Pitch
“Stop playing the major third so flat,” my violin teacher used to always say. Little did I know, however, that I was playing out of tune, we had different interpretations of pitch at first. For one thing, I started the piano six years before I even started to play the violin, let alone take lessons on it. To me, equal temperament was “in-tune”; to my violin teacher, having played in chamber groups mot of his life, equal temperament was not “in tune”. The second factor contributing to my “flatness” was the A4 standards we had. I was used to the A4 at 440Hz, while he, and his chamber group, prefer 444Hz. He believes, and I agree, that this makes their group sound more bright and alive. I have a decent ear, and so at first I was always playing what I knew to be true on the piano, and when I did that, I would become flat. On our third or fourth lesson, I finally asked him, “why do you keep saying that, I am perfectly in tune” (and I got out a piano app on my phone to prove it). He laughed, and then we started a discussion of pitch.
Pitch has changed over time. Focusing mainly on western music, whole number ratio “tuning,” or just intonation, has been around for thousands of years, with its “discovery” generally credited to Pythagoras. Thousands of years later, around the 1500’s mean tone became the standard, although, during the baroque period there were many different types of tuning used. Then about 100 years later, the advent of equal temperament came to. Equal temperament is usually credited to the mathematicians Zhu Zaiyu (in 1584) and Simon Stevin (in 1585), who independently discovered a way to measure an equally tempered 12-tone scale. The idea of equal temperament was played with in the baroque era, but it was not until around 1750 that this system of tuning became prevalent. During the baroque era too, the A4 was tuned to a semitone lower then it is today. This fluctuated between several semitones, eventually getting higher than 500Hz, but was finally regulated and standardized in 1939 at A4 440Hz (though even today this fluctuates slightly). Today, most children grow up unaware of the difference, and simply assume (like myself) that equal temperament and A4 44oHz is correct, but this is simply one interpretation of pitch. The interpretation of pitch can drastically change how a piece is heard, whether the A4 standard is deviated from or if the relationships between notes is different. However, each interpretation of pitch comes with its own set of pros and cons.
If equal temperament has become the standard for most modern western music, it must be better, right? Well, better is arbitrary. With equal temperament comes dissonance. In an equally tempered scale, the major third and the major sixth are both much sharper when compared to just intonation (something mean tone attempts to correct, but falls short(er) with the fourth and the fifth). This means that chords involving these notes will not retain their full harmonic value and instead produce a sound that may slightly warble, which is not as pleasant to listen to. Some instruments, such as the violin family, can play with just intonation, as there are no limitations the semitones that can be played. A common joke about violinists is that like lightning, they never strike the same place twice.
Not all instruments are capable of just intonation, however, as they are incapable of changing between tones either because of frets, like in the guitar, banjo, and viol, causing a single method of tuning to be used, usually equal temperament, or because of pre-set frequencies for each note, like the piano. If, however, only one key is played on and there are almost no accidentals, then just intonation can be used on these instruments. The moment that a key changed is desired, however, depending on the key, the instrument will sound significantly worse than an equal tempered instrument. Equal temperament allows the use of multi-keyed pieces, and a wider variety of good sounding note combinations then with just intonation.
Equal temperament vs. just intonation is not the only important interpretation of pitch; there is also the A4 standard. Usually lower pitches are associated with a “darker” tone, while higher pitches a “brighter” tone. Today, as mentioned earlier, the A4 standard is set at 440Hz, however this was not always the case. Higher notes are more audible, and so many earlier orchestras tuned up so that everyone in the entire concert hall could clearly hear the orchestra. So what could be so bad about changing the starting A4?
The downsides of changing pitch are quite substantial. Many modern wind instruments actually have trouble playing flat and, so changing the pitch will actually cause them to play out of tune, as they are not able to drastically change the pitch. Many modern bands tune to 446Hz for this reason. Then there is the argument from singers. Many operas dance on edge of the vocal range of singers, and so raising the pitch, even a semitone, can become out of the range for the vocalist, meaning that many operas cannot be preformed if the pitch is raised. Finally there is the argument of (as I call it) simplicity. Before the A4 was standardized, the pitch could vary between concerts by over a semitone between two concerts. Not only that, but each town was known for their different tuning pitch. Instrumentalists grew tired of constantly changing their pitch, and many played out of tune, as they were used to one way or the other, or had just finished a concert in another pitch. Point is, simplicity needed to come for the sake of all musicians. For these three reasons, among others, the A4 was standardized at 440Hz.
