Diagram of the Two Octaves Used in "Temperament," and of the Succession in Which They Are Tuned

Octaves used in 'Temperament'

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,
" 1D " 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 brass and wood-wind instruments are not so adjustable. The brass 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 bass 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.

It is presumed that you are now familiar with the succession of tones and intervals used in setting the temperament. Fix these things in your mind and the system is easy to understand and remember. Keep within the bounds of the two octaves laid out in Lesson X. Tune all fifths upward; that is, tune all fifths by their fundamentals. For example, starting on 1C, use it as fundamental, and by it, tune its fifth, which is G; then, having G tuned, use it as fundamental, and by it tune its fifth, which is D, and so on through. After tuning a fifth, always tune its octave either above or below, whichever way it lies within the bounds of the two octaves. After going through one or two experiments in setting temperament you will see the simplicity of this system and will, perhaps, not be obliged to refer to the diagram any more.

For various reasons, it is better to try your experiments on an upright piano, and the better the piano, the more satisfactory will be the result of the experiment. You should have no hesitancy or timidity in taking hold of a good piano, as you cannot damage it if you use good judgment, follow instructions, and work carefully. The first caution is, be very careful that you draw a string but slightly sharper than it is to be left. Rest the heel of the hand against some stationary part of the piano and pull very slowly, and in a direct right angle with the tuning pin so as to avoid any tendency to bend or spring the pin. We would advise now that you find an upright piano that is badly out of tune, if you have none of your own, and proceed to set a temperament.

The following instructions will suffice for your first experiments, and by them you may be able to get fairly good results; however, the theory of temperament, which is more thoroughly entered into in Lesson XII, must be studied before you can have a thorough understanding of the causes and effects.

After deciding, as per instructions on pitch which C you will tune first, place the tuning hammer (using the star head if pins are square) on the pin with the handle extending upwards or inclined slightly to the right. (The star head, which will fit the pin at eight different angles, enables the tuner to select the most favorable position.) To raise the pitch, you will, of course, pull the hammer to the right. In order to make a string stand in tune, it is well to draw it very slightly above the pitch at which it is to remain, and settle it back by striking the key repeatedly and strongly, and at the same time bearing gently to the left on the tuning hammer. The exact amount of over-tension must be learned by practice; but it should be so slight as to be barely perceptible. Aim to get the string tuned with the least possible turning of the hammer. The tension of the string should be evenly distributed over its entire length; that is, over its vibrating middle and its "dead ends" beyond the bridges. Therefore it is necessary to strike the key strongly while tuning so as to make the string draw through the bridges. By practice, you will gain control of the hammer and become so expert that you can feel the strings draw through the bridges and the pins turn in the block.

Having now tuned your three Cs, you will take 1C as a starting point, and by it, tune 1G a perfect fifth above. Tune it perfect by drawing it gradually up or down until all pulsations disappear. Now after making sure you have it perfect, flatten it until you can hear slow, almost imperceptible waves; less rapid than one per second. This flattening of the fifth is called tempering, and from it comes the word "temperament." The fact that the fifth must always be tuned a little flatter than perfect, is a matter which always causes some astonishment when first learned. It seems, to the uninitiated, that every interval should be made perfect; but it is impossible to make them so, and get a correct scale, as we shall see later on.

Now tune 2G by the 1G just tuned, to a perfect octave. Remember that all octaves should be left perfectall waves tuned out. Now try 2G with 2C. If your octaves are perfect, this upper fifth will beat a little faster than the lower one, but the dissonance should not be so great as to be disagreeable. Proceed to your next fifth, which is 2D, then its octave, 1D, then its fifth and so on as per directions on the system card. You can make no chord trials until you have tuned E, an interval of a major third from C.

