difference in pitch of any given interval in all the keys, and that
makes use of the fewest intervals in tuning and the easiest
ones--those in which a discrepancy is most readily perceived by the
ear, is the best system to adopt and follow. Such a system is the one
followed by the author for years with the most satisfying results. He
does not claim any high honor by this statement, but does claim that,
while his system differs but slightly from some of the others, it is
more certain to produce the best results, is the simplest to
understand, is the easiest to follow, and, consequently, is the best.
To become a piano tuner of the highest skill, many things are
necessary; but what may be lacking at the outset may be acquired by
study and practice. More depends upon the ear than upon anything else;
but no person, however talented, has a sufficiently acute perception
to tune perfectly without some culture. Some practice in tuning is
necessary to bring the ear to that acuteness of perception so
indispensable in certain portions of the instrument. It may also be
said that no extraordinary talent for music is absolutely necessary,
since many of the best tuners are not musicians in any sense of the
word. Patience and perseverance, associated with conscientiousness and
an insatiable desire to excel, are among the foremost requirements.
Having these it only remains to gain a thorough knowledge of every
detail of the work; a little practice will bring skill and dexterity.
Finally, we would impress the student with the strenuous importance of
thoroughly mastering the lessons which immediately follow. You should
be inspired with the utmost confidence, both in yourself and in the
possibilities of the profession to those who merit a reputation. And,
while this lesson contains little technical instruction, if by its
study the pupil is impressed with the maxims herein presented, and is
inspired to make earnest effort in his future work, both in acquiring
and in practicing the art of Piano Tuning, the author will feel that
its mission is, by no means, the least significant one in the course.
LESSON VIII.
~THE TEMPERAMENT.~
Some tuners favor the term, "laying the bearings," others say "setting
the temperament." The former is more commonplace, as it merely
suggests the idea of laying a number of patterns by which all others
are to be measured. The latter term is extremely comprehensive. A
lucid definition of the word "temperament," in the sense in which it
is used here, would require a discourse of considerable length. The
following statements will elicit the full meaning of the term:
The untutored would, perhaps, not think of setting a temperament to
tune by. He would likely begin at some unfavorable point, and tune by
various intervals, relying wholly upon his conception of pitch for the
accuracy of the tones tuned, the same as a violinist in tuning his
four strings. To be sure, pitch has to be reckoned as a rude guide in
setting the tones; but if pitch alone were the guide we would never
attain to any degree of perfection in scale forming. We could never
adjust our tones to that delicate fineness so much appreciated, which
gives to the instrument its surpassing brilliancy.
~Beats, Waves, Pulsations.~--To obtain absolute accuracy the tuner is
guided by beats, waves or pulsations. These three words refer to one
and the same thing, a phenomenon that occurs in certain intervals when
two tones are sounded together that are not in exact tune. These terms
must not be confounded with the term "sound wave" or "vibrations" so
often used in discussions on the theory of sound. However, we think
the student is thoroughly familiar with these terms. The rate of
vibration of two tones not in a favorable ratio, may produce the
phenomenon known as "beats, waves, or pulsations." Vibrations may
exist either with or without pulsations.
These pulsations are most perceptible in the unison, the octave and
the fifth. They are more easily perceived in the unison than in the
octave, and more easily in the octave than in the fifth. They are also
perceptible in the perfect fourth, the major and minor third and some
other intervals, but on account of their obscurity, and because these
intervals are unnecessary in tuning they have long since been
abandoned in "temperament making" (with the exception of the perfect
fourth) by most tuners, although a few still make use of it. We do not
say that the fourth is unsafe to tune by, but you will see later on
why it is not best to make use of it.
_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 compass 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 buttons, 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
assistance 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 illustrates the two octaves of the key-board, and shows
how each key is designated in giving the system of temperament.
~Pitch.~--The Piano Manufacturers' Association 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 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.
[C] The three strings composing the trio or unison are numbered 1st,
2d or middle, and 3d, from left to right.
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.