Anyone know?

On an OU course I'm currently doing the opinion has been stated that the 48 preludes and fugues were written merely as exercises... I'm not so sure.

I'd be interested to hear if anyone knows, one way or t'other, or has any evidence, or opinions or theories.

Very curious!

(And no, don't worry, you're not helping me cheat on a TMA or anything! )

edit: ARGH! I am tireder than I thought, I can't believe I wrote right not write in the subject title *hides face in shame*

Equal temperament.

Yes, I'm aware of the well-tempered aspect of it (though I think well tempered differs from equal temprament does it not??) - I mean, what were the pieces intended for? Simply to show off his well tempered clavier? As studies for students? As potential concert pieces?

edit: ARGH! I am tireder than I thought, I can't believe I wrote right not write in the subject title *hides face in shame*

Hi Sarah-flute
On the title page for the first volume of the Well-Tempered Clavier Back wrote that they were "for the profit and use of musical youth deserving instruction and especially for the pastime of those who are already skilled in this study". They are an absolute treasure trove waiting to be explored. I love them

"for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study".

Yes, well tempered is slightly different from equal temperament. *Gold star awarded to sarah-flute*

Oops: margaret got there first!

Thanks, Margaret - that's a good starting point

So... for study but also for pleasure, would you say?

I can just about manage the easier C major prelude - I'm a bit far from being able to explore them Thank you for the quote, I didn't even realise there was such a thing related to the 48

edit: thanks FC too

I have always been lead to believe that "tempered" means "tuned" . Therefore, "The Well Tuned Klavier". Apparently, Bach liked all his students pianos to be in tune, so developed an excersise for each key so that he knew a student could play any one of them in tune.

What someone meant by "in tune" was changing though, wasn't it? The 48 demonstrated the possibility of a piano being "in tune" in any key, whereas just tuning or temperament would not allow such flexibility.

Do you see them as just exercises?

I guess what I am trying to work out is if Bach wrote them as exercises, just to demonstrate temperament, or whether he intended them also for the concert platform

(Tempered, I think, does indeed refer to tuning, but in terms of just vs well tempered, or the equal temperament we use today...)

So far as I'm aware the general consensus seems to be that he didn't write them as a coherent group at all: The two books were assembled (separately) from available material, orignally written for a variety of keyboard instruments and only put together (in 2 different collections 22 years apart) as an exercise to show off the concept of even temperament.

Taking as my source the sleeve notes from Glen Gould's 1975 recording: "Stylistic criticism has proved that the Well-Tempered Clavier cannot possibly have been composed in a single sequence, particularly not in the present cyclical configuration."

Ahhhh, now that is interesting isn't it!

I did know they were two collections, but did not know that the two books themselves were collated from other work... so presumably it's likely that some were originally intended as concert pieces, but it's equally possible that some were not....

Glad to be of service: The Glen Gould recording sleeve notes/booklet say a lot more than that, as you might expect, but they are quite long and I'm not going to plagiarize copy them here.

I find sleeve notes a valuable source of information generally.

I just wish Glen Gould didn't hum through some of the recordings!

I may ask around and see if anyone close by has a copy of the CD so I can take a butcher's at the notes myself. Thanks for the info

A lot more complicated than that I'm afraid!!

Well tempered refers to a tuning system which allowed complex chords to be played in any key. Before then instruments had to be tuned to a key, and were very limited in the other keys they could "visit" during a peice.

This is all linked to the mathematics of vibration and, to be honest, I understand it in mathematical terms better than in musical terms.

If you tune a string to (say) C, then tune a second one to the second harmonic of the first (i.e. to G), and a third one to the second harmonic of than one (i.e to D) you will end up with three strings each tuned a 5th apart.

You could play E as the second harmonic of string 3, the third harmonic of string 2 or the fourth harmonic of string 1. However, as the harmonic series is based on a recursive numbers (i.e. like 1 divided by 3), these three verisons of "E" will all be ever so slightly slightly different to each other.

The further into the harmonic series you go, the worse this problem gets until you run up against the "comma of pythagarus" (of triangle fame) where you just end up with discords.

Early music worked around this problem by simply avoinding notes in the harmonic series. Renaisance musicains leared how to cheat by slightly "detuning" each string so that the thirds and sixths weren't too far out of tune with each other which opened up a whole new world of music. "Well tempered" tuning was the first system that allowed ytou to use all the notes so that you could modulate to any key from any other.

Equal temprament is the modern equivalent. In actual fact they actually involve setting the strings ever so slightly out of tune so that you avoid blatent discords.