Having tuned 2E, you can now make your first trial: the chord of C. If you have tempered your fifths correctly, this chord will come out in pleasing harmony, and yet the E will be somewhat sharper than a perfect major third to C. Now, just for experiment, lower 2E until all waves disappear when sounded with 2C. You now have a perfect major third. Upon sounding the chord, you will find it more pleasing than before; but you cannot leave your thirds perfect. Draw it up again to its proper temperament with A, and you will notice it has very pronounced beats when sounded with C. Proceed with the next step, which is that of tuning 1B, fifth to 1E. When tuned, try it as a major third in the chord of G. At each step from this on, try the note just tuned as a major third in its proper chord. Remember, the third always sounds better if lower than you dare to leave it; but, on the other hand, it must not be left so sharp as to be at all unpleasant when heard in the chord. As to the position of the chord for these trials, the second position, that is, with the third the highest, is the most favorable, as in this position you can more easily discern excessive sharpness of the third, which is the most common occurrence. When you have gone through the entire system and arrived at the last fifth, 1F-2C, you should find it nearly as perfect as the rest, but you will hardly be able to do so in your first efforts. Even old tuners frequently have to go over their work a second or third time before all fifths are properly tempered. By this system, however, you cannot go far wrong if you test each step as directed, and your first chord comes up right. If the first test, G-C-E, proves that there is a false member in the chord, do not proceed with the system, but go over the first seven steps until you find the offending members and rectify. Do not be discouraged on account of failures. No one ever set a correct temperament at the first attempt.

QUESTIONS ON LESSON IX.

  1. Define the terms, "International Pitch," and "Concert Pitch."
  2. How would you arrive at the most favorable pitch at which to tune a piano, if the owner did not suggest any certain pitch?
  3. What is the advantage in using the continuous mute?
  4. Tell what is necessary in the tuning of a string to insure it to stand well?
  5. What would result in the major third C-E, if all the fifths, up to E, were tuned perfect?

LESSON X.


THEORY OF THE TEMPERAMENT.

The instructions given in Lessons VIII and IX cover the subject of temperament pretty thoroughly in a way, and by them alone, the student might learn to set a temperament satisfactorily; but the student who is ambitious and enthusiastic is not content with a mere knowledge of how to do a thing; he wants to know why he does it; why certain causes produce certain effects; why this and that is necessary, etc. In the following lessons we set forth a comprehensive demonstration of the theory of Temperament, requirements of the correct scale and the essentials of its mathematics.

Equal Temperament. Equal temperament is one in which the twelve fixed tones of the chromatic scale[D] are equidistant. Any chord will be as harmonious in one key as in another.

Unequal Temperament. Unequal temperament was practiced in olden times when music did not wander far from a few keys which were favored in the tuning. You will see, presently, how a temperament could be set in such a way as to favor a certain key (family of tones) and also those keys which are nearly related to it; but, that in favoring these keys, our scale must be constructed greatly to the detriment of the "remote" keys. While a chord or progression of chords would sound extremely harmonious in the favored keys, they would be so unbalanced in the remote keys as to render them extremely unpleasant and almost unfit to be used. In this day, when piano and organ music is written and played in all the keys, the unequal temperament is, of course, out of the question. But, strange to say, it is only within the last half century that the system of equal temperament has been universally adopted, and some tuners, even now, will try to favor the flat keys because they are used more by the mass of players who play little but popular music, which is mostly written in keys having flats in the signature.

Upon the system table you will notice that the first five tones tuned (not counting the octaves) are C, G, D, A and E; it being necessary to go over these fifths before we can make any tests of the complete major chord or even the major third. Now, just for a proof of what has been said about the necessity of flattening the fifths, try tuning all these fifths perfect. Tune them so that there are absolutely no waves in any of them and you will find that, on trying the chord G-C-E, or the major third C-E, the E will be very much too sharp. Now, let your E down until perfect with C, all waves disappearing. You now have the most perfect, sweetest harmony in the chord of C (G, C, E) that can be produced; all its members being absolutely perfect; not a wave to mar its serene purity. But, now, upon sounding this E with the A below it, you will find it so flat that the dissonance is unbearable. Try the minor chord of A (A-C-E) and you will hear the rasping, throbbing beats of the too greatly flattened fifth.

