Haydn's Haus

[Gurn Blanston]

Well, I just ordered it also. Even the hard copy should be here Friday, so in plenty of time to use for future sonatas essays.

[Jo498]

...

...You split up Chopin's preludes??

*faints*

At least the "raindrop" D flat major is often played apart from the rest; many of the shorter ones usually are not.

[Mandryka]

There's no aesthetic reason not to split them up or change the order of them as far as I know.  Same for The Well Tempered Clavier -- Colin Tilney changes the order.

[Madiel]

There's no aesthetic reason not to split them up or change the order of them as far as I know.  Same for The Well Tempered Clavier -- Colin Tilney changes the order.

I don't think Bach's work and Chopin's are remotely the same in this respect.

No aesthetic reason? Sure, apart from losing all the contrasts of tempo, pitch and volume, there's no reason at all!

EDIT: Try playing preludes 1, 3, 5 and 8 together without preludes 2, 4, 6 and 7. Go on, just try it. Then tell me how the ordering of the preludes is random.

[Karl Henning]

Bach wrote lots of sets of 6, and for him all numbers are meaningful. 2 lots of the trinity maybe.

That would be peculiar theology for Bach.  But 2 and 3 are both theologically significant numbers for the Christian (the dual nature of the Christ, and the Trinity), and 2 and 3 are factors of 6.

[Gurn Blanston]

That would be peculiar theology for Bach.  But 2 and 3 are both theologically significant numbers for the Christian (the dual nature of the Christ, and the Trinity), and 2 and 3 are factors of 6.

6 is also the first perfect number: it is both the sum and the multiple of its factors (1+2+3=6  1*2*3=6)  It was a very important number to people who cared about numbers, and Bach and Haydn both did. Mozart too, for that matter.

[Karl Henning]

6 is also the first perfect number: it is both the sum and the multiple of its factors (1+2+3=6  1*2*3=6)  It was a very important number to people who cared about numbers, and Bach and Haydn both did. Mozart too, for that matter.

Bien sûr.

[kishnevi]

6 is also the first perfect number: it is both the sum and the multiple of its factors (1+2+3=6  1*2*3=6)  It was a very important number to people who cared about numbers, and Bach and Haydn both did. Mozart too, for that matter.

But why not four.
The first square number.
The first nonprime.
And it too can be expressed as the sum of its factors (2×2=2+2)

[Ken B]

But why not four.
And it too can be expressed as the sum of its factors (2×2=2+2)

Because 1 is a factor. That's part of the definition of a perfect number.

[kishnevi]

Because 1 is a factor. That's part of the definition of a perfect number.

If 1 is a factor, so is the number itself.  1×6.
1 is therefore the fudge factor.


[Goes off to form Society for the Recognition of the Number One As The First Perfect Number.

[Mandryka]

How do you know that Haydn cared about numbers?

[Gurn Blanston]

How do you know that Haydn cared about numbers?

It is an inference. It isn't so much that he said so, as that his works are full of little canonic sections, inversions, reflections, cancrizans etc.. And palindromes (retrogrades) too. As well as music, these are all mathematical constructs which couldn't be done by someone without a healthy interest in numbers. Mozart is more overt, there is an interesting story from his sister how, shortly after he started writing music, he one day took a chalk and wrote numbers and formulae all over the walls and floors of the room, he was greatly taken up with them for a long while.



PS - It isn't like I'm going to spend $175 for this book, but you can read samples on Google books, if you Google 'haydn mathematics' and there are some quite interesting inclusions in the samples:

[asin]3642078362[/asin]

[Mandryka]

Ah yes -- there's a difference between being interested in numbers and being interested in numerology. Was Haydn a free-mason, or did he have any other sort of "spiritual"/"metaphysical" things going on for him?

We were getting close to saying that he was publishing in sixes because he saw something particularly cool about 6. 6 is more perfect that 1,2,3,4,5,7 etc. But any mathematician can find very exciting things about any number -- 1 obviously is the identity in multiplication, 2 the only even prime, 3 the first triangular number, 4 the sum of the first two primes . . .

