--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> Tom has a web page on this I'm trying to decipher:
>
> 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?
>

The DEFINITION of the scale is in the monochord numbers, which are the
first table in the webpage. I was working on the assumption that
people would start at the beginning and read towards the end...


Therefore the scale is defined to be (apologies for malformed Scala)

! sep.scl
Septenarius scale (choose either value of D)
12
!
1
196/186 = 98/93
196/176 or 196/175
196/165
196/156 = 49/39
196/147 = 4/3
196/139
196/131
196/124 = 49/31
196/117
196/110 = 98/55
196/104 = 49/26


The notation Gene dislikes is not a notation for numbers; it is a
notation for tempering of fifths. It's actually the way Werckmeister
set out his fifths. It's certainly not the definition of the tuning.

Anyway, you are correct that G#-D# is a typo on my part. Try a wide
fifth tempered by 496/495. Where Gene got 4448/4455 from I can't tell.

392/393 * 524/525 * 350/351 * 416/417 * 278/279 * 496/495 * 440/441
*(3^12)/(2^19) = 1

No need for any integer exceeding 525!

~~~T~~~