Post by Bandura on Jan 16, 2006 1:12:47 GMT -5
Tuning is often a most disorganized process with a bandurist, so we are
inserting this section, hopefully, to present a little theory, and a pretty
sound version of the practice.
THE BANDURA IS A TEMPERED INSTRUMENT
The bandura, like the piano and organ, is necessarily a tempered instrument,
since the pitch of a given note cannot be tuned during the process of
performing. It is true that the bandura can have different strings for
enharmonic unisons i.e. D# and Eb. This has led some to think that the
bandura can be regulated for "just" intonation such as would be played on
the violin. If D# or Eb or nay other note were always the same pitch in all
keys it would be possible, but unfortunately, such is not the case.
With perfect or "just" intonation, two interesting mathematical phenomena
are readily apparent. First, the frequency of say A-440 cps, is doubled for
the same note an octave higher, i.e. A-880. Second, the frequency is
increased by half its value for the fifth higher. A-440 then would be
perfectly in tune to E-660. But lack-a-day, in turning our table of computed
tempered frequencies, w find that A is 440 cps., the E fifth above is 629.26
instead of 660cps. What happened to the other 74 thousandths of a vibration
!?
MATHEMATICAL DEMONSTRATION
Let us for one and all go through the complete cycle of twelve tones,
computing each value from A-440, multiplying by one and a half (1.5) for the
fifth above, or three quarters (.75) for the fourth lower:
Ex 1
Now it is apparent that if fourths and fifths are perfectly tuned, each has
become progressively sharper until upon completing the cycle our original A
is now almost six vibrations sharp !
Therefore, in a given key, each note of the scale must be tuned to the root
tone. Thus C# in the key of A tuned perfectly with the A will be 550 cps. a
number that is mathematically consonant with both A-440 and its perfect 5th
E-660 making a smooth beat-free triad. However, C# tuned perfectly to the
key of D, even though the D is perfectly consonant with the A-440 will be of
a different pitch than the C# we had in the key of A !
THE DISCREPANCY IS GREATER FOR MORE REMOTE KEYS
The mathematical discrepancy becomes even wider when the common tone between
the two keys is not the tonic; for example, the keys of Eb and D have D
natural in their scales. Even though we make the two Ds the same pitch
exactly, the other common tones with different names i.e. G# and Ab will be
out of tune.
We hope that the above demonstration it is quite apparent that the tempered
scale is the best solution to freedom of modulation through all the keys,
and we find strength in recalling that Bach though so, too.
A PRACTICAL AND ACCURATE METHOD OF TUNING
Believing and doing are often too widely separated, so how is such a
tempered scale obtained in actual practice? The most accurate and
satisfactory way is to tune in fourths and fifths while setting the
temperment. This must be the first octave tuned, and greatest accuracy can
be obtained by tuning from middle or fourth octave C. This is because a
lower register allows you to count the beats and judge temperment more
easily, and the key of C will make for less error if your bandura is
slightly out of regulation.
WHAT ARE BEATS ?
When two strings which should be at the same pitch are not, for example, one
at A-440 and the other at A-442, a phenomenon occurs commonly called beats
or waves. Between these two tones there would be two beats per second, for
442 minus 440, which is not very much. If a fifth is out of tune, one string
at A-440 and the other E-657 there will be three beats per second, because
as you will remember reading above, the E should be 660 cps. to be perfectly
in tune.
If you have trouble hearing beats, practice listening for them by tuning
your C# and Db perfectly and lowering one of the pitches slowly, counting
the speed the beats as they increase. They do the same sort of thing with an
octave, a fifth, and all the other intervals until you recognise and hear
beats easily. A good ear is not really necessary for good tuning, only the
ability to count.
Again we have over simplified. Hearing beats on the bandura is difficult
since the tone decays and fades so quickly. In tempering fourths and fifths,
the tone fades so rapidly that rather than actually being able to count the
very slow beats you will have to hear a quality of out-of-tuneness. When the
two tones are only slightly out of tune with only one or two beats per
second, it is almost impossible to determine which tone is higher or lower
except by moving it. This makes it possible to err so that a fifth will be
tuned too wide rather than too narrow. Using the check indicated will almost
always help to spot this type of error before you have gone so far as to
throw the entire temperment off.
