Re: Ogolevets' theory of temperaments

Hello, there, everyone, and until I actually read Ogolevets, I can
only respond to what Brian McLaren and others have written.

From Brian's presentations, I might get the impression that Ogolevets
was concerned with new music based on a "Pythagorean" paradigm,
realized in tunings such as 17-tET and 22-tET. However, I would be
very interested in knowing the kind of vertical style involved: what
is the role of major and minor thirds and sixths, for example?

My advocacy of Pythagorean tuning, and what John Chalmers has referred
to as "para-Pythagorean" scales such as 29-tET, 46-tET, and 17-tET --
with 22-tET a very interesting scale also in this kind of role -- is
in a setting of the Gothic music of 13th-14th century Europe, or
derivative "neo-Gothic" styles. Here the patterns are radically
different from those of 18th-19th century European music.

Specifically, Gothic and neo-Gothic music is based on the use of
active and unstable thirds and sixths as points of some tension,
frequently leading to directed cadential resolutions involving melodic
motions by compact semitones (~50-90 cents). Often major thirds expand
to fifths, and major sixths to octave, while minor thirds contract to
unisons. Additionally, the minor seventh often contracts to a fifth
while a major second may expand to a fourth.

The unit of stable sonority is the complete trine (2:3:4) with outer
octave, lower fifth, and upper fourth; various kinds of sonorities
including unstable thirds and sixths resolve to complete trines, or
often to the prime trinic interval of the fifth.

In this kind of style, Pythagorean or "para-Pythagorean" tunings with
wide major thirds and sixths, and narrow minor thirds and diatonic
semitones, fit the texture and cadential action of the music.

For more on the original Gothic use of Pythagorean tuning, you might
visit:

http://www.medieval.org/emfaq/harmony/pyth.html

For a "Gentle Introduction to neo-Gothic progressions" discussing some
intervals, sonorities, and cadences, see:

/tuning/topicId_15038.html#15038 (1/Pt 1)
/tuning/topicId_15630.html#15630 (1/Pt 2A)
/tuning/topicId_15685.html#15685 (1/Pt 2B)
/tuning/topicId_16134.html#16134 (1/Pt 2C)

In contrast, typical 16th-19th century European music treats
thirds and sixths as stable and restful concords, specifically leaning
toward the simplest ratios of 5:4 and 6:5. The style is different, and
so is the intonational ideal.

As far as Zarlino goes, I would say that both his ideal of just
intonation and his practical advocacy of meantone tuning on keyboards
nicely reflects the musical ethos and style of his era, just as
Pythagorean tuning reflects that of the Gothic era.

To comment in a more informed manner on this thread, I would want to
know just what kind of music Ogolevets was advocating in 17-tET or
22-tET.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> In contrast, typical 16th-19th century European music treats
> thirds and sixths as stable and restful concords, specifically
leaning
> toward the simplest ratios of 5:4 and 6:5. The style is different,
and
> so is the intonational ideal.

Actually, Margo, beginning around 1800, a large number of instructors
and theorists began speaking of Pythagorean tuning as their ideal --
and this ideal persists in many "classical" string ensembles today.
Although triads and larger chords were now the norm, a generation of
keyboards with circulating temperaments fostered an acceptance of
near-Pythagorean thirds and sixths, despite their tense character.
This tension, along with the incisive and expressive small diatonic
semitones of Pythagorean tuning, suited (and shaped) the Romantic
aesthetic nicely. This view was far from universal, though, and at
least as many theorists still clung to a meantone ideal. But the
demise of the consonant thirds and sixths was well underway.

> To comment in a more informed manner on this thread, I would want to
> know just what kind of music Ogolevets was advocating in 17-tET or
> 22-tET.

I believe someone just said it was music in the Classical/Romantic
style . . . if I remember correctly.