Music Trade Review
Issue: 1926 Vol. 83 N. 2 - Page 30
Music Trade Review -- © mbsi.org, arcade-museum.com -- digitized with support from namm.org
TECHNICAL^SUPPLY DEPARTMENT
William BrendVftutefa/imcal Editor
An Interesting Tuning Method Devised by
Charles E, Richardson, of North Andover
A System That Should Be Read, Studied and Discussed, for It Is a Novel One and One That
Deserves Real Attention—Not the Method of Setting the Temperament But Its
Practical Value That Counts Providing the Results Are Good
I
T is with the greatest pleasure that I intro-
duce to readers the most interesting tuning
method devised by Charles E. Richardson,
of North Andover, Mass. Save Jay editing of
minor details I have found it quite impossible
to improve upon the author's admirable presen-
tation.
I want readers to read, study and frankly
criticize. This is a novel matter and deserves
extended discussion, for which I shall be glad
to give space. Mr. Richardson writes as fol-
lows:
"Tuners should be indebted to you for your
fairness in giving advocates of different systems
of setting temperament a chance to air their
theories and ideas. To me much of the valuable
and instructive matter published has been from
your pen; most of which I have appreciated so
much as to have carefully saved. (See articles
published November 3, 1923; February 21, 1925;
August 22, 1925; August 15, 1925; June 26, 1920;
November 10, 1923; November 14, 1925; Novem-
ber 21, 1925; November 28, 1925; December 5,
1925; November 7, 1925, etc., etc.) Much of
the information received from these has con-
tributed toward the evolution of the ideas pre-
sented below.
"As you have stated, it is not the method
of setting the temperament, but its practical
value which counts, providing the results show
a true and equal temperament. Still, there
seems to have been much discussion relative
to the two leading systems; i. e., the tempera-
ments set respectively between the two Fs and
between the two Cs. Those who use the C-to-C
method assert that the F-to-F system runs too
high to get sure results from the fast-beat rates
therefrom, especially on the upper intervals.
And in that method the system of using fourths
and fifths principally is uncertain. On the other
hand, the F-to-F system advocates claim that
when one has to tune intervals which are on
the lower strings, as in the C-to-C system, that
makes it uncertain, because of the tendency of
these strings to have overtones and false beats,
this being more so with the wound strings.
"The method I present here goes neither too
high nor too low, thereby overcoming in a
measure the objections mentioned above; yet
it has the good points of both temperaments.
"Still, even this is not the principal reason
for creating this method of equal temperament
setting. I devised it primarily for using A as
the starting note rather than C. Of course, any
good tuner can start with any pitch note re-
gardless of what method he uses, and set a
good temperament. But, to have a start where-
by there are proofs from the beginning, is one
of the arguments made for certain systems. A
seems to be the most logical and practical note
to use for the start. In the musical world,
among all singers, all teachers of music, orches-
tra and band leaders, in the trade, and even
among tuners (though they use the C fork) A
is the note used to discuss pitch. Tuners who
use the A fork, especially those whose clientele
is mainly musical, find that they are better un-
derstood and therefore looked upon with more
confidence.
Description of the Method
"It will be noticed in giving the different steps
of this temperament that after the beginning,
with one exception, every third or sixth has a
fourth or fifth as a proof; or if a fourth or fifth
is used to set a note, then a third or sixth can
be used as a proof. While my system is based
principally upon the so-called third and sixth
method, by reversing it, as explained above, the
fourth and fifth idea (slow-beat method), can
be used instead. All good tuners, of course, use
all intervals in fine work. The exception men-
tioned above is when the F sharp is set. This
has as a proof the third from low D which has
a slow beat, and so makes as good a proof as a
fourth or fifth. It will be noticed that while
thirds and sixths may be more easily understood,
especially by beginners, it is possible for a
greater error to arise unnoticed in these inter-
vals than in a fourth or fifth. Therefore, fourths
and fifths are indispensable for fine work, either
to tune by or to prove with.
"Those who use the fourth and fifth method
will feel that in the method shown below there
seems to be much 'jumping around.' This is
to keep each note, as it is tuned, in close rela-
tion to the starting notes, so that any error may
be discovered as soon as possible. At the same
time the intention is to keep A in the middle as
a sort of fulcrum, whereby the whole tempera-
ment is balanced around it.
