Mark Gould and Sensi

I'm going through old posts to try and work out what
temperament classes Mark Gould might have been talking
about or implying. I have a copy of his paper somewhere.
Until I find it the best I can do is find what I wrote
about it before.

/tuning-math/message/4101

I gave a temperament there which is unambiguously specified
in terms of its mapping. When I plug it into my website,
I can see that it's now called "Sensi". I don't know where
this name came from. If it really ties in with Mark's
paper it should be called "Gould".

There's something else in that thread that I'm not clear
about, though. I remember something about it mapping 9:8
but not 3:2. So maybe it's properly defined in the
2.5.7.9-limit.

Graham

Hm. I have a nonatonic here from him, 212121221 in 14-ET.
Different system?

I found another message from you in which you describe
several systems of his. The one below seems to be

"11 from 41 is 9:8 plus 8:7 making 9:7, or a 7:8:9 chord."

-Carl

At 04:07 AM 8/14/2011, you wrote:
>I'm going through old posts to try and work out what
>temperament classes Mark Gould might have been talking
>about or implying. I have a copy of his paper somewhere.
>Until I find it the best I can do is find what I wrote
>about it before.
>
>/tuning-math/message/4101
>
>I gave a temperament there which is unambiguously specified
>in terms of its mapping. When I plug it into my website,
>I can see that it's now called "Sensi". I don't know where
>this name came from. If it really ties in with Mark's
>paper it should be called "Gould".
>
>There's something else in that thread that I'm not clear
>about, though. I remember something about it mapping 9:8
>but not 3:2. So maybe it's properly defined in the
>2.5.7.9-limit.
>
>
> Graham
>
>
>------------------------------------
>
>Yahoo! Groups Links
>
>
>

Carl Lumma <carl@lumma.org> wrote:
> Hm. I have a nonatonic here from him, 212121221 in 14-ET.
> Different system?

Could be. 9&14 could be Superpelog or Beep.

> I found another message from you in which you describe
> several systems of his. The one below seems to be
>
> "11 from 41 is 9:8 plus 8:7 making 9:7, or a 7:8:9 chord."

I found that in Robert's archive, where it's message 4314
in s___5/msg_4300-4324.html

The way the diatonics are defined, 9:7 should be the
generator and the difference between 9:8 and 8:7 should be
11 generator steps. I think that's consistent with this:

http://x31eq.com/cgi-bin/rt.cgi?limit=2.9.7&ets=11+41

Sensi is different, although it has a 9:7 generator.

"11 from 31, with 6:5 and 11:9 adding up to 16:11" might be
Casablanca. The generator mapping is <0 19 14 4 1]. 16:11
is -1 generator steps. 6:5 is 19-14 = 5 generators. 11:9
is 1-19*2 = -37. So, no, that won't give an 11 note scale.

Let's try 11c&31. The generator mapping is <0 -12 -17 4 1]
but let's call it <0 12 17 -4 -1] so 16:11 is the
generator. Then, 6:5 is 12-17 = -5 generators. 11:9 . . .
clearly won't be 6 generators.

I can't get this one to work out. Or the 11 from 27.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> The way the diatonics are defined, 9:7 should be the
> generator and the difference between 9:8 and 8:7 should be
> 11 generator steps. I think that's consistent with this:

If we assume 9/7 is the generator that means it tempers out the comma |5 -12 0 5> = 527824/531441, but the most obvious route from there is not a 9/7 generator at all, but magic. If you don't add five into the mix, then a generator of 243/196 would make sense, but that's just magic where you pretend the flat major third isn't a major third.

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Graham Breed
> <gbreed@...> wrote:
>
> > The way the diatonics are defined, 9:7 should be the
> > generator and the difference between 9:8 and 8:7 should
> > be 11 generator steps. I think that's consistent with
> > this:
>
> If we assume 9/7 is the generator that means it tempers
> out the comma |5 -12 0 5> = 527824/531441, but the most
> obvious route from there is not a 9/7 generator at all,
> but magic. If you don't add five into the mix, then a
> generator of 243/196 would make sense, but that's just
> magic where you pretend the flat major third isn't a
> major third.

It's half magic, like I said at the start. The mapping's
for magic but the 11 note MOS only uses every other note.

11 from 19 would also be consistent with Sensi. I'm not
sure where I got that from and Mark never confirmed what
coincided with what he was thinking about.

I thought I saw something about half magics recently. So
if anybody's looking at this 11 from 41 again, note that
Mark was there first.

Graham