If you write music that has no harmony, this is not a problem, you don't need equanl temparment and you can tune all you strings (or wahtever) to the natural (pythagorian) harmonic series. This is why eastern music often uses a lot more complex rhythms than western music - their musical cultures avoided the problems involved in harmony and concentrated more on rhythm.

Not well explained I know. Amandal is a string player and a physiscist so she'll do a better job I'm sure. That or do a web search!

Ooh, a Bach WTC topic. Thankfully it's a 3-day weekend .

As has been mentioned, well-tempered is not the same as equal-tempered - the latter did not become popular until the 19th century if I recall. The last to be converted were the organists, amongst whom equal temperament was referred to as 'that barbaric temperament'.

If you look at the cover of the WTC*, you'll see a series of curly lines. These can be interpreted as the setup for a temperament - how to tune the notes with respect to each other. The resulting temperament sounds quite good, and is very close to some of the temperaments found independently by theoreticians. The theory about the curly lines temperament is backed up by an analysis of the harmonic intervals occurring throughout the WTC - it can be seen that Bach doesn't often use the intervals that sound naff in 'his' temperament. For instance, he avoids the fifth between B and F# - the B major prelude opens with a major third between B and D# in the left hand, and a B in the right. It isn't until several beats time that the F# is introduced above the B, by which point the B has died down in volume and the slightly awkward interval isn't as apparent.

As has also been mentioned, the WTC was in part assembled from other pieces. This can be seen from the prelude and fugue where (if I recall, the book is on the other side of the room) the prelude is in F# major and the fugue is in Gb major. This pairing were obtained by sharpening an existing prelude in F and flattening a fugue in G.

* Bach referred to them as WTC and WTC II, not WTC I and WTC II

True, but (copying again, but paraphrasing) there are quite a few other "Temperaments" (tunings) which were generally in use about the baroque time:

Equal Temperament has each octave didvided into 12 equal steps: Each interval produces about the some amount of slight dissonance.

Pythagorean Temperament, invented by Pythagoras, has no dissonance in 4ths and 5ths. 3rds produce dissonance but melodies are euphnious

Just Major Temperament (and Just Minor Temperatment) eliminate dissonances in 3rds and 5ths. Doesn't do melody and can't be transposed but is said to be capable of beautiful sonority (!)

Mean Tone Temperament is a compromised Just tuning to allow transposition.

Werckmeister Temperament or (Well-Tempered) combines Mean Tone and Pythagorean. Perfomances possible in all keys

Kirnberger Temperament is an improvement of Mean Tone and Just tunings: Perfomances possible in all keys


There, now I know all that, what does it mean? Frankly, I'm not sure: I understand the physics of the difference between harmonic sequence tuning and Well tempered or Equal Tempered, and can hear it. I know there is a diferrence between Well Tempered and Equal Tempered: I'm just not sure what it is or whether I could hear it if I did!!

Edit: I just tried out all of these on the digital piano and I was right: I can't hear a difference between Equal Tempered and Well Tempered (= Werkmeister Tempered)

I think the Well-tempered clavier is written for his sons' studies.
By the way, is there any pieces in this book is about Grade 7? I would like to learn some of Bach's pieces.

Yes but even if you accept that (and I don't think most people do) his sons included CPE, JC and WF Bach all of whom were noted keyboard players (and composers) in their own right, so I for one don't feel too bad about not finding TWC easy!

As for grade 7, I've never seen one listed below grade 8, but that may well be because they list the prelude and the fugue together. I would have thought that several of the preludes on their own might well be grade 7 or less, the C major from TWC (bk1, no1) for example

Bach hated mean tone temperament. Hate probably isn't a strong enough word, he disliked it that much....



The trick is to play fifths and major thirds, switching between the two. The difference becomes apparent soon enough. I find the major third between B and D# jars in equal temperament - given all the thirds are the same, I've always found this to be quite curious.... I'm frustrated by the few choices of temperament on digital pianos, I guess it's not really a major selling point of the product - 'Now with Young II temperament' .

My digital piano defaults to equal temperament but can be switched to all the ones I mentioned - I got the info from the instruction manual!!

I have tried the specific intervals you menitoned in both Equal and Werkmeister, comparing the two: It takes a few seconds to switch between the two temperaments, so maybe I'm missing something but I have to say that whilst any passing bat may have fallen screaming to the floor with it's hands over its ears (!), I still can't convince myself that I can hear a difference.

Also, I agree with Bach!

passing bat may have fallen screaming to the floor with it's hands over its ears



WTC 1 + 2

I'm sure these were written for performance as well as private study. There are so many beautiful pieces. Definitely a desert island pick for me. I particularly like the minor pieces in flats. Something really compelling in the harmonies.