THE METHOD
Tune 4th C to the standard pitch. A "C" tuning fork of 523.25 cps., which
sounds an octave above 4th C will be in temperment with A-440 and is what
you want.
Ex 2
Follow the outlined procedure on the staff. It is arranged so that in order
to temper the fourths and fifths wider and narrower, respectively, each note
is tuned slightly flat, except for the two Fs which must be tuned slightly
sharp.
Tune the 4th F to C; then tune the 4th G to C; tune the 4th D to the G. Now
check the interval F and D. If you have tuned your fourths slightly wide,
and the fifth slightly narrow, you should have beats in the F-D interval at
the rate of about eight per second. This is correct, so proceed. Tune the
4th A to the D and check F and A, which should have beats slightly slower
than the F-D or about seven per second. Now tune the 4th E to the A and
check G-E. It should have about nine beats per second. In this order check
F-A, F-D, G-E, C-E; they should increase the speed of their beats in the
ratio of 7, 8, 9 and 10 per second. Now tune the B to the E, and check G-B
which should have beats at about seven and one half per second, or just
faster than F-A, and just slower than F-D.
A similar pattern is reproduced for the secondary row of sharps and flats.
This row is tuned a semitone below the main row. When the main row is in C
major, the secondary row is in B major. Two of these strings ; the E and the
B have the same tuning as in the main row. From the B note there the pattern
is reproduced as if it were C, i.e. by having all the notes in the above
method down a semitone.
TEMPERED OCTAVE SETS CORRECT RELATIONSHIPS
Bravo! T You have just set the temperment! All the rest of the bandura must
be tuned to this octave in order to have the proper relationship. Tune down
through the lowest part of the bandura before tuning the upper strings. Tune
E 5th to the E 4th; D 5th to the D 4th and so on. The reason for tuning the
longest and thus lowest strings first is because of their high tension; as
they are adjusted, they have a tendency of throwing the upper octaves out if
they have been tuned first.
CHECK CONSTANTLY
As you tune downwards in octaves, also check in twelths, - an octave and a
fifth, and in tenths. There should be quite a noticeable beat in the tenths,
but should still sound good, and the speed of the beats should decrease as
you get lower. The twelths should be almost perfectly smooth. Octaves are to
be tuned perfectly, except as you descend into the bass, they must be
stretched slightly wider to compensate for the human ear which will hear
them as being sharp when played loudly. A corresponding correction should be
made in the extreme treble, stretching the octaves slightly wider to
compensate for the ear which will hear the high notes as flat! Do not over
do this, your own ear will tell you when it sounds right, and probably you
will make the correction automatically without trying for it.
CHECK AND RECHECK
After all the strings have been tuned, recheck the temperment octave, and
then proceed on up, tuning the upper octave to the lower. Check in fifths,
fourths, tenths, twelfths and chords. Never tune a lower octave to an upper,
except of course below the temperment octave, in which case never tune an
upper octave to a lower! Never tune one of the notes of your temperment
octave to any other octave, but always recheck and correct the temperment.
Just staying organized and following these rules will save a lot of time and
greatly improve your tuning.
ELECTRONIC TUNERS
In recent times inexpensive chromatic tuners have become almost standard and
inexpendable, and are used by bandurists everywhere. These tuners however,
do not compensate for the strings in the upper and lower registers.
Furthermore, if you accidentally left your tuner on overnight and your
battery goes flat whilst tuning or just before a performance what will you
resort to. It may be beneficial to go through the method outlined and be
able to reproduce it when the occasion may arise.
Keep in mind that different tuners tune differently. Often in an ensemble
situation stings may be tuned differently because people have used different
brands of electronic tuners. Also be aware that the setting for "a" ie a=440
is the same for all tuners.
