Thomas Dressler
New member
The subject of temperament came up in another forum, and it has come up once or twice here, recently in joking. I think it's a very interesting topic and one that needs to be explained for those who are not familiar with the idea. So what I'm going to do in this post is outline some of the basic ideas of temperament.
In reality, the subject is extremely complex, but I'm going to try to make it as simple as possible. (So those who are experienced in the subject may find it over-simple, but try to bear with me because it's also difficult to understand for those who haven't thought about it.)
When tuning a keyboard instrument with 12 notes to an octave, you quickly find that there is a puzzle which it is impossible to solve. That is that if you start with C and tune the fifth (C-G) perfectly in tune, then tune the fifth above that (G-D) perfectly in tune, and continue through the circle of 5ths until you arrive back at C, this ending C is going to be sharper than your original C. And not only that, but when you play thirds, they are going to be WAY sharp. So the basic puzzle is that if you want to cram all 12 notes into an octave, you have to flatten some of your fifths. The amount of "overshoot" when you tune all the fifths pure is called the "Pythagorean Comma." So you have to somehow flatten your fifths somewhere to make up for the comma.
One of the earliest methods, and it's called "Pythagorean," is to make ONE fifth really flat, the amount of the comma, and leave the others pure. You just have to make sure you flatten some obscure fifth that is not commonly used, and make sure you never use it. It's an interesting kind of temperament with its sharp thirds that are almost intolerable to our ears. It works best for music written with the assumption that thirds are dissonant and fifths are the important consonances--Medieval and some early Renaissance music. For any music that uses thirds as a consonance, it sounds pretty bad.
The next option, that used mostly during the Renaissance, is Meantone. It's a complicated concept, but it is much simplified if you use a particular kind of meantone called 1/4 comma. In the case of meantone, the comma is spread out rather than just being hidden in one particular fifth. The idea of spreading the comma out evenly among all of them, called equal temperament, was known to musicians and theorists, but they rejected it, because it makes all of the fifths equally flat, and all of the thirds equally sharp--nothing is pure. They liked pure intervals. So during the Renaissance, the solution to the puzzle was to put more of the comma on some intervals than others. So in some keys, you'd get really nice intervals. As a matter of fact, in Meantone, you get lots of pure thirds, but the fifths are mostly pretty flat. But for their methods of composition, those pure thirds were important. The caveat with it is that you can play in certain keys really well, but others sound pretty bad. From C major up to about three sharps or three flats sound good. They just didn't play music in the other keys.
During the late 17th century, a German theorist named Werckmeister invented another way of tuning which compromised a little more but allowed you to play tolerably in all the keys. His most commonly used temperament, which we usually just call Werckmeister, has better fifths than Meantone, but it doesn't have the pure thirds. And it has the interesting effect that the more sharps or flats you're using for a given key, the more jangly the key sounds. In other words, C major, and F major (the best key in Werckmeister) have a very restful, pure, peaceful sound, more than in equal temperament. As you move to keys like A flat, the intervals are more out of tune and the music jangles more. Werckmeister was a commonly known system of tuning in those days, and while there's no evidence I know of that proves that JS Bach or Buxtehude used it, my own belief is that Buxtehude used it and so did Bach, at least early on. (This is based on experience with their music and how it's written and how it sounds in different temperaments.)
JS Bach became very interesting in writing in all the keys. Remember, the concept of major and minor mode were being more fully developed in his lifetime. He eventually wrote the two sets of keyboard pieces called "The Well-Tempered Clavier" which has pieces written in all the keys. It has been argued on and off in the hundreds of years since his death that he meant for these pieces to be played in equal temperament. Most scholars disagree with this, though it was a common belief until the late 20th century. Recently, Bradley Lehman did an interesting study of the title page of the Well-Tempered Clavier, which seems to have a handwritten puzzle by Bach which explains how he meant the keyboard to be tuned. It does NOT indicate equal temperament. It's interesting, but somewhat complicated. To read more about it click here . You can also listen to my own modification of this temperament on my website . Just look on the soundclips page. You can also hear various other temperaments there.
Not long after the death of JS Bach, there was quite a controversy over the introduction of equal temperament, which spreads the comma out evenly among all the fifths and thirds, so all the keys are equally in/out of tune. One of Bach's students, Kirnberger, adamantly argued that his teacher rejected equal temperament because he liked the differences in key color. Equal makes them all sound the same. This battle was being fought up into the 19th century, with the Germans, for the most part, adopting equal temperament early on. There is actually plenty of evidence that in England and the United States, some organs of English design were being tuned in Meantone up until the mid 19th century. This is a very interesting and possibly very important fact, because it affects the sound of the instruments and also affects what music could have been played on them. The Germans in America, starting with David Tannenberg in the 18th century, were tuning in something very close to equal and possibly real equal.
Music in the 19th century began to use kaleidoscopic changes of key and equal temperament became more common, until by the 20th century, it became almost ubiquitous. It was in the later 20th century that musicians interested in historic performing practices began to rediscover the old temperaments and use them for older music.
Nowadays their use is common enough that when designing an organ, serious consideration needs to be given to what temperament will be used. When playing a harpsichord, one has the luxury of being able to retune for different kinds of music.
