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.
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)
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.
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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