"It will be observed that each third or sixth
as it is tuned has, in most cases, a similar in-
terval adjacent to it for comparison and as a
check, as well as the usual fourths and fifths
as proofs. To beginners it will be easier to set
a third or sixth interval so that the beat rates
are the same as the third or sixth next to it,
then flatten or sharpen the note being set (as
may be required) until the beats are slightly
faster or slower as needed. As with all methods
the beginning is the most important; if the first
three or four steps are set correctly, the rest
comes along easily. Those who are interested
William Braid White
Associate, American. Society of Mechanical
Engineers; Chairman, Wood Industries
Division, A. S. M. E.; Member, American
Physical Society; Member, National Piano
Technicians' Association.
Consulting Engineer to
the Piano Industry
Tonally and Mechanically Correct Scales
Tonal and Technical Surveys of Product
Tonal Betterment Work In Factories
SPECIAL SUMMER COURSE
Jane 1 to August 6, 1926
PIANO TUNING—ACTION
REGULATING AND REPAIRS
CO-OPERATIVE PIANO TUNING SCHOOL
The T. M. C. A. of Philadelphia
1421 Arch Street
References to manufacturers of unquestioned
position in industry
For particulars,
address
209 South State Street, CHICAGO
30
enough to give my method a fair and impartial
test will obtain good results. To those who
feel that 'the C fork is good enough' this tem-
perament will not be of interest.
"The theory of the equal temperament has
been ably explained in The Review in the past,
and in your 'Modern Piano Tuning,' but I might
risk repeating, especially for beginners, that all
major thirds, sixths and fourths are expanded,
minor thirds and fifths contracted. A major
third inverted makes a minor sixth, or vice-
versa. A fourth inverted makes a fifth, or vice-
versa. It will be noticed that beat rates given
are reckoned from 440-A pitch. (Taken from
table by J. C. Deagan of beat rates of each
note E. T.) Figures in parentheses mean the
beats per second (approximately). While such
beat rates are used as a guide, good tuners know
about what rate a beat should be in any interval,
intuitively, without actual counting. With all
temperaments, the gradual increase in beat rates
of the thirds and sixth, etc., from the lowest to
the highest (or the reverse) affords good proof
of the results. (For practical guidance where
the decimal in a beat rate is over .50, the next
highest whole number is used, while for deci-
mals under .50, the next lowest whole number
is used.)
Formula for the Method
A-fork temperament (Richardson) tuned from
D3 to D4. Pitch A-440.
"1. Tune A to fork. (A below middle or
one-lined C.)
"2. Tune F (below) to A a major third about
6.93 beats a second.
"3. Tune D4 to F a major sixth (7.92), or to
A a fourth, about five beats in five seconds.
(Tune with one note and prove with the other
note throughout.)
"4. Tune B flat to D a major third (9.25), or
to F a fourth, about four beats in five seconds.
"5. Tune D3 (down) with its octave above.
Prove by minor third D to F, which should beat
the same as the major sixth (inversion) F to
D (7.92). Also prove with A, a fifth (about
two beats in four seconds.) While these
two proofs are adequate, those who are partic-
ular can use the major third B flat to D,
which inverted makes the minor sixth D to
B flat, which should both beat the same (9.25),
though harder to hear.
"6. Tune F sharp to A sharp (B flat) a major
third (7.34), or to D a major third (5.85). Prove
by comparing thirds, F sharp-A sharp, and F-A,
the third F sharp-A sharp to beat slightly faster.
The major third F sharp-A sharp should beat
slower than minor third D-F. Compare the
thirds, D-F sharp, F sharp-A sharp, B flat
(A sharp)-D, and notice the differences in the
beat progressions as a foundation for the tem-
perament, etc.
"7. Tune C sharp to A, a major third (8.73),
or to F sharp a fifth, about three beats in five
seconds. Compare with adjacent third B flat-D,
which is faster.
"8. Tune E to C sharp, a major sixth (7.48),
or with A a fourth, about four beats in five
seconds. Compare with sixth F-D, which is
slightly faster.
"9. Tune G sharp to E, a major third (6.54),
or a fourth to C sharp, about five beats in five
Tuners
and Repairers
Our new illustrated catalogue of Piano and
Player Hardware Felts and Tools is now
ready. If you haven't received your copy
please let us know.
OTTO R. TREFZ, JR.
