Bruckner (was: comma shifts in performance)

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@juno.com>
To: <tuning@yahoogroups.com>
Sent: Tuesday, October 29, 2002 11:55 AM
Subject: [tuning] Re: comma shifts in performance

> --- In tuning@y..., "monz" <monz@a...> wrote:
>
> > near the end of his life, Bruckner had a visit from
> > Tanaka, who demonstrated his "enharmonium", a 53-tone
> > JI reed-organ with this tuning:
> > http://sonic-arts.org/monzo/tanaka/Tanaka-lattice.jpg
>
> What a fascinating story!

yes, well, it really *is* a fascinating story!
here's the whole scoop on Bruckner:

/tuning/topicId_19457.html#19457

when paul says that Bruckner was one of the few
composers of the "common-practice" period who thought
in JI, he's talking about what's mentioned in the
first paragraph of this story. the lattice of
pitches of, for example, the C-major scale, was
in Bruckner's conception thus:

A --- E --- B
5:3 5:4 15:8
VI III VII
/ \ / \ / \
/ \ / \ / \
F --- C --- G --- D
4:3 1:1 3:2 9:8
IV I V II

so when it says:

>> 'the fifth above step II (in major [Stufentheorie])
>> is "impure" or, like Bruckner kept saying, a
>> "mathematical dissonance ", which must be smaller
>> than the pure fifth by approximately a ninth whole-tone.

it refers to the 40:27 narrow "5th" between
D 9:8 and A 5:3.

i gave a lecture at Microfest 2001 in Pomona CA
on "Microtonality in Berlin and Vienna in the early 1900s".

much of the material i spoke about is sprinkled thruout
the appropriate years (1889 and 1891 - Bruckner,
1904 - Mahler, 1906 - Stein and Busoni, 1909 -Schoenberg
and Webern) in my webpage "A Century of New Music in Vienna"
http://sonic-arts.org/monzo/schoenberg/Vienna1905.htm

(the music that loads with the page is pretty loud)

-monz
"all roads lead to n^0"