I've heard about a piano competition where the competitors had to memorise the entire WTC and be prepared to play any of the P + Fs on request. Apparently Shostakovich was inspired to write his set of 48 as a result. Anyone know the details of the story?

My opinion, totally uninformed as it is , is also that they're not "just studies".

Shosti I think was judging the 1950 Bach centenary competition and heard Tatiana Nikolayeva play the Bach. He wrote his specifically for her to play, but he only wrote 24. Maybe he intended to write more.

Actually Tatiana Nikolayeva died whilst playing the Shostakovich Preludes and Fugues at a public concert in San Francisco in 1993. How sad, but appropriate somehow.

Edit: Found this They were not required to memorise all 48 but Nikolayeva did.

I don't think they did use equal temperament that much in baroque times.
My husband can tell the difference between Werkmeister and equal, and tunes these both by ear, as well as Vallotti, Young, temperament ordinaire, the one which seems to be indicated on that title page of the 48 as YAP says, and a few others...
I'm not sure that well tempered is really a temperament as such, only a description of accurate tuning in general, and perhaps reflecting Bach's preferred temperament, which was not completely equal, but closer to equal than mean-tone is.

Thanks for that. I'm hopeless at remembering the details of anecdotes!

I didn't realize they were that difficult

Actually I ought to correct that statement as after Googling around I found this was not actually totally true, so in the interests of absolute accuracy...

"Tatiana Nikolayeva was stricken with a cerebral hemorrhage while playing the Shostakovich Preludes and Fugues at a public concert in San Francisco on November 13, 1993: she died 9 days later."

That's probably what would happen to me if I tried to play Shostakovich fugues....

</bad taste>

This thread is so interesting! I've borrowed the 2nd volume of the Well Tempered Clavier from my piano teacher, and I'm just about to get the first one! I wondered what the title meant so this thread has helped me to understand it!

I don't think it's right to say this was "invented" by pythagarus - pythagorean temperament is just a part of nature that he was able to describe in mathematical terms. Bit like saying pythagarus "invented" right angle triangles.

I was fishing on a windy loch yesterday - the noise made by a the wid blowing through a modern braided fishing line held taut by a slight bend in a modern carbon fibre rod is unbeliveble. The way the sound jumps betwen the harmonics (pythagorean) as the wind changes is really haunting sound. I was fishing with my piano tuner - he'd never fished with braided lines before so had never heard it and was amzed. It really is weird.

For some reason I find that statement very amusing! I wonder how many people go fishing with their piano tuner.

I go skating with my harpsichord tuner....

Backwards?

In a sense I suppose you're right, and as I admitted I was plagiarising paraphrasing the instruction manual for my digital keyboard, which actually says it was "devised" by Pythagoras. I suppose there may be a fine line between "devised" and "invented" but I'm not sure! On the other hand, musical instruments that need tuning don't exist in nature so I supose the first person to actually codify a method of tuning could certainly be said to have devised it, if not invented it.

Besides, whilst nobody would seriously claim he invented right angled triangles, he was the first person to prove that, for ALL right angled triangles, the square on the hypoteneuse is the sum of the squares on the other two sides. Since there is more than one possible proof (the one I was taught isn't his) I don't see why he can't claim to have "devised" the proof, or (if you are that way inclined) "invented" it!

He took his Maths seriously too: When a pupil proved that the square root of 2 is irrational, thereby proving the existence of irrational numbers, Pythagoras was so upset that he had the pupil tortured to death. I'm glad I never had teachers like that!

And there was me thinking that Pythagoras was a good mathematician... surely every mathematician knows that a good proof is one without a disproof! Hadn't he heard of Pi? And what about 'e'? Or was it just the fact that root(2), an 'imperfect' number, was the ratio for opposite/adjacent to the hypotenuse in an isosceles right-angled triangle?

In relation to the thread title... hehe, I recall I was rather shocked when I found that Sarah was accountable for this mistake! I wouldn't worry about it though... I recall the old days of the forums when there was no Forums Cafe, when I wrote '4' interchangeabley with the word 'for' in a certain thread title! Not to mention when I did not capitalise the first letter of every post too! Now that's embarassing when I look back on it!

~Wobby~

I had something similar with a roof-mounted car aerial which had been knocked into the vertical position after a carwash. At a certain speed it hummed a note - let's call it C. At a higher speed a D was added to the C. Faster again and an E came in. Eventually an F# joined in, at which point the sound became very eerie.

If anyone starts making jokes about tuna here I shall shoot them. I mean it. I am armed.

Perhaps he was just being tetchy.

Bach the piano composer?

