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 Before delving into the topic of pitch, let's first get a simple understanding of musical tones. 

Musical tones have fixed "frequencies," representing the number of vibrations of sound waves in the air. The unit of frequency used to be referred to as "cycles per second" (CPS), and it's now called "Hertz" (Hz), with both units being equivalent. For instance, 100 Hz means there are 100 vibrations in one second, also expressed as 100 CPS. The faster the vibrations, the higher the numerical value, and the higher the pitch of the sound. The musical scales are derived from fixed ratios of vibrations between different musical tones: an octave is 2:1, a fifth is 3:2, a fourth is 4:3, a major third is 5:4, and a minor third is 6:5. This tuning method is known as just intonation.

From this, we can understand that the relationships between musical tones are relative, not absolute. We need a reference pitch and then find the corresponding notes relative to that pitch to create a scale. This reference pitch is what we call the concert pitch or standard pitch. Before discussing the concept of concert pitch, let me emphasize once again that, as mentioned earlier, relative pitch is the true foundation of musical training, and the notion of absolute pitch is nonexistent. The perception of pitch is human-made and not an inherent trait. Focusing on training absolute pitch goes against the essence of music.

Now, let's talk about the concert pitch. Because concert pitch is a human-made choice rather than a universal law, throughout history, there have been various pitch standards, especially in the centuries before the development of modern measurement techniques. It's easy to understand that in ancient times, people couldn't accurately measure how many vibrations per second a string or a musical pipe produced. Therefore, they had to find various methods to establish consistent pitch standards. Before the invention of tuning forks, pitch fluctuations were, from today's perspective, drastically significant (tuning forks were invented by John Shore of England in 1711, with A=423.5 Hz). I recall reading a document that listed the determined pitches for organ construction in churches across different European cities, which serves as a relatively objective source for understanding historical pitch variations. Although I can't find that specific document at the moment, I can share some similar data I have on hand:

Pitches of La above Middle C in different times and places:

• Venice in the 17th century: A=465 Hz
• France in the 18th century: A=392 Hz
• England in 1720: A=380 Hz
• Hamburg, Leipzig, Weimar (where Bach performed): A=480 Hz
• Handel's pitchfork in 1740: A=422.5 Hz
• Pitchfork in 1780: A=409 Hz

It's known that Handel preferred A=423 Hz, while Mozart liked A=422 Hz. In general, during the Baroque period, pitch variations ranged from the highest A=465 to A=392. Northern Germany tended to be higher, while southern Germany was lower. Venice had higher pitches, while Rome had lower ones.

These objective data should help illustrate the historical "chaos" of the pitch. As musicians began to travel more frequently, this problem became even more serious. The music community then developed various methods to address this issue, such as adjusting pipe organs to match strings and orchestras, or vice versa. It's understandable that pitch standards were a matter of human choice, not a natural occurrence. For makers of wind instruments, if their instruments were slightly higher than those of their competitors, their instruments would sound more brilliant and splendid. String instruments could also be tuned higher to emphasize their brilliance during performances. Allow me to share an example from string instruments:

Paganini's First Violin Concerto is known to be in D major, but when Paganini originally performed it, it was actually in the darker key of E-flat major. The score given to the orchestra was naturally in the more challenging key of E-flat major. However, he tuned the fourth string up a half-step, enabling him to play the piece using the fingerings of D major—adding two open strings and having all four strings tuned a half-step higher than the orchestra's E-flat major—resulting in a more brilliant sound with simpler fingerings. This tuning technique has a specific term called "Scordatura" (mis-tuning or special tuning), and apart from the standard GDAE tuning, all other tunings can be referred to as Scordatura. It was quite common before the Baroque period, and Saint-Saëns' "Danse Macabre" also uses Scordatura by lowering the E string by a half-step.

Nevertheless, the practice of using higher pitches to please audiences had implications, as it led to more frequent string breaks for string players (who were using gut strings at the time). The higher demands of the upper register also created additional pressure for singers. With the increasing development of concerts, the call for a unified pitch became even more urgent.

For more intricate historical details, a larger space would be necessary. Let's focus on the modern concert pitch. In 1859, the French government enacted a law setting A=435 Hz, which was a compromise solution. After all, A=450 Hz would be too high for singers, while A=422 Hz might not be stimulating enough for listeners. This standard became popular in Europe for a considerable period. In 1896, the UK determined A=439 Hz as their standard after consultations and calculations. Although some attempts at standardizing pitch emerged, the true consensus was hard to achieve given the diverse traditions, renowned opera houses, orchestras, and piano makers in different countries. It's quite surprising that the push for an agreement on the pitch in the music world came from radio broadcasting. Thanks to technology, the rise of live broadcasts of musical performances in the 1930s brought conflicting pitch issues between countries and orchestras to the forefront. With the support of the broadcasting industry, a consensus was finally reached between Europe and the United States in 1939. Despite the trend of increasingly higher pitches, they compromised and settled on A=440 Hz, which was very close to the A=439 Hz of the Royal Philharmonic Orchestra. Thus, the international music community finally established the concept of a "standard pitch."

To conclude, it should be understood that the notion of a pitch standard is a human-made choice, not a naturally ordained principle or something that has existed since antiquity. One might humorously say that if you don't need to communicate with others through music, you can adjust the pitch as you, please. However, in reality, no one would want their pitch to be out of harmony with others.

Since it's a human-made concept, practical implementation is challenging (variations in temperature and humidity on stage can directly affect pitch). Therefore, calling it a "rule" might be less accurate than considering it a "suggestion." Although the International Organization for Standardization reaffirmed A=440 Hz as ISO 16 in 1955 for the so-called Concert Pitch, British orchestras maintain this pitch. However, some American orchestras like the New York Philharmonic, and Boston Symphony Orchestra, as well as certain European countries including France, Italy, Denmark, and Hungary, prefer A=442 Hz for their concert pitch. Currently, almost all German, Austrian, and mainland European orchestras use A=443 Hz. The Berlin Philharmonic slightly lowered its pitch from the earlier A=445 Hz to A=443 Hz. The Vienna Philharmonic uses A=444 Hz. I remember that in 1993, when the Taipei Philharmonic performed at the Vienna Musikverein, the piano was tuned to A=445 Hz.

Furthermore, the modern trend of historically informed performance practice often employs A=415 Hz, often referred to as Baroque pitch. However, returning to the data mentioned at the beginning, it's important to recognize that this Baroque pitch is another form of "compromise" rather than an absolute standard. Under the general circumstance of A=440 Hz, A=415 Hz is a whole half-step lower in equal temperament. This compromise has a significant advantage—when performing with both Baroque and modern instruments, a simple half-step transposition can bridge the gap, allowing collaboration without the need for returning or acquiring different instruments.

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