Re :FW: [tuning] Werckmeister's Septinarius temperament

hi again

a mistake : 1568=196*8

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Mohajeri Shahin
Sent: Tuesday, February 13, 2007 2:43 PM
To: tuning@yahoogroups.com
Subject: RE: [tuning] Werckmeister's Septinarius temperament

Hi gene

your scale has degrees of 1568-edl
you can see something about this EDl-based well temperament and 196-EDL and The Septenarius, Werckmeister's mythical tuning in :
http://240edo.googlepages.com/equaldivisionsoflength(edl <http://240edo.googlepages.com/equaldivisionsoflength(edl> )

it is interesting that 1568=196*7.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Gene Ward Smith
Sent: Monday, February 12, 2007 11:47 PM
To: tuning@yahoogroups.com
Subject: [tuning] Werckmeister's Septinarius temperament

Tom has a web page on this I'm trying to decipher:

http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html <http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html>

It it he presents the deviations from JI fifths for his two
reconstructions of this temperament in terms of a new (to me) and
horrible notation for positive rational numbers, whereby p/q > 1 is
written +p:q and p/q < 1 is written -p:q. Could we PLEASE stick to the
standard mathematical notation everyone learned in grade school?

Now that I've vented about that (sorry Tom, but you hit my pet peeve
button) I'll give the deviations for "D=175", starting from C-G and
working the circle of fifths around to F-C: 392/393, 524/525, 350/351,
1, 1, 416/417, 1, 1, 1, 1, 440/441, 1

Now, a problem with this is that the prodcut of this deviations isn't
524288/531441, so octaves are slightly tempered. Presuming this isn't
intentional, at least one of these ratios is off, and in fact G#-D# is
given as 496/496. If instead we make that 4448/4455, we get untempered
fifths. In the vague hope that this is more or less what is intented,
here's a first go at what this temperament would be:

! sep.scl
Septanarius scale?
12
!
1568/1485
28/25
196/165
49/39
4/3
196/139
196/131
784/495
196/117
98/55
49/26
2