2110 Fairmount Ave.
Phila., Pa.
TECHNICAL^SUPPLY DEPARTMENT
William BrendVftutefa/imcal Editor
An Interesting Tuning Method Devised by
Charles E, Richardson, of North Andover
A System That Should Be Read, Studied and Discussed, for It Is a Novel One and One That
Deserves Real Attention—Not the Method of Setting the Temperament But Its
Practical Value That Counts Providing the Results Are Good
I
T is with the greatest pleasure that I intro-
duce to readers the most interesting tuning
method devised by Charles E. Richardson,
of North Andover, Mass. Save Jay editing of
minor details I have found it quite impossible
to improve upon the author's admirable presen-
tation.
I want readers to read, study and frankly
criticize. This is a novel matter and deserves
extended discussion, for which I shall be glad
to give space. Mr. Richardson writes as fol-
lows:
"Tuners should be indebted to you for your
fairness in giving advocates of different systems
of setting temperament a chance to air their
theories and ideas. To me much of the valuable
and instructive matter published has been from
your pen; most of which I have appreciated so
much as to have carefully saved. (See articles
published November 3, 1923; February 21, 1925;
August 22, 1925; August 15, 1925; June 26, 1920;
November 10, 1923; November 14, 1925; Novem-
ber 21, 1925; November 28, 1925; December 5,
1925; November 7, 1925, etc., etc.) Much of
the information received from these has con-
tributed toward the evolution of the ideas pre-
sented below.
"As you have stated, it is not the method
of setting the temperament, but its practical
value which counts, providing the results show
a true and equal temperament. Still, there
seems to have been much discussion relative
to the two leading systems; i. e., the tempera-
ments set respectively between the two Fs and
between the two Cs. Those who use the C-to-C
method assert that the F-to-F system runs too
high to get sure results from the fast-beat rates
therefrom, especially on the upper intervals.
And in that method the system of using fourths
and fifths principally is uncertain. On the other
hand, the F-to-F system advocates claim that
when one has to tune intervals which are on
the lower strings, as in the C-to-C system, that
makes it uncertain, because of the tendency of
these strings to have overtones and false beats,
this being more so with the wound strings.
"The method I present here goes neither too
high nor too low, thereby overcoming in a
measure the objections mentioned above; yet
it has the good points of both temperaments.
"Still, even this is not the principal reason
for creating this method of equal temperament
setting. I devised it primarily for using A as
the starting note rather than C. Of course, any
good tuner can start with any pitch note re-
gardless of what method he uses, and set a
good temperament. But, to have a start where-
by there are proofs from the beginning, is one
of the arguments made for certain systems. A
seems to be the most logical and practical note
to use for the start. In the musical world,
among all singers, all teachers of music, orches-
tra and band leaders, in the trade, and even
among tuners (though they use the C fork) A
is the note used to discuss pitch. Tuners who
use the A fork, especially those whose clientele
is mainly musical, find that they are better un-
derstood and therefore looked upon with more
confidence.
Description of the Method
"It will be noticed in giving the different steps
of this temperament that after the beginning,
with one exception, every third or sixth has a
fourth or fifth as a proof; or if a fourth or fifth
is used to set a note, then a third or sixth can
be used as a proof. While my system is based
principally upon the so-called third and sixth
method, by reversing it, as explained above, the
fourth and fifth idea (slow-beat method), can
be used instead. All good tuners, of course, use
all intervals in fine work. The exception men-
tioned above is when the F sharp is set. This
has as a proof the third from low D which has
a slow beat, and so makes as good a proof as a
fourth or fifth. It will be noticed that while
thirds and sixths may be more easily understood,
especially by beginners, it is possible for a
greater error to arise unnoticed in these inter-
vals than in a fourth or fifth. Therefore, fourths
and fifths are indispensable for fine work, either
to tune by or to prove with.
"Those who use the fourth and fifth method
will feel that in the method shown below there
seems to be much 'jumping around.' This is
to keep each note, as it is tuned, in close rela-
tion to the starting notes, so that any error may
be discovered as soon as possible. At the same
time the intention is to keep A in the middle as
a sort of fulcrum, whereby the whole tempera-
ment is balanced around it.
