Thank you for the careful explanation and translation. Not being a musician, I think I will find the upcoming demonstration very helpful in understanding historical temperaments more.
An important aspect: equally pure sounding keys doesn't necessarily mean the fifth all are equal. E.g. a bad fifth with a very good major third can give the same impression of pureness of the chord than a better fifth with a less good third. CPE didn't write explicitly about physical facts 'only' about equally pure sounding keys.
Yes, but not so much that some fifths would sound bad: if you tune all fifths proportionally perfect (so with adjustments for the increase in beats, so not all exactly 1/12 what the result is when tuned on ear only), than everything will be perfectly equal, at least as much as is achievable. You're right: that sentence is important. Gleich rein. I believe more and more that he used a kind of temperament in which every key did sound really well, but some a bit better. Joris Potvlieghe said to me that he tuned (if for Bach), in a way all fifths were narrowed a bit (= what I do), but than make some thirds slightly better than others, not too much, not checking the fifths anymore, but then you have a situation where some fifths again are pure. Interesting, not?
Sounds to me that this is Kirnberger's 3rd temperament, very easy to tune. The 'old' method he may be referring to is likely to be one of the Werckmeister. For earlier music, one would tune in Zarlino (for, say, Frescobaldi), and Tempérament Ordinaire for Couperin, Froberger, Rameau, Royer.
No doubt I believe CPEBach's temperament is an almost equal temperament with some very very slight differences. One thing the HIP did kind of disservice is to connect temperaments of the 17th century to 18th c. music, that had evolved much in a few decades
I think it is indisputable that CPE Bach intended there to be some pure fifths as most, not all, are to be narrowed slightly. For all keys to sound equally pure it does not follow that the temperament needs to be equal. Impurities have to exist in at least some chords whatever temperament is chosen and sometimes quite large impurities can be well hidden amongst purer chords. I think all keys should sound equally good but at the same time have their own unique character which derives primarily from subtle variation of interval sizes. But then how do you define sounding equally good? If the 1722 "squiggle" of JS Bach is a temperament guide and not just ornamentation (and it does seem a bit random and asymmetrical for pure ornament) there are three loops that do not have smaller loops within them. Would that signify three untempered, i.e. pure, fifths? If so, CPE is probably maintaining a family tradition!
Bottom line I believe is the fact that if you would like to expand your daily practice to more remote keys (btw, who could do that at the time?), you have to compromise in tuning, since, that we can be fairly sure about, intervals really out of tune were not accepted? So Werckmeister III for the WTC is out of the picture with this, not saying that one should not apply it, only, not wanting to connect that to the context of that time. The 1722 title page to me, is not giving any clue at all, it is a bit of fantasy. Why would anyone feel the need to mystify something that was just clear? The other aspect though is, not to look at these from the numbers of beats, or from calculation, but from the practice. Starting from the Wohltemperirte Harmonia of Werckmeister, narrowing down all fifths by 1/12 is not so remote from tempering most fifths. It are nuances, if one would still like to favor some keys slightly above another. But than you have Bartold Fritz, a book that apparently was highly recommended by Bach, talking about equal temperament. And not surprising, since it is very, very close.
Thank you for this - very insightful. I am curious also about 'reine harmonie, as the Dutch expression goes. In relation to your discssion around C.P.E. Bach, how do we understand "rein?" In other words, do we mean strict mathematical purity of the thirds? Or does Bach imply there is, so to speak, a "lesser" purity, one which is very slightly modified from the mathematical model. As you point out it is quite possible to tune in such a way that one can play in all 24 keys, yet some will still sound less "pure" than others. Was this a step along the route toward equal temperament in which all keys sound equally bad, so to speak?
Hi Thomas, I believe I mention the term 'rein' somewhere in the middle, rein means the opposite of out of tune. It is not 'without beats' as a 'pure fifth'. At least, so do I read it.
Yes. I read it the same way, although Dutch is not my native language. I've also wondered about the interpretation of this word with regard to the famous 'Alkmaar orgelstrijd' and its debate over 'reine harmonie.' Some have interpreted the term as meaning quarter comma meantone, while others aren't so certain. Your definition seems to make the most sense to me.
Great lecture. I don't like ET personally, but I have to agree with you now that the CPEB Bach book points more to ET than anything else. The "most fifths narrow" indeed can be seen as a practical way of tuning approximate ET as it's hard to get them all equally narrow. I even tuned my harpsichord in ET for a day. Not bad, but in particular in the h-moll French suite the sound is a bit bland; I miss those wide poignant subdominant thirds (C#E#), but I can imagine some people are glad they are not there. CPEB's book is available on google books and even searchable! Nowadays with more and more historical manuscripts becoming available to everyone we no longer have to rely on "respected Doctor Professors" to tell us what the historical evidence is for tuning and we can draw our own conclusions. Wim, do you know where I can obtain the 1707 Werckmeister article? The 1691 article is readily available but I've not succeeded in finding the 1707 article.
all this fuss about the exact nuances of cpe's tuning ^^ it's all in the text: tune until you are pure enough. which will be purer than anyone could possibly play on a violin anyway
Well there is lot of discussion on that passage, that as I read is nothing more than a practical description of an almost equal temperament. Purer than a violin... well not so much I'd say, a keyboard cannot beat a violin in this regard, not even close
All i know is that music wasn’t dull like 12tet as we have today.
Thank you for the careful explanation and translation. Not being a musician, I think I will find the upcoming demonstration very helpful in understanding historical temperaments more.
That I hope too, Alex, thanks for watching !