This is a basic outline of what temperament is about. It can be a complicated subject, and I welcome both basic questions about it and more advanced discussions.
In reality, the subject is extremely complex, but I'm going to try to make it as simple as possible. (So those who are experienced in the subject may find it over-simple, but try to bear with me because it's also difficult to understand for those who haven't thought about it.)
When tuning a keyboard instrument with 12 notes to an octave, you quickly find that there is a puzzle which it is impossible to solve. That is that if you start with C and tune the fifth (C-G) perfectly in tune, then tune the fifth above that (G-D) perfectly in tune, and continue through the circle of 5ths until you arrive back at C, this ending C is going to be sharper than your original C. And not only that, but when you play thirds, they are going to be WAY sharp. So the basic puzzle is that if you want to cram all 12 notes into an octave, you have to flatten some of your fifths. The amount of "overshoot" when you tune all the fifths pure is called the "Pythagorean Comma." So you have to somehow flatten your fifths somewhere to make up for the comma.
One of the earliest methods, and it's called "Pythagorean," is to make ONE fifth really flat, the amount of the comma, and leave the others pure. You just have to make sure you flatten some obscure fifth that is not commonly used, and make sure you never use it. It's an interesting kind of temperament with its sharp thirds that are almost intolerable to our ears. It works best for music written with the assumption that thirds are dissonant and fifths are the important consonances--Medieval and some early Renaissance music. For any music that uses thirds as a consonance, it sounds pretty bad.
The next option, that used mostly during the Renaissance, is Meantone. It's a complicated concept, but it is much simplified if you use a particular kind of meantone called 1/4 comma. In the case of meantone, the comma is spread out rather than just being hidden in one particular fifth. The idea of spreading the comma out evenly among all of them, called equal temperament, was known to musicians and theorists, but they rejected it, because it makes all of the fifths equally flat, and all of the thirds equally sharp--nothing is pure. They liked pure intervals. So during the Renaissance, the solution to the puzzle was to put more of the comma on some intervals than others. So in some keys, you'd get really nice intervals. As a matter of fact, in Meantone, you get lots of pure thirds, but the fifths are mostly pretty flat. But for their methods of composition, those pure thirds were important. The caveat with it is that you can play in certain keys really well, but others sound pretty bad. From C major up to about three sharps or three flats sound good. They just didn't play music in the other keys.
During the late 17th century, a German theorist named Werckmeister invented another way of tuning which compromised a little more but allowed you to play tolerably in all the keys. His most commonly used temperament, which we usually just call Werckmeister, has better fifths than Meantone, but it doesn't have the pure thirds. And it has the interesting effect that the more sharps or flats you're using for a given key, the more jangly the key sounds. In other words, C major, and F major (the best key in Werckmeister) have a very restful, pure, peaceful sound, more than in equal temperament. As you move to keys like A flat, the intervals are more out of tune and the music jangles more. Werckmeister was a commonly known system of tuning in those days, and while there's no evidence I know of that proves that JS Bach or Buxtehude used it, my own belief is that Buxtehude used it and so did Bach, at least early on. (This is based on experience with their music and how it's written and how it sounds in different temperaments.)
JS Bach became very interesting in writing in all the keys. Remember, the concept of major and minor mode were being more fully developed in his lifetime. He eventually wrote the two sets of keyboard pieces called "The Well-Tempered Clavier" which has pieces written in all the keys. It has been argued on and off in the hundreds of years since his death that he meant for these pieces to be played in equal temperament. Most scholars disagree with this, though it was a common belief until the late 20th century. Recently, Bradley Lehman did an interesting study of the title page of the Well-Tempered Clavier, which seems to have a handwritten puzzle by Bach which explains how he meant the keyboard to be tuned. It does NOT indicate equal temperament. It's interesting, but somewhat complicated. To read more about it click here . You can also listen to my own modification of this temperament on my website . Just look on the soundclips page. You can also hear various other temperaments there.
Not long after the death of JS Bach, there was quite a controversy over the introduction of equal temperament, which spreads the comma out evenly among all the fifths and thirds, so all the keys are equally in/out of tune. One of Bach's students, Kirnberger, adamantly argued that his teacher rejected equal temperament because he liked the differences in key color. Equal makes them all sound the same. This battle was being fought up into the 19th century, with the Germans, for the most part, adopting equal temperament early on. There is actually plenty of evidence that in England and the United States, some organs of English design were being tuned in Meantone up until the mid 19th century. This is a very interesting and possibly very important fact, because it affects the sound of the instruments and also affects what music could have been played on them. The Germans in America, starting with David Tannenberg in the 18th century, were tuning in something very close to equal and possibly real equal.
Music in the 19th century began to use kaleidoscopic changes of key and equal temperament became more common, until by the 20th century, it became almost ubiquitous. It was in the later 20th century that musicians interested in historic performing practices began to rediscover the old temperaments and use them for older music.
Nowadays their use is common enough that when designing an organ, serious consideration needs to be given to what temperament will be used. When playing a harpsichord, one has the luxury of being able to retune for different kinds of music.
This is a basic outline of what temperament is about. It can be a complicated subject, and I welcome both basic questions about it and more advanced discussions.