Standard pitch
What is
a standard pitch?
Generally speaking, a standard pitch is the pitch used as a
frequency reference (in Hz) for tuning a musical instrument. Usually
either a tuning fork or an electric tuner are used, unless you are
capable of determining an absolute pitch. Most electric tuners use
A=440Hz (a1=440Hz) standard by a default, so the pitch an instrument
tuned using these tuners shall be A=440Hz.
Instruments like guitar, lute, and ukulele are often used as a solo
instrument, where the use of the standard pitch is not an absolute
necessity. However, it becomes necessary, once you are to play with
other instruments in duet or ensemble. Even in a solo situation, each
instrument has its own "better sounding" pitch, because any
instrument has a vibrating body which usually has a preferred
frequency to resonate. Adjusting pitch means that string tension is
altered, which also affects sound, sustain, playability of the
instrument, and how much it is stressed (and possibly damaged). If
you have an instrument made in or prior to 19th century, I'd strongly
recommend you to use similar strings and pitch used at the period.
This would lessen the possibility of damaging the instrument and
recreate the sound people of the period had enjoyed.
According to Mr. Taro Takeuchi, a world renowned player of early
stringed instruments, two different pitches coexisted in late 18th
century England. Normal pitch used in homes and at practice was a
half to full tone lower than the concert pitch. A violin method of
the period is said to instruct "It is preferred to use lower pitch in
practice, because lower tension makes easier to play and gentler for
an instrument. It's more effective to limit the use of higher tension
to a large concert hall where volume is required." I've also heard
that A. Segovia used to tune his guitar a full tone higher at
concerts with noisy audience.
Considering the fact that the pitch was chosen accordingly in the
past, "where the instrument had been played" becomes as important a
factor as its structure, the selection of strings, etc. In what
situation a particular instrument used to be played? For whom it was
played? They are intriguing questions to think about...
Various standard pitches
In a modern era, it becomes normal to use A=440Hz (a1=440Hz to be
more specific) as a standard pitch. But the standard pitch used in
the past varied quite a lot depending on the locality and period.
Tuning fork to tune music instruments was invented in early 18th
century, widely used, and many of old ones survived in the world.
Using these surviving specimens, it is possible to reconstruct how
the standard pitch changes. Other than the tuning forks, surviving
pipe organs and their music, surviving wind instruments pitch, etc.
are used for the same purpose. Based on these evidences, heated
arguments are often exchanged on the standard pitch of the past.
According to references I can find, an abbreviated history of the
standard pitch is the following,
In baroque era Germany, multiple standard pitches were
used in 17th and 18th centuries, including the time of J.S. Bach.
Chorton (c.465Hz/c.466Hz/c.440Hz) primarily used in churches and
outdoors and Kammerton (c.392Hz/c.415Hz) used indoors are among them.
Kammerton seemed to be a French pitch originally and brought into
Germany by oppressed French protestants.
A standard pitch of 392Hz was said to be used in the palace of
Versailles in France.
In 1711, John Shore, a trumpeter of the English Court,
invented the tuning fork to tune his lute. It soon became widely used
in the world.
In 1813, A=412Hz was adopted for orchestras in England (this
was later raised to A=452Hz in 1859)
In 1839, A=440 was adopted in Stuttgart, Germany.
In 1858, French government adopted A=448Hz for opera.
In 1859, many tuning forks from all over Europe were brought
to Paris in an effort of unifying the standard pitch. A=435Hz is
adopted as an unified standard pitch.
In 1887, Italian government adopted A=435Hz.
Some said that usual standard pitch was around 430Hz till the later
part of 19th century. But, after the turn of the century, A=440Hz
became widely adopted in the world as "The New Philharmonic Pitch"
starting in 1938. And now, the standard pitch has finally been
settled in 440Hz, though many orchestras currently seem to adopt a
little higher pitch of 442-446Hz.
It is regularly attempted to play Bach's organ music and other
baroque era music in a standard pitch of the period. And the best way
to reproduce the sound of the period for these music has been
actively debated among the musicians. On the contrary, it is also
popular to play baroque era violins in a modern pitch with a proper
structural reinforcement.
Ensemble and pitch
Are you aware the fact that the pitch of an instrument changes as
the temperature? I tried to find a good example of this subject on
the Internet and learned some experimental results are posted on wed
sites for Syakuhachi (Japanese bamboo flute). This change seems to be
often regarded a serious problem among wind players. According to
these sites, the frequency of an instrument rises 4Hz as the
temperature rises 5 degree in Celsius. It is quite possible to have a
large temperature changes depending on a location and season of the
concert. For example, room temperature in Wiener in winter may be
around 10 degree and that in southern Italy in summer may be close to
30, which makes a temperature difference of almost 20 degree
(therefore, 15Hz difference in frequency). It would be hard to keep a
pitch high enough to be proper pitch in winter, without keeping the
instrument warm somehow (especially hard in wind instruments).