As I described above, there are many different interpretations each with their own set of pros and cons. If this is the case though, what is “right”? Honestly, I do not believe there is a single method that can be justified for all of music. I believe that there needs to be leeway for the musician to interpret. I also believe that the interpretation of pitch is situational. There are some circumstances, take a string quartet for example, that can play with just intonation. However add in a piano, and now the string players will need to adapt. Pitch will continue to be debated until the end of time, as there is not a single way to interpreted pitch. Though with the current instruments and music equal temperament and an A4 of 440 are favored, the instruments of tomorrow may require an even different tuning system reigniting this same debate. For now though we are left with a puzzling question, “was I actually playing flat?”
Pitch has changed over time. Focusing mainly on western music, whole number ratio “tuning,” or just intonation, has been around for thousands of years, with its “discovery” generally credited to Pythagoras. Thousands of years later, around the 1500’s mean tone became the standard, although, during the baroque period there were many different types of tuning used. Then about 100 years later, the advent of equal temperament came to. Equal temperament is usually credited to the mathematicians Zhu Zaiyu (in 1584) and Simon Stevin (in 1585), who independently discovered a way to measure an equally tempered 12-tone scale. The idea of equal temperament was played with in the baroque era, but it was not until around 1750 that this system of tuning became prevalent. During the baroque era too, the A4 was tuned to a semitone lower then it is today. This fluctuated between several semitones, eventually getting higher than 500Hz, but was finally regulated and standardized in 1939 at A4 440Hz (though even today this fluctuates slightly). Today, most children grow up unaware of the difference, and simply assume (like myself) that equal temperament and A4 44oHz is correct, but this is simply one interpretation of pitch. The interpretation of pitch can drastically change how a piece is heard, whether the A4 standard is deviated from or if the relationships between notes is different. However, each interpretation of pitch comes with its own set of pros and cons.
If equal temperament has become the standard for most modern western music, it must be better, right? Well, better is arbitrary. With equal temperament comes dissonance. In an equally tempered scale, the major third and the major sixth are both much sharper when compared to just intonation (something mean tone attempts to correct, but falls short(er) with the fourth and the fifth). This means that chords involving these notes will not retain their full harmonic value and instead produce a sound that may slightly warble, which is not as pleasant to listen to. Some instruments, such as the violin family, can play with just intonation, as there are no limitations the semitones that can be played. A common joke about violinists is that like lightning, they never strike the same place twice.
Not all instruments are capable of just intonation, however, as they are incapable of changing between tones either because of frets, like in the guitar, banjo, and viol, causing a single method of tuning to be used, usually equal temperament, or because of pre-set frequencies for each note, like the piano. If, however, only one key is played on and there are almost no accidentals, then just intonation can be used on these instruments. The moment that a key changed is desired, however, depending on the key, the instrument will sound significantly worse than an equal tempered instrument. Equal temperament allows the use of multi-keyed pieces, and a wider variety of good sounding note combinations then with just intonation.
Equal temperament vs. just intonation is not the only important interpretation of pitch; there is also the A4 standard. Usually lower pitches are associated with a “darker” tone, while higher pitches a “brighter” tone. Today, as mentioned earlier, the A4 standard is set at 440Hz, however this was not always the case. Higher notes are more audible, and so many earlier orchestras tuned up so that everyone in the entire concert hall could clearly hear the orchestra. So what could be so bad about changing the starting A4?
The downsides of changing pitch are quite substantial. Many modern wind instruments actually have trouble playing flat and, so changing the pitch will actually cause them to play out of tune, as they are not able to drastically change the pitch. Many modern bands tune to 446Hz for this reason. Then there is the argument from singers. Many operas dance on edge of the vocal range of singers, and so raising the pitch, even a semitone, can become out of the range for the vocalist, meaning that many operas cannot be preformed if the pitch is raised. Finally there is the argument of (as I call it) simplicity. Before the A4 was standardized, the pitch could vary between concerts by over a semitone between two concerts. Not only that, but each town was known for their different tuning pitch. Instrumentalists grew tired of constantly changing their pitch, and many played out of tune, as they were used to one way or the other, or had just finished a concert in another pitch. Point is, simplicity needed to come for the sake of all musicians. For these three reasons, among others, the A4 was standardized at 440Hz.
As I described above, there are many different interpretations each with their own set of pros and cons. If this is the case though, what is “right”? Honestly, I do not believe there is a single method that can be justified for all of music. I believe that there needs to be leeway for the musician to interpret. I also believe that the interpretation of pitch is situational. There are some circumstances, take a string quartet for example, that can play with just intonation. However add in a piano, and now the string players will need to adapt. Pitch will continue to be debated until the end of time, as there is not a single way to interpreted pitch. Though with the current instruments and music equal temperament and an A4 of 440 are favored, the instruments of tomorrow may require an even different tuning system reigniting this same debate. For now though we are left with a puzzling question, “was I actually playing flat?”