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