So, you see, we are confronted with a difficulty. If we tune our fifths perfect (in which case our fourths would also be perfect), our thirds are so sharp that the ear will not tolerate them; and, if we tune our thirds low enough to banish all beats, our fifths are intolerably flat.

The experiment above shows us beautifully the prominent inconsistency of our scale. We have demonstrated, that if we tune the members of the chord of C so as to get absolutely pure harmony, we could not use the chord of A on account of the flat fifth E, which did duty so perfectly as third in the chord of C.

There is but one solution to this problem: Since we cannot tune either the fifth or the third perfect, we must compromise, we must strike the happy medium. So we will proceed by a method that will leave our fifths flatter than perfect, but not so much as to make them at all displeasing, and that will leave our thirds sharper than perfect, but not intolerably so.

We have, thus far, spoken only of the octave, fifth and third. The inquisitive student may, at this juncture, want to know something about the various other intervals, such as the minor third, the major and minor sixth, the diminished seventh, etc. But please bear in mind that there are many peculiarities in the tempered scale, and we are going to have you fully and explicitly informed on every point, if you will be content to absorb as little at a time as you are prepared to receive. While it may seem to us that the tempered scale is a very complex institution when viewed as a specific arrangement of tones from which we are to derive all the various kinds of harmony, yet, when we consider that the chromatic scale is simply a series of twelve half-stepstwelve perfectly similar intervalsit seems very simple.

Bear in mind that the two cardinal points of the system of tuning are:

  1. All octaves shall be tuned perfect.
  2. All fifths shall be tuned a little flatter than perfect.

You have seen from Lesson VIII that by this system we begin upon a certain tone and by a circle of twelve fifths cover every chromatic tone of the scale, and that we are finally brought around to a fifth, landing upon the tone upon which we started.

So you see there is very little to remember. Later on we will speak of the various other intervals used in harmony: not that they form any prominent part in scale forming, for they do not; but for the purpose of giving the learner a thorough understanding of all that pertains to the establishing of a correct equal temperament.

If the instruction thus far is understood and carried out, and the student can properly tune fifths and octaves, the other intervals will take care of themselves, and will take their places gracefully in any harmony in which they are called upon to take part; but if there is a single instance in which an octave or a fifth is allowed to remain untrue or untempered, one or more chords will show it up. It may manifest itself in one chord only. A tone may be untrue to our tempered scale, and yet sound beautifully in certain chords, but there will always be at least one in which it will "howl." For instance, if in the seventh step of our system, we tune E a little too flat, it sounds all the better when used as third in the chord of C, as we have shown in the experiment mentioned on page 94 of this lesson. But, if the remainder of the temperament is accurate, this E, in the chord in which E acts as tonic or fundamental, will be found to be too flat, and its third, G sharp, will demonstrate the fact by sounding too sharp.

The following suggestions will serve you greatly in testing: When a third sounds disagreeably sharp, one or more fifths have not been sufficiently flattened.[E] While it is true that thirds are tuned sharp, there is a limit beyond which we cannot go, and this excessive sharpness of the third is the thing that tuners always listen for.

The fundamental sounds better to the ear when too sharp. The reason for this is the same as has already been explained above; namely, if the fundamental is too sharp the third will be less sharp to it, and, therefore, nearer perfect.

After you have gone all over your temperament, test every member of the chromatic scale as a fundamental of a chord, as a third, and as a fifth. For instance: try middle C as fundamental in the chord of C (G-C-E or E-G-C or C-E-G). Then try it as third in the chord A flat (E flat-A flat-C or C-E flat-A flat or A flat-C-E flat). Then try it as fifth in the chord of F (C-F-A or A-C-F or F-A-C). Take G likewise and try it as fundamental in the chord of G in its three positions, then try it as a third in the chord of E flat, then as fifth in the chord of C. In like manner try every tone in this way, and if there is a falsely tempered interval in the scale you will be sure to find it.

