positive/skhismic systems (was: Re: Dictionary query)

> From: paulerlich <paul@stretch-music.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Thursday, January 10, 2002 7:20 PM
> Subject: [tuning-math] Re: Dictionary query
>
>
> --- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> > OK, but if they don't post anything here, please do give me
> > more info.
>
> I have some of the original Bosanquet papers . . . I'll try to bring
> them in.

Hmmm ... I have a copy of Bosanquet's book ... let me know where
to find the info.

> Well, let me put it this way. For meantone systems, the meaning of
> _which_ comma you're talking about is clear from the way meantone
> works. If you're describing a non-meantone system as "x/y-comma"
> whatever, then it's ambiguous. At least specify _which_ comma you're
> talking about, that will at least make the specification
> mathematically precise. But functionally, schismic temperaments are
> best described by the fraction of the schimsa that's tempered
> out . . . 1/8 schisma is Helmholtian, 1/9 schism is Sabat-Garibaldi's
> Dinarra tuning . . . am I making any sense?

Right, sure, I know about both of those.

What has me puzzled is the large size of the "fraction of the skhisma"
that's tempered out in the examples on my webpage.

You and Gene already discussed 22-EDO, but what about 17- and
39-EDO, where the "5th" is +2 and nearly +3 skhismas wider,
respectively, than a 3:2? And even 29-EDO's "5th" is nearly
a whole skhisma wider.

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

> What has me puzzled is the large size of the "fraction of the
skhisma"
> that's tempered out in the examples on my webpage.
>
> You and Gene already discussed 22-EDO, but what about 17- and
> 39-EDO, where the "5th" is +2 and nearly +3 skhismas wider,
> respectively, than a 3:2? And even 29-EDO's "5th" is nearly
> a whole skhisma wider.

I don't know why you would put 39-tET in this category. As for 17 and
29, have a look at the implied major thirds in these systems . . .
that should clear up your confusion.