source file: m1495.txt
Date: Wed, 5 Aug 1998 17:05:55 -0400

Subject: TUNING digest 1494: Numerological Postings

From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>

Numerology is fun but finding counterexamples is just too easy, and
possibly distracts from the profound and elegant properties of the number=
s
themselves. =


For example, Paul Erlich's citation mentions the 12 apostles; most modern=

scholarship attributes the significance of the number 12 to the associati=
on
that early Jewish Christians would make with the number of Jewish tribes.=

So is the number 12 Christian or Jewish? =


The calendric significance of the numbers 7 and 12 is practically univers=
al
and are part of a shared Jewish and Christian cultural inheritance.

There is indeed a strong neo-platonic (and by extension, neo-pythagorean)=

element to post-Pauline Christianity, and the doctrine of the trinity and=

related doctrines (e.g. Pseudo-Dionysius's three heirarchies of three
orders of angels) are tempting to give importance to such numbers, but th=
e
number 10, which was identified as Jewish, is in fact the very Pythagorea=
n
sum (the Tetrachys) of the numbers one through four. Since medieval
Christianity and post-scriptural Judaism share the neo-platonic component=
,
this is not surprising. =


While all were aware of properties belonging to the pythagorean sequence =
of
12 fifths, the treatment of a scale type as X tones out of a set of Y
tones, interestingly, seems not to have been a major component of practic=
al
scale theory in any of the cultures discussed above (the classical Greek
systems were generally conceived as placeholders for varying interval
contents, pythagorean sequences being only one among many possibilities,
the later view of the harmoniae as keys rather than modes possibly an
exception to this point; Jewish and Christian cantillation seems to have
been diatonic, with at most one or two additions to a theoretical
pythagorean sequence, _if_ that was indeed the intonation in question, a
matter of high speculation), and in Europe well into the late middle ages=
,
instrumental representations of 12 tone sets in practice must have been
extremely rare.

''X out of Y theory'' was, however, a mainstay of Chinese theory and
practice (in the form 5+2 out of 12 or some larger pythagorean cycle) as
well as Indian sruti theory (5 or 6 or 7 out of 22, with the schisma
ignored possibly pythagorean), becomes important to fretting theory in
classical Islamic cultures (again, neo-platonic, and traditionally
hospitable to both Jewish and Christian musicians) and only later in
fretting and keyboard theory in Europe, or in Javanese/Balinese and
mainland southeast Asian seven tone sets.     =