiar with the beats in the unison. By gradual progress you will avoid confusing the ear, each step being thoroughly mastered before advancing to the next. Remember, there is nothing that is extremely difficult in learning to tune if you but understand what has to be done, go about it systematically, and have plenty of patience.

In this lesson we give you our system of setting the temperament; that is, the succession in which the different tones of the temperament are tuned. We advise, however, that you do not attempt to set a temperament until after studying Lesson IX, which enters into the theory of temperament, testing, etc.

Two octaves are used for the temperament: an octave above, and an octave below middle C. Middle C can be told by its being, the C nearest the name of the piano on the name board. In other words, it is the fifth C from the highest C, and the fourth from the lowest in the modern piano, which has seven and a third octaves.

The diagram ill.u.s.trates the two octaves of the key-board, and shows how each key is designated in giving the system of temperament.

~Pitch.~--The Piano Manufacturers' a.s.sociation has established what is known as "international pitch." Tuning-forks made to this pitch are marked "C-517.3," meaning that our 3C vibrates 517.3 per second.

Concert pitch is nearly a half step higher than this. Some manufacturers still tune their instruments to this higher pitch.

If it is desired to tune a piano to a certain pitch, say concert pitch, tune the C that is an octave above middle C by a concert pitch tuning-fork or pipe. If, however, the piano is too much below that, it is not safe to bring it up to it at one tuning. But, say it will permit tuning to concert pitch; after this C (3C) is well laid, tune middle C (2C) by it, then tune the C octave below middle C (1C) to middle C. Having 1C for a starting point, proceed by tuning a fifth up, then its octave, then a fifth, then an octave, always tuning the octave whichever way is necessary to keep within the two octaves.

The simplicity of this system can be readily seen; yet for the use of beginners, we give on the following page the whole succession of intervals as they are taken in setting the temperament.

DIAGRAM OF THE TWO OCTAVES USED IN "TEMPERAMENT," AND OF THE SUCCESSION IN WHICH THEY ARE TUNED.

C? D? F? G? A? C? D? F? G? A?

C D E F G A B C D E F G A B C *

1C, 1D, 1E, etc. 2C, 2D, 2E, etc. 3C -------------------- ---------------------

Middle C begins second octave; known by the asterisk (*) under it.

~THE FISCHER SYSTEM OF SETTING TEMPERAMENT.~

First, tune 3C by tuning pipe, or as directed.

By this, tune 2C, and by 2C tune 1C; then tune as follows:

By 1C tune 1G fifth above, " 1G " 2G octave above, " 1G " 2D fifth above, " 2D " 1D octave below, By 1D tune 1A fifth above, " 1A " 2A octave above, " 1A " 2E fifth above, " 2E " 1E octave below, " 1E " 1B fifth above, " 1B " 2B octave above, " 1B " 2F? fifth above, " 2F? " 1F? octave below, " 1F? " 2C? fifth above, " 2C? " 1C? octave below, " 1C? " 1G? fifth above, " 1G? " 2G? octave above, " 1G? " 2D? fifth above, " 2D? " 1D? octave below, " 1D? " 1A? fifth above, " 1A? " 2A? octave above, " 1A?(B?) 2F fifth above, " 2F " 1F octave below, " 1F try 2C fifth above.

You will observe this last fifth brings you back to the starting-point (C). It is called the "wolf," from the howling of its beats when the tuner has been inaccurate or the piano fails to stand.

QUESTIONS ON LESSON VIII.

1. What is the cause of the beats or pulsations?

2. Have you practiced tuning the unison?

3. Can you distinguish the beats clearly?

4. Have you practiced tuning the octave?

5. Do you thoroughly understand the system of setting the temperament as set forth in this lesson?

LESSON IX.

~SPECIFIC INSTRUCTIONS IN TEMPERAMENT SETTING.~

~Pitch.~--It is a matter of importance in tuning an instrument that it be tuned to a pitch that will adapt it to the special use to which it may be subjected. As previously explained, there are at present two different pitches in use, international pitch and concert pitch, the latter being about a half-step higher than the former. The tuner should carry with him a tuning pipe or fork tuned to 3C in one or the other of these pitches. The special uses to which pianos are subjected are as follows:

1st, As a concert piano.--In the opera house, music hall, and occasionally in the church, or even in a private dwelling, the piano is used along with orchestral instruments. All orchestral instruments are supposed to be tuned to concert pitch. The stringed instruments can, of course, be tuned to any pitch; but the bra.s.s and wood-wind instruments are not so adjustable. The bra.s.s instruments are provided with a tuning slide and their pitch can be lowered somewhat, but rarely as much as a half-step, while the clarinet should not be varied from its fixed pitch if it can be avoided. It is desirable, then, that all pianos used with orchestra should be tuned to concert pitch if possible.

