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"raised pythagorean 'leading tone'", "flat chords" {was: Beethoven JI tuning experiment & 'lateral' harmonies}

🔗D.C. Carr <d.c.carr@xxxxxx.xxx>

6/6/1999 3:23:29 AM

[Excerpting:]

"""From: monz@juno.com
Subject: Beethoven JI tuning experiment & 'lateral' harmonies

[...] The (culturally-conditioned?) preference for a sharpened
Pythagorean 'leading-tone' makes this chord sound flat, at
least in this piece, and to my ears. It sounds a lot better
using the Pythagorean pitch for the leading tone, and choosing
the 'root' and '5th' which make a nice 4:5:6 triad with it,
in the corresponding area of the harmonic lattice.[....]"""

I wonder whether the term "sharpened Pythagorean 'leading-tone'"
here isn't perhaps pleonastic and potentially confusing too? A
Pythagorean Major third would be tuned wider than a pure one; does
monz mean that the third is even wider than a Pythagorean one would
be? Can one actually speak of a Pythagorean leading tone? My
understanding - limited, to be sure - is that intervals can be
Pythagorean, but not tones. And would 'raised' not be a better term
than 'sharpened', unless of course he's referring to the use of a #
sign before the note; but in that case he's lost me completely.

The description of a flat sounding chord also has me wondering.
monz might mean that the *third of the chord* is lower than he
expected, but not likely that there's a flat sign in front of it.
But a *chord* might sound flat [= dull?] for some other reason than
the tuning, so maybe he's not referring to the third at all.

As a relative novice to tuning matters, may I plead for more precise
expression? The subject is too complex to tolerate unclear use of
terms like sharp and flat.

Thanx for the chance to rant.....

�ale C. Carr