What I'm getting at is that the cool thing which distinguishes 6 from other numbers is probably not a mathematical thing, it's a metaphysical thing (like two trinities or something, so something to do with the numerical values of letters, that sort of thing.) Presumably there's some metaphysical, spiritual, (neo) platonic, masonic hocus pocus underlying why perfect numbers are called "perfect."

[Karl Henning]

Nor need one be a mathematician to be fascinated by numbers;  and any composer who works in the medium for any time understands the usefulness of numbers.  And if they're going to be of use, why not have a little fun with them?

[Gurn Blanston]

Ah yes -- there's a difference between being interested in numbers and being interested in numerology. Was Haydn a free-mason, or did he have any other sort of "spiritual"/"metaphysical" things going on for him?

We were getting close to saying that he was publishing in sixes because he saw something particularly cool about 6. 6 is more perfect that 1,2,3,4,5,7 etc. But any mathematician can find very exciting things about any number -- 1 obviously is the identity in multiplication, 2 the only even prime, 3 the first triangular number, 4 the sum of the first two primes . . .

What I'm getting at is that the cool thing which distinguishes 6 from other numbers is probably not a mathematical thing, it's a metaphysical thing (like two trinities or something, so something to do with the numerical values of letters, that sort of thing.)

He was a Freemason. Sisman does about a page and a half on why 6 & 12 were the magic numbers for opus size. It didn't become 3 until the 1790's, it was 12 for most of the 17th and 18th centuries. Haydn went with 6 because it was a tradition by then. So did Mozart. Bach did too, he didn't invent the concept, he went along with it because there were metaphysical reasons why it made sense to them. IOW, it wasn't just a random or convenient number they (all composers) decided to go with, so to speak. Opuses, and before that 'Books' of works, were all very much of a kind in that regard.

[Gurn Blanston]

Nor need one be a mathematician to be fascinated by numbers;  and any composer who works in the medium for any time understands the usefulness of numbers.  And if they're going to be of use, why not have a little fun with them?

Even I, an arithmephobe, am fascinated by the peculiarities of certain numbers. Like the 'perfect number' thing I wrote above. I only remembered that because I thought it was cool.

[Mandryka]

I wonder where these sets of 6 and 12 begin. You know, even early baroque composers like Chambonnieres,  Frescobaldi and Sweelinck didn't publish in them as far as I recall (I need to check that though to be sure), still less so earlier ones like Tye. And there are plenty of baroque exceptions -- 30 Essercizi, for example,and all those orders by Francois Couperin . . .Neither did CPEB.

It's complicated.

[Gurn Blanston]

I wonder where these sets of 6 and 12 begin. You know, even early baroque composers like Chambonnieres,  Frescobaldi and Sweelinck didn't publish in them as far as I recall (I need to check that though to be sure), still less so earlier ones like Tye. And there are plenty of baroque exceptions -- 30 Essercizi, for example,and all those orders by Francois Couperin . . .Neither did CPEB.

It's complicated.

I really don't want to type out that whole essay, but that info is in there. Probably elsewhere too. Early 18th cent., you have Vivaldi with 12 per opus, Corelli's entire published works consists of 6 opera of 12 each. Then with 6, Bach has 6 suites for keyboard, 6 partitas and sonatas for violin, 6 cello suites, 6 sonatas for violin and harpsichord, 6 Brandenburg concertos... Sisman gives many examples and she didn't even cover all the ones I have at home. Only the big names. Period wise I would say at latest, the Late Baroque, although she mentions several 'Books' of 12 and 24 works too, I just can't remember what they are right now.   

[Madiel]

Interesting all this talk about mathematicallyperfect numbers. The other explanation I'd always heard is that 6 is just short of 7 - now there's a number laden with religious significance. The theory goes that you don't want to be perfect, so you fall just short.

[mszczuj]

I supposed that all was sold by dozens.