An important aspect: equally pure sounding keys doesn't necessarily mean the fifth all are equal. E.g. a bad fifth with a very good major third can give the same impression of pureness of the chord than a better fifth with a less good third. CPE didn't write explicitly about physical facts 'only' about equally pure sounding keys.
Yes, but not so much that some fifths would sound bad: if you tune all fifths proportionally perfect (so with adjustments for the increase in beats, so not all exactly 1/12 what the result is when tuned on ear only), than everything will be perfectly equal, at least as much as is achievable. You're right: that sentence is important. Gleich rein. I believe more and more that he used a kind of temperament in which every key did sound really well, but some a bit better. Joris Potvlieghe said to me that he tuned (if for Bach), in a way all fifths were narrowed a bit (= what I do), but than make some thirds slightly better than others, not too much, not checking the fifths anymore, but then you have a situation where some fifths again are pure. Interesting, not?
Gleich rein could really mean all equally pure, that is, all are balanced to an equally high level of (almost) purity.
I'll admit: I want to believe that Lehman is wright. To my taste, Bach-Lehman sounds bright and full of life. But I'm not an expert.
Thanks Manel !
Dude, those candles are made of win! Who can argue with a scolar studying by candlelight?
It's so nice standing there... the chapel goes way back before the Bach family
Sounds to me that this is Kirnberger's 3rd temperament, very easy to tune. The 'old' method he may be referring to is likely to be one of the Werckmeister. For earlier music, one would tune in Zarlino (for, say, Frescobaldi), and Tempérament Ordinaire for Couperin, Froberger, Rameau, Royer.
No doubt I believe CPEBach's temperament is an almost equal temperament with some very very slight differences. One thing the HIP did kind of disservice is to connect temperaments of the 17th century to 18th c. music, that had evolved much in a few decades
I think it is indisputable that CPE Bach intended there to be some pure fifths as most, not all, are to be narrowed slightly. For all keys to sound equally pure it does not follow that the temperament needs to be equal. Impurities have to exist in at least some chords whatever temperament is chosen and sometimes quite large impurities can be well hidden amongst purer chords. I think all keys should sound equally good but at the same time have their own unique character which derives primarily from subtle variation of interval sizes. But then how do you define sounding equally good? If the 1722 "squiggle" of JS Bach is a temperament guide and not just ornamentation (and it does seem a bit random and asymmetrical for pure ornament) there are three loops that do not have smaller loops within them. Would that signify three untempered, i.e. pure, fifths? If so, CPE is probably maintaining a family tradition!
Bottom line I believe is the fact that if you would like to expand your daily practice to more remote keys (btw, who could do that at the time?), you have to compromise in tuning, since, that we can be fairly sure about, intervals really out of tune were not accepted? So Werckmeister III for the WTC is out of the picture with this, not saying that one should not apply it, only, not wanting to connect that to the context of that time. The 1722 title page to me, is not giving any clue at all, it is a bit of fantasy. Why would anyone feel the need to mystify something that was just clear? The other aspect though is, not to look at these from the numbers of beats, or from calculation, but from the practice. Starting from the Wohltemperirte Harmonia of Werckmeister, narrowing down all fifths by 1/12 is not so remote from tempering most fifths. It are nuances, if one would still like to favor some keys slightly above another. But than you have Bartold Fritz, a book that apparently was highly recommended by Bach, talking about equal temperament. And not surprising, since it is very, very close.
Thank you for this - very insightful. I am curious also about 'reine harmonie, as the Dutch expression goes. In relation to your discssion around C.P.E. Bach, how do we understand "rein?" In other words, do we mean strict mathematical purity of the thirds? Or does Bach imply there is, so to speak, a "lesser" purity, one which is very slightly modified from the mathematical model. As you point out it is quite possible to tune in such a way that one can play in all 24 keys, yet some will still sound less "pure" than others. Was this a step along the route toward equal temperament in which all keys sound equally bad, so to speak?
Hi Thomas, I believe I mention the term 'rein' somewhere in the middle, rein means the opposite of out of tune. It is not 'without beats' as a 'pure fifth'. At least, so do I read it.
Yes. I read it the same way, although Dutch is not my native language. I've also wondered about the interpretation of this word with regard to the famous 'Alkmaar orgelstrijd' and its debate over 'reine harmonie.' Some have interpreted the term as meaning quarter comma meantone, while others aren't so certain. Your definition seems to make the most sense to me.
Great lecture.
I don't like ET personally, but I have to agree with you now that the CPEB Bach book points more to ET than anything else. The "most fifths narrow" indeed can be seen as a practical way of tuning approximate ET as it's hard to get them all equally narrow. I even tuned my harpsichord in ET for a day. Not bad, but in particular in the h-moll French suite the sound is a bit bland; I miss those wide poignant subdominant thirds (C#E#), but I can imagine some people are glad they are not there.
CPEB's book is available on google books and even searchable! Nowadays with more and more historical manuscripts becoming available to everyone we no longer have to rely on "respected Doctor Professors" to tell us what the historical evidence is for tuning and we can draw our own conclusions.
Wim, do you know where I can obtain the 1707 Werckmeister article? The 1691 article is readily available but I've not succeeded in finding the 1707 article.
Great to read, thank you very much for the thoughts!
3:35
all this fuss about the exact nuances of cpe's tuning ^^ it's all in the text: tune until you are pure enough. which will be purer than anyone could possibly play on a violin anyway
Well there is lot of discussion on that passage, that as I read is nothing more than a practical description of an almost equal temperament. Purer than a violin... well not so much I'd say, a keyboard cannot beat a violin in this regard, not even close