2d, As an accompaniment for singing.--Some persons use their pianos mainly for accompanying. It may be that singers cannot sing high, in which case they are better pleased if the piano is tuned to international pitch, while others, especially concert singers, have their pianos at a higher pitch. Where a piano is used in the home to practice by, and the singer goes out to various places to sing with other instruments, we have always advised to have the piano tuned as near concert pitch as it would bear, for the reason that if one practices with an instrument tuned to concert pitch he may feel sure of reaching the pitch of any instrument he may be called upon to sing with elsewhere.

The great majority of pianos are left entirely to the tuner's judgment in regard to pitch. The tuner knows, or should know, to what pitch to tune the piano to insure the best results. The following suggestions will be found entirely safe to follow in deciding the question of the pitch to which to tune:

Ascertain if the piano is used with orchestra, and if clarinets and cornets are used. If so, and the piano is not too much below concert pitch, and bids fair to stand the tension, draw your 3C up to concert pitch and proceed to lay your temperament. If the piano is nearly as low as international pitch, do not try to bring it up at one tuning to concert unless the owner demands it, when you may explain that it will not stand in tune long. The slightest alteration possible, in the pitch of an instrument, insures the best results, so far as standing in tune is concerned.

If everything be left to your judgment, as it generally is, and the instrument is for general, rather than special use, set your temperament at such a pitch as will require the least possible alteration. This may be arrived at in the following way: Ascertain which portion of the instrument has fallen the most. The overstrung ba.s.s strings generally stand better than any other, and in most cases you will find the C which is two octaves below middle C to be higher (relatively) than any other C in the piano. If so, take it as a basis and tune by perfect octaves up to 3C.

The supposition is, that all strings in an instrument gradually grow flatter; and in a well-balanced instrument they should do so; but the fact is, that in certain cases some of the strings will grow sharper.

The cause is this: The tension of the strings on one side of a brace in the metal plate or frame is greater than on the other side; and if there is any yielding of the structure, the result is that the overpowered strings are drawn tighter. This condition, however, is rare in the better grade of pianos. Here is a rule which is safe, and will prove satisfactory in ninety-nine per cent. of your practice where no specific pitch is prescribed:

Take the three Cs included in the temperament and the C that is an octave below 1C, and try each of them with its octave until you ascertain which is the sharpest with respect to the others; then, bring the others up to it. You now have your pitch established in the Cs and can begin on 1C and proceed to set the temperament. Before applying this rule, it is well to try 3C with tuning pipe or fork to see if the piano is below international pitch. We would not advise tuning any modern piano below international pitch. Aim to keep within the bounds of the two prescribed pitches; never higher than concert, nor lower than international. If, however, you should be called on to tune an old instrument that has become extremely low, with very rusty strings, and perhaps with some of them broken, that by all appearances will not stand even international pitch, you may be compelled to leave it somewhat below.

~The Continuous Mute.~--Do not try to set a temperament without a continuous mute. Its purpose is to mute all outside (1st and 3d[C]) strings of all the trios included in the temperament so that none but the middle strings sound when struck by the hammers. The advantage of this can be seen at once. The tuner tunes only the middle strings in setting the temperament and thereby avoids the confusion of hearing more than two strings at once. The continuous mute is then removed and the outside strings tuned to the middle. Without the continuous mute, he would be obliged to tune all three of the strings of the unison before he could tune another interval by it, and it would not be so safe to tune by as a single string, as there might be a slight discrepancy in the unison giving rise to waves which would confuse the ear. The tuner should hear but two strings at once while setting a temperament; the one he is tuning by and the one he is tuning. A continuous mute is a strip of muting felt of the proper thickness to be pushed in between the trios of strings. Simply lay it across a portion of the strings and with a screwdriver push it in between the trios just above where the hammers strike. In the square piano, which has but two strings to a key, the continuous mute cannot be used and you will be obliged to tune both strings in unison before leaving to tune another interval. This is one of the reasons why the square piano does not, as a rule, admit of as fine tuning as the upright.