You now understand that the correctness of your temperament depends entirely upon your ability to judge the degree of flatness of your fifths; provided, of course, that the strings stand as tuned. We have told you something about this, but you may not be able at once to judge with sufficient accuracy to insure a good temperament. Now, we have said, let the fifths beat a little more slowly than once a second; but the question crops up, How am I to judge of a second of time? The fact is that a second of time is quickly learned and more easily estimated, perhaps, than any other interval of time; however, we describe here a little device which will accustom one to estimate it very accurately in a short time. The pendulum oscillates by an invariable law which says that a pendulum of a certain length will vibrate always in a corresponding period of time, whether it swings through a short arc or a long one. A pendulum thirty-nine and a half inches long will vibrate seconds by a single swing; one nine and seven-eighths inches long will vibrate seconds at the double swing, or the to-and-fro swing. You can easily make one by tying any little heavy article to a string of either of these lengths. Measure from the center of such heavy article to the point of contact of the string at the top with some stationary object. This is a sure guide. Set the pendulum swinging and count the vibrations and you will soon become quite infallible. Having acquired the ability to judge a second of time you can go to work with more confidence.

Now, as a matter of fact, in a scale which is equally tempered, no two fifths beat exactly alike, as the lower a fifth, the slower it should beat, and thus the fifths in the bass are hardly perceptibly flat, while those in the treble beat more rapidly. For example, if a certain fifth beat once a second, the fifth an octave higher will beat twice a second, and one that is two octaves higher will beat four times a second, and so on, doubling the number of beats with each ascending octave.

In a subsequent lesson, in which we give the mathematics of the temperament, these various ratios will be found accurately figured out; but for the present let us notice the difference between the actual tempered scale and the exact mathematical scale in the point of the flattening of the fifth. Take for example 1C, and for convenience of figuring, say it vibrates 128 per second. The relation of a fundamental to its fifth is that of 2 to 3. So if 128 is represented as 2, we think of it as 2 times 64. Then with another 64 added, we have 192, which represents 3. In other words, a fundamental has just two-thirds of the number of vibrations per second that its fifth has, in the exact scale. This would mean a fifth in which there would be no beats. Now in the tempered scale we find that G vibrates 191.78 instead of 192; so we can easily see how much variation from the mathematical standard there is in this portion of the instrument. It is only about a fourth of a vibration. This would mean that, in this fifth we would hear the beats a little slower than one per second. Take the same fifth an octave higher and take 2C as fundamental, which has 256 for its vibration number. The G, fifth above, should vibrate 384, but in the tempered scale it beats but 383.57, almost half a vibration flat. This would give nearly 2 beats in 3 seconds.

These figures simply represent to the eye the ratios of these sounds, and it is not supposed that a tuner is to attain to such a degree of accuracy, but he should strive to arrive as near it as possible.

It is well for the student to practice temperament setting and regular tuning now if he can do so. After getting a good temperament, proceed to tune by octaves upward, always testing the tone tuned as a fifth and third until his ear becomes sufficiently true on the octave that testing otherwise is unnecessary. Tune the overstrung bass last and your work is finished. If your first efforts are at all satisfactory you should be greatly encouraged and feel assured that accuracy will reward continued practice.

QUESTIONS ON LESSON X.

  1. What is meant by the term "equal temperament"?
  2. What is meant by the term "unequal temperament"?
  3. Webster defines the term "temperament" thus: "A system of compromises in the tuning of pianofortes, organs, etc." Explain fully what these compromises are.
  4. In testing chords to ascertain if temperament is correct, what is the main thing to listen for as a guide?
  5. In what three chords would you try the tone A, in testing your temperament?
  6. With what results have you demonstrated the experiments in this and the previous lesson?

LESSON XI.


THE TECHNIQUE OR MODUS OPERANDI OF PIANO TUNING.

At this juncture, it is thought prudent to defer the discussion of scale building and detail some of the requirements connected with the technical operations of tuning. We do this here because some students are, at this stage, beginning to tune and unless instructed in these things will take hold of the work in an unfavorable way and, perhaps, form habits that will be hard to break. Especially is this so in the matter of setting the mutes or wedges. As to our discussion of scale building, we shall take that up again, that you may be more thoroughly informed on that subject.

