Re: TD 381: Reply to "the Monz" on fifthtones

> 4. Chronological List of the works of Alois H�ba
> From: Joe Monzo <monz@juno.com>

> 'semitone' refers to the usual 12-tET scale
> 'quarter-tone' refers to 24-tET
> '5th-tone' I believe refers to 31-tET (not 30-tET)
> '6th-tone' refers to 36-tET
> '12th-tone' refers to 72-tET - *not* Schoenberg's '12-tone method'

Hello, there.

Agreeing with you, I would say that 31-tet involves a division of the
whole-tone into five equal parts, with a small semitone (generally
taken as chromatic) of two parts and a large semitone (generally taken
as diatonic) of three parts.

This is the theoretical fifthtone scheme both of Nicola Vicentino
(1555), and of Fabio Colonna (1618), although one might suspect that
it was realized in practice by something like 1/4-comma meantone with
pure major thirds, where those "equal" fifthtones would actually be
slightly unequal. In 31-tet, they are indeed equal, at ~38.7 cents.

In terms of Easley Blackwood's scheme, if I recall it correctly, we
have the whole-tone equal to 5/31 octave and the diatonic semitone
equal to 3/31 octave, giving us a ratio "R" between these two
intervals of 5:3.

Maybe "fifthtone" could also fit 30-tet, since here 1/30 octave is
indeed exactly a fifth of 1/6 octave, the whole-tone of 200 cents. In
31-tet, both the whole-tone and its five divisions are smaller, so
that in both tunings the whole-tone is divided into five parts.

If one wanted to argue historical precedent, then maybe "fifthtone"
should be default apply especially to 31-tet, based on the approximate
models of Vicentino and Colonna, and the more mathematically precise
models in the later 17th century by Rossi and Huyghens.

Most appreciatively,

Margo Schulter
mschulter@value.net

Thanks to Daniel Wolf for confirming that Haba's 16th Quartet
is, as I thought, in 31-tET, and to Margo Schulter for her
historical speculations.

I believe this is the only piece Haba wrote in 31-tET, and
also believe it was due to his interaction with Fokker (in
the 1960s?), and not to any specific interest in the historical
theorists mentioned by Margo (excepting Huyghens, on whose
work Fokker's was based).

Haba's microtonal works and theories were mainly in 24-tET
and 36-tET.

Haba possessed absolute pitch, and his interest in
microtonality in the first place stems from his exposure
to Wallachian folk-songs in family music-making with his
brothers and mother when he was child; he recognized when
he began his musical studies that these songs contained
intervals outside the 12-tET scale.

After high school, he obtained teaching jobs while continuing
to study music, eventually going to the Prague Conservatory at
the outbreak of World War 1, until he was drafted.

Stationed in Vienna near the end of the war, Haba
encountered Willi von Moellendorff, who performed on a
quarter-tone harmonium, and he wrote his first 24-tET
compositions. He later became a pupil of Franz Schreker,
attended Schoenberg's Private Society concerts, and became
somewhat of a follower of Schoenberg's ideas; he was strongly
influenced by the 'athematic' approach used by Schoenberg
in _Erwartung_.

Haba followed Schreker when he moved to Berlin, and there
studied 'oriental' music (meaning near-eastern) and met
Ferrucio Busoni, who had advocated 36-tET in his _Sketch
for a New Aesthetic of Music_. Busoni encouraged Haba
more than anyone else to continue his microtonal explorations,
and Haba began composing in 18- and 36-tET.

At this point, Haba decided to set up a microtonal school,
but was forced out of Berlin when the Nazis came to power.
He returned to Prague and pursued his dream, until after
10 years of resistance he finally established a microtonal
school at the Conservatory, which lasted until 1951, when
the Soviet-backed communist government dissolved it.

(info from PhD dissertation on Haba's _New Harmonielehre_,
by Suzette Mary Battan, Eastman School of Music, 1980)

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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