On 10 Sep 2009, at 10:57, Torsten Anders wrote:
On 10.09.2009, at 09:03, Hans Aberg wrote:
It seems to be that that staff indicates the Pythagorean tuning,
with accidentals to indicate offsets relative that. Right?
This uniform structure of the Helmholtz-Ellis and Sagittal notation
makes it possible to not only notate just intonation but also
arbitrary equal temperaments (equal divisions of the octave) with
them. The example below shows the pitches of 41-tone equal
temperament with Helmholtz-Ellis notation. Note that other
enharmonic pitches are possible, for example, Db and C#L (C#
transposed down by a septimal comma) share the same 41-tone equal
temperament pitch class (namely pitch class 3, the fourth note
below).
Yes, but I tend to think that ETs and Pythagorean tuning, quarter-
comma meantone, and other diatonic pitch systems would be best
notated by departing from them, and then adding intermediate pitch
accidentals relative that. Strictly speaking, it depends on which
music instrument you have. Mine is a 2-dimensional keyboard. I
figured it would take too much work learning new playing pattern for
each tuning, especially in rapind movements, ornamentation, etc. I
do not know of a good way to play intermediate pitches yet, though.
I think this way of notating should be possible with the system I
described in my other mail.
Hans