The best electronic tuner is an strobe tuner.
inserting this section, hopefully, to present a little theory, and a pretty
sound version of the practice.
THE BANDURA IS A TEMPERED INSTRUMENT
The bandura, like the piano and organ, is necessarily a tempered instrument,
since the pitch of a given note cannot be tuned during the process of
performing. It is true that the bandura can have different strings for
enharmonic unisons i.e. D# and Eb. This has led some to think that the
bandura can be regulated for "just" intonation such as would be played on
the violin. If D# or Eb or nay other note were always the same pitch in all
keys it would be possible, but unfortunately, such is not the case.
With perfect or "just" intonation, two interesting mathematical phenomena
are readily apparent. First, the frequency of say A-440 cps, is doubled for
the same note an octave higher, i.e. A-880. Second, the frequency is
increased by half its value for the fifth higher. A-440 then would be
perfectly in tune to E-660. But lack-a-day, in turning our table of computed
tempered frequencies, w find that A is 440 cps., the E fifth above is 629.26
instead of 660cps. What happened to the other 74 thousandths of a vibration
!?
MATHEMATICAL DEMONSTRATION
Let us for one and all go through the complete cycle of twelve tones,
computing each value from A-440, multiplying by one and a half (1.5) for the
fifth above, or three quarters (.75) for the fourth lower:
Ex 1
Now it is apparent that if fourths and fifths are perfectly tuned, each has
become progressively sharper until upon completing the cycle our original A
is now almost six vibrations sharp !
Therefore, in a given key, each note of the scale must be tuned to the root
tone. Thus C# in the key of A tuned perfectly with the A will be 550 cps. a
number that is mathematically consonant with both A-440 and its perfect 5th
E-660 making a smooth beat-free triad. However, C# tuned perfectly to the
key of D, even though the D is perfectly consonant with the A-440 will be of
a different pitch than the C# we had in the key of A !
THE DISCREPANCY IS GREATER FOR MORE REMOTE KEYS
The mathematical discrepancy becomes even wider when the common tone between
the two keys is not the tonic; for example, the keys of Eb and D have D
natural in their scales. Even though we make the two Ds the same pitch
exactly, the other common tones with different names i.e. G# and Ab will be
out of tune.
We hope that the above demonstration it is quite apparent that the tempered
scale is the best solution to freedom of modulation through all the keys,
and we find strength in recalling that Bach though so, too.
A PRACTICAL AND ACCURATE METHOD OF TUNING
Believing and doing are often too widely separated, so how is such a
tempered scale obtained in actual practice? The most accurate and
satisfactory way is to tune in fourths and fifths while setting the
temperment. This must be the first octave tuned, and greatest accuracy can
be obtained by tuning from middle or fourth octave C. This is because a
lower register allows you to count the beats and judge temperment more
easily, and the key of C will make for less error if your bandura is
slightly out of regulation.
WHAT ARE BEATS ?
When two strings which should be at the same pitch are not, for example, one
at A-440 and the other at A-442, a phenomenon occurs commonly called beats
or waves. Between these two tones there would be two beats per second, for
442 minus 440, which is not very much. If a fifth is out of tune, one string
at A-440 and the other E-657 there will be three beats per second, because
as you will remember reading above, the E should be 660 cps. to be perfectly
in tune.
If you have trouble hearing beats, practice listening for them by tuning
your C# and Db perfectly and lowering one of the pitches slowly, counting
the speed the beats as they increase. They do the same sort of thing with an
octave, a fifth, and all the other intervals until you recognise and hear
beats easily. A good ear is not really necessary for good tuning, only the
ability to count.
Again we have over simplified. Hearing beats on the bandura is difficult
since the tone decays and fades so quickly. In tempering fourths and fifths,
the tone fades so rapidly that rather than actually being able to count the
very slow beats you will have to hear a quality of out-of-tuneness. When the
two tones are only slightly out of tune with only one or two beats per
second, it is almost impossible to determine which tone is higher or lower
except by moving it. This makes it possible to err so that a fifth will be
tuned too wide rather than too narrow. Using the check indicated will almost
always help to spot this type of error before you have gone so far as to
throw the entire temperment off.
