5-limit yantra commas

These start out as 2, 4/3, 6/5, 10/9 and then

16/15 father
25/24 dicot
81/80 meantone
2048/2025 diaschismic
15625/15552 kleismic
32805/32768 schismic
semithirds |38 -2 -15>
ennealimmal |1 -27 18>
kwazy |-53 10 16>
monzismic |54 -37 2>

The maximal yantra for any given comma, tempered by that comma, might
be worth looking at. An example would be yantra_5(22), which is the
largest yantra for which 81/80 is the smallest scale step. Tempering
it gives a 17-note scale which is Meantone[18] minus a note--in terms
of generators of a fifth, the numbers from 0 to 17, except for 15.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

If we take the consecutive commas in pairs as we did for the 7-limit,
we get equal temperaments; they go
1, 1, 3, 3, 7, 12, 34, 53, 118, 441, 612, 612...

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> If we take the consecutive commas in pairs as we did for the 7-
limit,
> we get equal temperaments; they go
> 1, 1, 3, 3, 7, 12, 34, 53, 118, 441, 612, 612...

This is the same set of equal temperaments found here,

http://www.kees.cc/tuning/s235.html

which is referred to from here:

http://www.kees.cc/tuning/perbl.html

If you don't understand why this is so, it's time for you to
reconsider Kees's work . . . ;)

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> > wrote:
> >
> > If we take the consecutive commas in pairs as we did for the 7-
> limit,
> > we get equal temperaments; they go
> > 1, 1, 3, 3, 7, 12, 34, 53, 118, 441, 612, 612...
>
> This is the same set of equal temperaments found here,
>
> http://www.kees.cc/tuning/s235.html
>
> which is referred to from here:
>
> http://www.kees.cc/tuning/perbl.html
>
> If you don't understand why this is so, it's time for you to
> reconsider Kees's work . . . ;)

Yantras are naturally weighted by log(p), so it isn't surprising to
find some connection. Are you saying the two will always lead to
exactly identical results?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> > > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > > wrote:
> > >
> > > If we take the consecutive commas in pairs as we did for the 7-
> > limit,
> > > we get equal temperaments; they go
> > > 1, 1, 3, 3, 7, 12, 34, 53, 118, 441, 612, 612...
> >
> > This is the same set of equal temperaments found here,
> >
> > http://www.kees.cc/tuning/s235.html
> >
> > which is referred to from here:
> >
> > http://www.kees.cc/tuning/perbl.html
> >
> > If you don't understand why this is so, it's time for you to
> > reconsider Kees's work . . . ;)
>
> Yantras are naturally weighted by log(p), so it isn't surprising to
> find some connection. Are you saying the two will always lead to
> exactly identical results?

Yes.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> > Yantras are naturally weighted by log(p), so it isn't surprising to
> > find some connection. Are you saying the two will always lead to
> > exactly identical results?
>
> Yes.

Succinct but not convincing. The metric for yantras would give
triangle shapes for balls. If we take 5 as perpendicular to 3, right
triangle shapes, with the shorter sides in a log3:log5 proportion.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > > Yantras are naturally weighted by log(p), so it isn't
surprising to
> > > find some connection. Are you saying the two will always lead to
> > > exactly identical results?
> >
> > Yes.
>
> Succinct but not convincing. The metric for yantras would give
> triangle shapes for balls.

This may be the metric for yantra *pitches*, but you were
constructing those ETs by combining yantra *intervals* (namely, by
eating the smallest intervals (pi(limit) of them) in each yantra). So
it would be more appropriate to look at the balls defined by yantra
*intervals*.