News-to-me-ly,
GC

Eight years ago I bought a book called The Short-Tempered Clavier (Preludes and Fugues in all the major and minor keys except the really hard ones). It was composed by JSB's youngest son (PDQ Bach) and is edited for post-modern fingers by Professor Peter Schickele. The performance notes (in five languages) are as amusing as the pieces!

For newcomers to PDQ Bach I would also recommend the 1712 Overture for Really Large Orchestra. A recording with Professor Schickele conducting the Greater Hoople Off-Season Philharmonic is available in all good music outlets.

Yep, that too....
Needless to say, we leave the harpsichord at home; as it has three legs, it would only become ill-tempered if it tried to skate on one leg...

Please note - my reference to tuna is in my signature - the joke predates this thread

Quite so. Pass, friend.

No but vibrations exist - the wind whistles around things and makes those hauting noises and the reason for that is that any vibrating body has a natural frequencey (the fundemental) and it can make a number of different sounds that are harmonics of that note.

People have found stone age flutes / whistles made out of bits of bone. You can work out how people wanted to tune them because they have found discarded ones where the flute maker drilled a hole in the wrong place, put the whole thing out of tune and so gave up and started a new one. There was a sound clip on the nature web site a while ago so you could listen to them. They were tuned to a "natural" harmonic series that was eventually described in mathematical terms by pythagarus.

Strangely enough I met my piano tuner thriough hsi tuning my piano, it turned out we were both keen on fishing and we ended up doing a lot of fishing trips together!

If I were you, I'd get a copy of Angela Hewitt's recording of the 48. Not only is her interpretation less, how shall we say, idiosyncratic, but the sleeve notes are extremely interesting, copious and illuminating.

Edward

I suspect the whole temperament debate is a bit of a red herring, at least as far as the question of whether WTC is 'merely' a set of exercises goes. The idea that it is a set of exercises in composing music for a particular tuning can probably be dismissed on the grounds that the pieces were written over a long period of time rather than as a cohesive body of work.

On the other hand, Bach was composing counterpoint which is always an exercise in the disciplined application of a strict set of rules. Counterpoint = exercise (whatever the temperament). And as the rules of counterpoint came into being because they codify music which is good to hear, it is inevitable that the results should lend themselves to being performed. Counterpoint = performability (whatever the temperament - so long as it is written in a suitable key for the given temperament).

I do not agree with the suggestion, implied by the word 'merely', that 'exercise' and 'great music' are somehow incompatible or mutually exclusive. Yes, they are exercises (in counterpoint) and yes they are great music. It's the word 'merely' that's wrong, imo.

Best wishes

barry

Perhaps you could burble on in an OU TMA about how these two things can be the same?! For some psychologists, true happiness is experienced when we are in a state of 'flow' - ie., totally engaged in what we are doing, intellectually absorbed, experiencing what we are doing as new and creative. So it is perfectly possible to play studies as truly great as these for pleasure, or for Bach to have gained great pleasure from the rigorous challenge of their creation. Given the chap had several more brains than normal and in the Art of Fugue produced several nigh impossibilities off his own bat well above an dbeyond the original brief/ challenge , he must have had to work quite hard to get into this state of flow....

I checked James Gaines on this (Evening in the Palace of reason). Apparently the first book was written while in the detention centre of the County Judge at Weimar. Note from the ducal records:

On November 6 1717, the quondam concertmaster and organist Bach was confined to the County Judge's place of detention for too stubbornly forcing the issue of his dismissal

Gaines puts this together with the contemporary Gerber's note that the WTC was put together in "a place where ennui, boredom and the absence of any kind of musical instrument forced him to resort to this pastime".

So it was all just a spot of musical timewasting on a par with suduko then!

Returning to thread-ly

If anyone's interested in hearing a stunning performance of the 48, Angela Hewitt's doing it in 2 recitals at the RFH next year & tickets are already going very fast. If you book online, you can choose your seat. I've booked choir seats for both not the most comfortable, but you get a wonderful close-up view.

Oh yes - love Angela's playing of the 48! *salivating*

Re: "merely" - not my sentiment - person in question was asking why we listened to them as concert music when they "are only exercises".


I was shocked when I realised I'd made it


Hehehehe sounds brilliant!




Thanks for the illuminating thoughts, folks.

StuMac: interesting about the harmonics, thanks!

Robodoc: you will find the harmonic series quite easily by overblowing on your flute: you should be able to get a few of them and as your embouchure develops you will find more. I can just about manage a high Bb from the low C, but I wouldn't recommend trying for that just yet - but it does vividly demonstrate StuMac's point about the natural harmonic series. In order to play in tune with what modern ears expect to hear, one actually has to modify certain of the very high harmonics to play the top register in tune.