Re: [tuning-math] Digest Number 863

Carl wrote:

> >> Is the final fugue of the WTC1 a serial piece? Why or why not?
> >
> >I feel like this is a trick question, but: No, because it's not written
> >with a tone-row. Can you derive the countersubject from the subject via
> >serial procedures?
>
> No trick questions from me, unless I'm tricking myself!
>
> So does the subject fail to be a tone row because some notes are used
> more than once before all of them are used?

No. There are examples of 5-note tone rows (Stravinsky's setting of "Do
Not Go Gentle..."), 18-note rows (Schoenberg's String Trio, a really
beautiful piece) --however many you want. But in serial pieces, there's an
underlying row, and operations of various kinds turn that underlying row
into melodic line, harmonies, "key areas", whatever. There's nothing
remotely like that in a Bach fugue. Why not just say there's a subject
which reappears in various transpositions (sometimes tonally adjusted),
accompanied by material that is more or less free?

I'm not saying that being able to "12-count", which is what beginning
music students do when they think they're "analysing" a serial piece, is
the most important thing to do to a 12-tone piece--it's just sufficient to
demonstrate that a piece *is* serial.

> As for transforming it into the countersubject, can you give me two
> subjects of the same length that cannot be transformed into one
> another with serial procedures? I'll believe you if you say yes.

No, not if you can have arbitrary operations.

> What are the allowed serial procedures?

Well if you're composing, you can do what you want to a row. (There's no
Floating Head of Death that be summoned to stop you.) Anything that you do
to all the members of a series is by definition a serial procedure. In
most well-known serial pieces, you find the composer using transpositions
and inversions of the row to generate harmony and melody. The operations
are usually on the ordered row (prime or retrograde), or on its unordered
constituent hexachords, or more rarely on its unordered constituent
tetrachords or even trichords.

If you want to apply serialisation to dynamics or durations etc, you can
do that too. Babbitt serialised as many dimensions of music as he could
think of, it seems. It's this ultra-constrained music that people often
sounds no different, on the surface, from stochastic music.

see you -jon

>> As for transforming it into the countersubject, can you give me two
>> subjects of the same length that cannot be transformed into one
>> another with serial procedures? I'll believe you if you say yes.
>
>No, not if you can have arbitrary operations.
//
>> What are the allowed serial procedures?
>
>Well if you're composing, you can do what you want to a row.

Aha! And a row is just any sequence of notes then, eh, of any
length?

-Carl