Some mechanics do more work in a given time than others, do it as well or better, and with less exertion. This is because they have method or system in their work so that there are no movements lost. Every motion is made to count for the advancement of the cause. Others go about things in a reckless way, taking no thought as to time and labor-saving methods.

In spite of any instruction that can be given, the beginner in piano tuning will not be able to take hold of his work with the ease and the grace of the veteran, nor will he ever be able to work with great accuracy and expedition unless he has a systematic method of doing the various things incident to his profession.

In this lesson, as its subject implies, we endeavor to tell you just how to begin and the way to proceed, step by step, through the work, to obtain the best results in the shortest time, with the greatest ease and the least confusion.

Manipulation of the Tuning Hammer.

It may seem that the tightening of a string by turning a pin, around which it is wound, by the aid of an instrument fitting its square end, is such a simple operation that it should require no skill. Simply tightening a string in this manner is, to be sure, a simple matter; but there is a definite degree of tension at which the vibrating section of the string must be left, and it should be left in such a condition that the tension will remain invariable, or as near so as is possible. The only means given the tuner by which he is to bring about this condition are his tuning hammer and the key of the piano, with its mechanism, whereby he may strike the string he is tuning.

The purpose of the tuning hammer is that of altering the tension. The purpose of striking the string by means of the key is twofold: first, to ascertain the pitch of the string, and second, to equalize the tension of the string over its entire length. Consider the string in its three sections, viz.: lower dead end (from hitch pin to lower bridge), vibrating section (section between the bridges), and upper dead end (from upper bridge to tuning pin).

When placing the hammer on the tuning pin and turning to the right, it is evident that the increased tension will be manifest first in the upper dead end. In pianos having agraffes or upper bridges with a tightly screwed bearing bar which makes the strings draw very hard through the bridge, some considerable tension may be produced in the upper dead end before the string will draw through the bridge and increase the tension in the vibrating middle. In other pianos the strings "render" very easily over the upper bridge, and the slightest turn of the hammer manifests an alteration of pitch in the vibrating section. As a rule, strings "render" much more easily through the upper, than the lower bridge. There are two reasons for this: One is, that the construction of the lower bridge is such as to cause a tendency in this direction, having two bridge-pins which stand out of line with the string and bear against it in opposite directions; the other is that the lower bridge is so much farther from the point where the hammer strikes the string that its vibration does not help it through as it does at the upper bridge.

Now, the thing desired is to have the tension equally distributed over the entire length of the string. Tension should be the same in the three different sections. This is of paramount importance. If this condition does not obtain, the piano will not stand in tune. Yet, this is not the only item of importance. The tuning pin must be properly "set," as tuners term it.

By "setting the pins," we mean, leaving it so balanced with respect to the pull of the string that it will neither yield to the pull of the string nor tend to draw it tighter. Coming now to the exact manipulation of the tuning hammer, there are some important items to consider.[F] Now, if the tuning hammer is placed upon the tuning pin with the handle straight upward, and it is pulled backward (from the tuner) just a little, before it is turned to the right, the tension will be increased somewhat before the pin is turned, as this motion, slight as it may seem, pulls the pin upward enough to draw the string through the upper bridge an infinitesimally small distance, but enough to be perceptible to the ear. Now if the hammer were removed, the tendency of the pin would be to yield to the pull of the string; but if the pin is turned enough to take up such amount of string as was pulled through the bridge, and, as it is turned, is allowed to yield downward toward the pull of the string, it will resume its balance and the string will stand at that pitch, provided it has been "rendered" properly over the bridges.

We set forth these details that you may have a thorough understanding of what is meant by setting the pins, and while it is not always advisable to follow this method in tuning, there are some pianos that will stand more satisfactorily when treated in this way. This method is recommended where the string has become rusty at the upper bridge, as it is loosened at the bridge before it is started to wind around the pin which prevents it breaking at that point. We believe that ninety per cent. of strings break right where they start around tuning pin. A very good way to draw a string up is to give the hammer an alternate up and down motion, pulling the handle lightly to you, then from you, as you draw it up; not enough to bend or break the pin or to crush the wood around the pin, but just enough to make the string take on its increased tension equally.