"It will be observed that each third or sixth
as it is tuned has, in most cases, a similar in-
terval adjacent to it for comparison and as a
check, as well as the usual fourths and fifths
as proofs. To beginners it will be easier to set
a third or sixth interval so that the beat rates
are the same as the third or sixth next to it,
then flatten or sharpen the note being set (as
may be required) until the beats are slightly
faster or slower as needed. As with all methods
the beginning is the most important; if the first
three or four steps are set correctly, the rest
comes along easily. Those who are interested
William Braid White
Associate, American. Society of Mechanical
Engineers; Chairman, Wood Industries
Division, A. S. M. E.; Member, American
Physical Society; Member, National Piano
Technicians' Association.
Consulting Engineer to
the Piano Industry
Tonally and Mechanically Correct Scales
Tonal and Technical Surveys of Product
Tonal Betterment Work In Factories
SPECIAL SUMMER COURSE
Jane 1 to August 6, 1926
PIANO TUNING—ACTION
REGULATING AND REPAIRS
CO-OPERATIVE PIANO TUNING SCHOOL
The T. M. C. A. of Philadelphia
1421 Arch Street
References to manufacturers of unquestioned
position in industry
For particulars,
address
209 South State Street, CHICAGO
30
enough to give my method a fair and impartial
test will obtain good results. To those who
feel that 'the C fork is good enough' this tem-
perament will not be of interest.
"The theory of the equal temperament has
been ably explained in The Review in the past,
and in your 'Modern Piano Tuning,' but I might
risk repeating, especially for beginners, that all
major thirds, sixths and fourths are expanded,
minor thirds and fifths contracted. A major
third inverted makes a minor sixth, or vice-
versa. A fourth inverted makes a fifth, or vice-
versa. It will be noticed that beat rates given
are reckoned from 440-A pitch. (Taken from
table by J. C. Deagan of beat rates of each
note E. T.) Figures in parentheses mean the
beats per second (approximately). While such
beat rates are used as a guide, good tuners know
about what rate a beat should be in any interval,
intuitively, without actual counting. With all
temperaments, the gradual increase in beat rates
of the thirds and sixth, etc., from the lowest to
the highest (or the reverse) affords good proof
of the results. (For practical guidance where
the decimal in a beat rate is over .50, the next
highest whole number is used, while for deci-
mals under .50, the next lowest whole number
is used.)
Formula for the Method
A-fork temperament (Richardson) tuned from
D3 to D4. Pitch A-440.
"1. Tune A to fork. (A below middle or
one-lined C.)
"2. Tune F (below) to A a major third about
6.93 beats a second.
"3. Tune D4 to F a major sixth (7.92), or to
A a fourth, about five beats in five seconds.
(Tune with one note and prove with the other
note throughout.)
"4. Tune B flat to D a major third (9.25), or
to F a fourth, about four beats in five seconds.
"5. Tune D3 (down) with its octave above.
Prove by minor third D to F, which should beat
the same as the major sixth (inversion) F to
D (7.92). Also prove with A, a fifth (about
two beats in four seconds.) While these
two proofs are adequate, those who are partic-
ular can use the major third B flat to D,
which inverted makes the minor sixth D to
B flat, which should both beat the same (9.25),
though harder to hear.
"6. Tune F sharp to A sharp (B flat) a major
third (7.34), or to D a major third (5.85). Prove
by comparing thirds, F sharp-A sharp, and F-A,
the third F sharp-A sharp to beat slightly faster.
The major third F sharp-A sharp should beat
slower than minor third D-F. Compare the
thirds, D-F sharp, F sharp-A sharp, B flat
(A sharp)-D, and notice the differences in the
beat progressions as a foundation for the tem-
perament, etc.
"7. Tune C sharp to A, a major third (8.73),
or to F sharp a fifth, about three beats in five
seconds. Compare with adjacent third B flat-D,
which is faster.
"8. Tune E to C sharp, a major sixth (7.48),
or with A a fourth, about four beats in five
seconds. Compare with sixth F-D, which is
slightly faster.
"9. Tune G sharp to E, a major third (6.54),
or a fourth to C sharp, about five beats in five
Tuners
and Repairers
Our new illustrated catalogue of Piano and
Player Hardware Felts and Tools is now
ready. If you haven't received your copy
please let us know.
OTTO R. TREFZ, JR.
2110 Fairmount Ave.
Phila., Pa.
Future scanning projects are planned by the International Arcade Museum Library (IAML).