THE METHOD
Tune 4th C to the standard pitch. A "C" tuning fork of 523.25 cps., which
sounds an octave above 4th C will be in temperment with A-440 and is what
you want.
Ex 2
Follow the outlined procedure on the staff. It is arranged so that in order
to temper the fourths and fifths wider and narrower, respectively, each note
is tuned slightly flat, except for the two Fs which must be tuned slightly
sharp.
Tune the 4th F to C; then tune the 4th G to C; tune the 4th D to the G. Now
check the interval F and D. If you have tuned your fourths slightly wide,
and the fifth slightly narrow, you should have beats in the F-D interval at
the rate of about eight per second. This is correct, so proceed. Tune the
4th A to the D and check F and A, which should have beats slightly slower
than the F-D or about seven per second. Now tune the 4th E to the A and
check G-E. It should have about nine beats per second. In this order check
F-A, F-D, G-E, C-E; they should increase the speed of their beats in the
ratio of 7, 8, 9 and 10 per second. Now tune the B to the E, and check G-B
which should have beats at about seven and one half per second, or just
faster than F-A, and just slower than F-D.
A similar pattern is reproduced for the secondary row of sharps and flats.
This row is tuned a semitone below the main row. When the main row is in C
major, the secondary row is in B major. Two of these strings ; the E and the
B have the same tuning as in the main row. From the B note there the pattern
is reproduced as if it were C, i.e. by having all the notes in the above
method down a semitone.
TEMPERED OCTAVE SETS CORRECT RELATIONSHIPS
Bravo! T You have just set the temperment! All the rest of the bandura must
be tuned to this octave in order to have the proper relationship. Tune down
through the lowest part of the bandura before tuning the upper strings. Tune
E 5th to the E 4th; D 5th to the D 4th and so on. The reason for tuning the
longest and thus lowest strings first is because of their high tension; as
they are adjusted, they have a tendency of throwing the upper octaves out if
they have been tuned first.
CHECK CONSTANTLY
As you tune downwards in octaves, also check in twelths, - an octave and a
fifth, and in tenths. There should be quite a noticeable beat in the tenths,
but should still sound good, and the speed of the beats should decrease as
you get lower. The twelths should be almost perfectly smooth. Octaves are to
be tuned perfectly, except as you descend into the bass, they must be
stretched slightly wider to compensate for the human ear which will hear
them as being sharp when played loudly. A corresponding correction should be
made in the extreme treble, stretching the octaves slightly wider to
compensate for the ear which will hear the high notes as flat! Do not over
do this, your own ear will tell you when it sounds right, and probably you
will make the correction automatically without trying for it.
CHECK AND RECHECK
After all the strings have been tuned, recheck the temperment octave, and
then proceed on up, tuning the upper octave to the lower. Check in fifths,
fourths, tenths, twelfths and chords. Never tune a lower octave to an upper,
except of course below the temperment octave, in which case never tune an
upper octave to a lower! Never tune one of the notes of your temperment
octave to any other octave, but always recheck and correct the temperment.
Just staying organized and following these rules will save a lot of time and
greatly improve your tuning.
ELECTRONIC TUNERS
In recent times inexpensive chromatic tuners have become almost standard and
inexpendable, and are used by bandurists everywhere. These tuners however,
do not compensate for the strings in the upper and lower registers.
Furthermore, if you accidentally left your tuner on overnight and your
battery goes flat whilst tuning or just before a performance what will you
resort to. It may be beneficial to go through the method outlined and be
able to reproduce it when the occasion may arise.
Keep in mind that different tuners tune differently. Often in an ensemble
situation stings may be tuned differently because people have used different
brands of electronic tuners. Also be aware that the setting for "a" ie a=440
is the same for all tuners.
The best electronic tuner is an strobe tuner.