In regard to the lower bridge, the strings will rarely "render" through them properly unless brought to a tension a little higher than it is desired they shall be left. If this is done, a few sharp blows of key will generally make them equalize all right; then press the hammer gently to the left, not enough to turn the pin in the socket, but to settle it back to a well-balanced position. After a little practice the tuner can generally guess precisely how much over-tension to allow. If the pin is left slightly sprung downward, its tendency will be to spring upward, thereby sharpening the string; so be careful to leave the pins in perfect balance, or as tuners say, "properly set."

The foregoing, while applicable to the whole scale, is not so urgent in the over-strung bass. The strings are so heavy and the tension is so great that they will generally "render" quite freely over the bridges, and it is only necessary to bring them up to pitch, handling the hammer in such a manner as to leave the pins well balanced; but it is not necessary to give them over-tension and beat them down again; in fact it is not advisable, as a rule. At all times, place the hammer on the pin as far as it will go, and strike the key while drawing a string up.

In tuning the square piano, it is not possible to set the hammer upon the pin with the handle in line with, and beyond the string, as is the rule in the upright. Where the square has the square pin, the hammer (with star head) can always be set with the handle to the right of the string somewhat, but usually almost in line with the string and almost directly over it, and the manipulation of the hammer is much the same, though the tuner is at a greater disadvantage, the pins being farther from him and he has not such a good rest for his hand. Many old squares have the oblong pin. In this case, use the double hammer head. On the one side the hole in the head is made with the longer diameter in line with the handle, and on the other side the hole is made with the longer diameter at right angles with the handle; so that if you cannot get a favorable position with one end you can with the other.

We have said nothing about which hand to use in striking the keys and in wielding the hammer, but it is customary to handle the hammer with the right hand and it is always advisable for two very good reasons: It gives the tuner a much more favorable position at the instrument; and, as the right hand is more used in ordinary every-day operations and is more trained in applying degrees of force and guiding tools, it is more easily trained to manipulate the hammer properly. Training the hand in the skilful use of the hammer is of the utmost importance and comes only by continued practice, but when it is trained, one can virtually "feel" the tones with the hammer.

At first, the young tuner is almost invariably discouraged by his slow progress. He must remember that, however fine his ear and however great his mechanical ability, he has much to acquire by training in both, and he must expect to be two or three times longer in finishing off a job of tuning at the outset than will be necessary after he has had a few months' practice. You can be your own trainer in these things if you will do a little rational thinking and be content to "hasten slowly." And as to using the left hand, we would not advise it in any event.

Setting the Mutes or Wedges in the Upright.

As stated in a previous lesson, the mutes should be so placed that only two strings are heard at one time: the one the tuner is tuning, and the one he is tuning by. It is true that this is an easy matter, but it is also true that very few tuners know how to do it in a way to save time and avoid placing the mutes two or more times in the same place. By using a little inventive genius during early practice the author succeeded in formulating a system of muting by which he accomplished the ends as stated above, and assures the reader that a great deal of time can be saved by following it.

After removing the muffler or any other instrumental attachment which may be in the piano in the way of placing the mutes, the first thing to do is to place the continuous mute so that all the outside strings of the trios are damped. The temperament is then set by tuning the middle strings, of the twenty-five trios comprised in the two-octave temperament as demonstrated in a previous lesson. After satisfying yourself by trials or test that the temperament is true, you then remove the continuous mute and proceed to bring the outside strings in unison with the middle one. Now, your 1C is sometimes found to be the first pair in the over-strung bass, which usually has two strings to a key, while in other pianos, 1C is the first trio in the treble stringing, and in many cases it is the second trio in the treble. For illustration, we will say it is the second in the treble. In speaking of the separate strings of a trio we will number them 1st, 2d, and 3d, from left to right, as in foot-note, page 89, Lesson IX. Setting the mutes in bringing up the unisons in the temperament is exceedingly simple.

The following diagram will, we think, demonstrate clearly the method employed: