Kopie von: Diatonic

---------- Weitergeleitete Nachricht ----------

Von: Daniel Wolf, 106232,3266
An: INTERNET:tuning@eartha.m, INTERNET:tuning@eartha.mills.edu
Datum: 22.11.96 10:59

Betreff:Kopie von: Diatonic

It is perhaps more useful to think of diatonic or pentatonic _environments_
instead of scales or modes. I think that this was an extreme problem for
medieval music theory, applying Greek ideas - especially octave species -
to a repertoire (chant) with a basis in Jewish cantillation. The practical
instructions found in the treatises, particularly for singing with the aid
of hexachords, are more useful. As Paul Hahn points out, the hexachord is
the maximum Pythagorean structure without an augmented 4th/diminished 5th,
and as such, can be used to control the placement of this interval while
guiding decisions about ficta. Both chant and early polyphony are - for us
- uncomfortably inconsistant when interpreted in terms of tonicity, so that
the identification of a single octave species for a given piece is
difficult, and probably tells us little about the structure of the piece.
As scalar theorists, we too often forget that most music is vocal and
unaccompanied, so that a fixed scale is an unnecessary precondition to
composition or performance. That a melody composed from phrases lying with
the compass of a pythagorean hexachord, and whose hexachords interlock at
fourth and fifth intervals, will tend to produce a gamut with 7 tones is
logical, but the appearance of particular 7-tone scales must be kept in the
category of consequence and not cause. Moreover, the frequency of melodies
in the repertoire with fewer than seven tones - and the existence of
repertoire with more eight or more tones is a reminder that seven has no
particular monopoly. What is, however, clear is that 5 or 7 or 12 (...)
tones exhibit the _closing interval_ (in 7, the tritone, in 12 , the wolf)
feature of MOS scales. What may be interesting is to devise hexachord-like
solfegio systems for higher-number MOS*s, in which the closing interval is
avoided through transposition of the solfege unit.

I am curious to learn from Heinz Bohlen how his infill of the Major triad
differs from that of Heinrich Schenker.

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