Comment on notation

If we take the Hemiennealimmal temperament, which one gets by ignoring the "schismninas" sagittal proposes to ignore, and then zeros out one of the commas associated to 11-limit symbols as well, one gets the following list of vals:

729/704 [198, 312, 457, 554, 684]

33/32 [18, 28, 41, 50, 62]

36/35 [18, 30, 44, 52, 63]

6561/6400 [90, 142, 208, 252, 311]

45/44 [108, 170, 249, 302, 373]

45927/45056 [306, 484, 709, 858, 1058]

55/54 [36, 58, 85, 102, 125]

81/80 [90, 142, 208, 252, 311]

5120/5103 [198, 314, 460, 556, 685]

All of these except for the last, for 5120/5103, are non-standard. Have you two notated the 198-et, by the way?

If we take the ratio of two continguous intervals on the above list, and toss 5120/5103 which we have already considered, we get the following vals, all of which are standard, and in which the notation simplies itself:

413343/409600 [72, 114, 167, 202, 249]

2200/2187 [126, 200, 293, 354, 436]

243/242 [72, 114, 167, 202, 249]

385/384 [72, 114, 167, 202, 249]

8019/8000 [72, 114, 167, 202, 249]

1240029/1239040 [342, 542, 794, 960, 1183]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:
> If we take the Hemiennealimmal temperament, which one gets by
ignoring the "schismninas" sagittal proposes to ignore, and then zeros
out one of the commas associated to 11-limit symbols as well, one gets
the following list of vals:
>
> 729/704 [198, 312, 457, 554, 684]
>
> 33/32 [18, 28, 41, 50, 62]
>
> 36/35 [18, 30, 44, 52, 63]
>
> 6561/6400 [90, 142, 208, 252, 311]
>
> 45/44 [108, 170, 249, 302, 373]
>
> 45927/45056 [306, 484, 709, 858, 1058]
>
> 55/54 [36, 58, 85, 102, 125]
>
> 81/80 [90, 142, 208, 252, 311]
>
> 5120/5103 [198, 314, 460, 556, 685]

Why does this matter? Can you interpret it for me please.

> All of these except for the last, for 5120/5103, are non-standard.

I don't know what you mean by non-standard.

> Have you two notated the 198-et, by the way?

No, but I just tried, and it is difficult. The biggest problem is in
finding a valid symbol for 10deg198. Best I can come up with is

198: )|( |~ ~|( /| |\ /|~ (|( ~|\ /|\ .(|\ (|)

You will see that I have resorted to using a 5-schisma flag to notate
10deg198 as the 7-ediesis 27:28. It could equally be '/|) the 7-diesis
57344:59049. This is rather ugly either way.

Why do you think it worth notating?

> If we take the ratio of two continguous intervals on the above list,
and toss 5120/5103 which we have already considered, we get the
following vals, all of which are standard, and in which the notation
simplies itself:
>
> 413343/409600 [72, 114, 167, 202, 249]
>
> 2200/2187 [126, 200, 293, 354, 436]
>
> 243/242 [72, 114, 167, 202, 249]
>
> 385/384 [72, 114, 167, 202, 249]
>
> 8019/8000 [72, 114, 167, 202, 249]
>
> 1240029/1239040 [342, 542, 794, 960, 1183]

I don't know why this matters either. More interpretation needed.

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"
<d.keenan@u...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith
> <genewardsmith@j...>" <genewardsmith@j...> wrote:
> > Have you two notated the 198-et, by the way?
>
> No, but I just tried, and it is difficult. The biggest problem is in
> finding a valid symbol for 10deg198. Best I can come up with is
>
> 198: )|( |~ ~|( /| |\ /|~ (|( ~|\ /|\ .(|\ (|)
>
> You will see that I have resorted to using a 5-schisma flag to
notate
> 10deg198 as the 7-ediesis 27:28. It could equally be '/|) the 7-
diesis
> 57344:59049. This is rather ugly either way.

Ugly is a good way of putting it, since it is evident that (/| and
|\) aren't a cure-all for our half-apotome problems. The cleanest
way to do it here (as well as in a lot of those divisions that
require something very close to 1/2-apotome) would be '|)). The
thing that has been keeping us from using it is that we don't have a
rational complement for |)). But should that stop us from
having '|)), which is its own rational complement?

I hesitate to suggest this, but with the pinch we're in, we could
possibly allow ''|)) as the rational complement of |)) -- if we could
this once allow a double-5-schisma, just as we allowed a double-5
comma. I've noticed that the 19-schisma is only rarely twice the
number of degrees in an ET as the 5-schisma, or I might have
suggested )|)), even if it's a three-flagger.

--George