--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- 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~~~


Apparently you missed this earlier post of mine...

> 0: 1/1 0.000 unison, perfect prime
> 1: 98/93 90.661
> 2: 28/25 196.198 middle second
> 3: 196/165 298.065
> 4: 49/39 395.169
> 5: 4/3 498.045 perfect fourth
> 6: 196/139 594.923
> 7: 196/131 697.544
> 8: 49/31 792.616
> 9: 196/117 893.214
> 10: 98/55 1000.020 quasi-equal minor seventh
> 11: 49/26 1097.124
> 12: 2/1 1200.000 octave
>
> EDL is as old as the hills, isn't it?
>
> Cents schments, I'm digging the ratios,
>
> Hmmm....sounds pretty damn good!
>
> Thanks, Tom Dent!