new(?) commas

- Has anyone used the commas

1232:1235 (7.11.16/5.13.19)

12103:12100 (7.7.13.19/2.2.5.5.11.11)

1729:1728 (7.13.19/64.27)
- you could call this a 'Ramanujan comma'?

The first two came up in my attempts to analyze things happening in
circular modified-meantone... the last you could split up as 7/6 .
24/19 . 13/12?
~~~T~~~

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

> 1729:1728 (7.13.19/64.27)
> ...'Ramanujan comma'?
by
> split up 7/6 .
into
> 24/19 . 13/12?

http://mathworld.wolfram.com/Hardy-RamanujanNumber.html
http://en.wikipedia.org/wiki/1729_(number)
http://de.wikipedia.org/wiki/Hardy-Ramanujan-Zahl
http://www.imeem.com/snm/blogs/2004/12/28/QB5j_2N0/1729
http://www.uh.edu/engines/epi495.htm
http://users.tellurian.net/hsejar/maths/1729-SOP/index.htm
http://www.mathpages.com/home/kmath028.htm
http://www.nationmaster.com/encyclopedia/1729-(number)

&ct.
bye
A.S.

Tom,
 
You are calling a tiny ratio such as 1729:1728 a comma.  Isn't Skhisma or one of the other tiny ratio names more accurate?
 
-- Mark Rankin

--- On Tue, 1/27/09, Tom Dent <stringph@...> wrote:

From: Tom Dent <stringph@...>
Subject: [tuning] new(?) commas
To: tuning@yahoogroups.com
Date: Tuesday, January 27, 2009, 3:54 AM

- Has anyone used the commas

1232:1235 (7.11.16/5.13. 19)

12103:12100 (7.7.13.19/2. 2.5.5.11. 11)

1729:1728 (7.13.19/64. 27)
- you could call this a 'Ramanujan comma'?

The first two came up in my attempts to analyze things happening in
circular modified-meantone. .. the last you could split up as 7/6 .
24/19 . 13/12?
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> - Has anyone used the commas
>
> 1232:1235 (7.11.16/5.13.19)
>
> 12103:12100 (7.7.13.19/2.2.5.5.11.11)
>
> 1729:1728 (7.13.19/64.27)
> - you could call this a 'Ramanujan comma'?
>
> The first two came up in my attempts to analyze things happening in
> circular modified-meantone... the last you could split up as 7/6 .
> 24/19 . 13/12?
> ~~~T~~~
>
Hi Tom. I can't find the answer to the mystery major in the threads.
Could you tell it again please, thanks, Rick

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> >
> >
> > - Has anyone used the commas
> >
> > 1232:1235 (7.11.16/5.13.19)
> >
> > 12103:12100 (7.7.13.19/2.2.5.5.11.11)
> >
> > 1729:1728 (7.13.19/64.27)
> > - you could call this a 'Ramanujan comma'?
> >
> > The first two came up in my attempts to analyze things happening in
> > circular modified-meantone... the last you could split up as 7/6 .
> > 24/19 . 13/12?
> > ~~~T~~~
> >
> Hi Tom. I can't find the answer to the mystery major in the threads.
> Could you tell it again please, thanks, Rick
>

Ah ok... The chord was what I felt to be, surprisingly, harmonically a
good stand-in for 5:6:8 with pure sines - namely (5,6,8)x2+(1,1,1) =
11:13:17. Since the earlier 'minor' was 11:13:16 one might just add a
rather normal semitone to the top voice to get 'major' 1st inversion.

I think it was Cameron who guessed or heard correctly that it was
11-based.
~~~T~~~