How the pitch is adjusted differs from an instrument to another.
Drums, for example, can be adjusted the tension of their skins to
change pitch. In strings instruments, turning tuning pegs or using a
capo are ways to change pitch. In wind instruments, pitch can be
changed by sliding a head tube (thus changing tube length) slightly.
If one tried to change too much, one starts to encounter problems
like octave tone unbalance, etc. So, it is not possible to change
wind instruments' pitch arbitrary. There are many old wind
instruments with different pitches survive. It is probable that the
other instruments in an ensemble had adjusted their pitch to a wind
one, in the same way as orchestras are usually tuned today.
Musicians in the past must have been as conscious about how their
instruments sound as modern counterparts. So, they had to alter pitch
depending on the instrument composition, place (indoor/outdoor), and
season of the concert. I can imagine that it must have been hard to
use one unified standard pitch in every occasion for them.
In an ensemble with wind instruments, string instruments did probably
adjust their pitch to match the one wind instruments could
comfortablly use at each concert.
Tune an instrument in a given pitch
Most of current electric tuners can set the standard pitch in 1Hz
step between A=438Hz and A=445Hz. Then, how can one tune an
instrument with A=415Hz or A=392Hz? I'm sure those who often the
Crane web site are wise enough to answer this question. Yes, lower
the tuning a half tone from A=440Hz to get A=415Hz pitch and lower a
full tone to get A=392Hz, as described below. An octave higher in
tone (8va) is twice in the frequency and an octave lower in tone
(8vb) is a half in frequency. Now, automated chromatic tuners (detect
and display a tone in a half tune step) can be obtained in a low
price, and many of them can show the tone in a finer scale of cents.
One of these for guitars can be purchased from 2000 yen or so.
A =
b1(493.9Hz): a full tone higher than 440Hz (+100cent)
a1#(465Hz): a half tone higher than 440Hz (+50cent)
a1(440Hz): modern standard pitch
g1#(415Hz): a half tone lower than 440Hz (-50cent)
g1(392.0Hz): a full tone lower than 440Hz (-100cent)
f1(349.2Hz)
How tension and gauge of a string changes as
pitch?
I wanted to compare tension and gauge quantitatively and did some
calculations using a slide rule for string.
Suppose a string instruments has a certain "good sounding" tension
(resonance frequency in a broader sense), which is the case for the
most I saw, thinner gauge strings have to be used to obtain a higher
pitch without changing a tension. One the other hand, thicker ones
need to be used to lower the pitch.
For example, an old instrument played in late 18th century with a
pitch of A=392Hz, which is a 6 single stringed guitar with a scale
length of 630 mm and having an optimum tension of 5.0 kg, a 0.6 mm
gut string has to be used to obtain this pitch. In this case,
assuming the total tension is a simple sum of 6 strings with the same
tension, the total will be 30 kg.
What gauge should be chosen to get the same tension
for a different pitch?
Simplifying the results shown below, using 10% thiner string makes
one get a full tone higher.
On the instrument mentioned above, 0.6mm gut string gives A=392 with
string tension of 5.0kg.
On the same instrument, 0.57mm gut string gives A=415Hz with 5.0kg
tension.
On the same instrument, 0.55mm gut string gives A=430Hz with 5.0kg
tension.
On the same instrument, 0.54mm gut string gives A=440Hz with 5.0kg
tension.
On the same instrument, 0.52mm gut string gives A=452Hz with 5.0kg
tension.
How string tension changes as pitch, if one use the same strings?
For example, string tension increases 1.3kg, when the pitch is raised
a full tone without changing the string. So, the total tension on a 6
stringed guitar increases by about 8kg.
With A=392Hz pitch, 0.60mm gut string needs to be strung by a tension
of 5.0kg.
With A=415Hz pitch, 0.60mm gut string needs to be strung by 5.6kg
tension.
With A=430Hz pitch, 0.60mm gut string needs to be strung by 6.1kg
tension.
With A=440Hz pitch, 0.60mm gut string needs to be strung by 6.3kg
tension.
With A=452Hz pitch, 0.60mm gut string needs to be strung by 6.9kg
tension.
[IMPORTANT]
If one happens to use Augustine Regal's 1st string (nylon 0.76mm) on
the same instrument with a modern pitch of A=440Hz, the string
tension would be 8.6kg. The total tension exerted on the guitar in
this case would increase by 22 kg and become 52 kg, which is no
wonder that the instrument would be damaged.
As you can see above, the standard pitch used is an important factor
in selecting strings. It may be interesting to select a new set of
strings considering where you want to play your instruments or
whether the use of the modern pitch is suitable for them or not.
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