Re: [tuning] Re:: JI and the listening composer(for Graham)

graham@microtonal.co.uk wrote:

> In-Reply-To: <3D078527.6ADD4CD5@which.net>
> Alison Monteith wrote:
>
> > The gamelan scales I'm using have ratios of 7, 11, 13,17 and 19. My
> > website gives tuning data.
> > Those might be trickier to find a blanket ET for but I'm sure somebody
> > will one day.
>
> Open wide!
>
> I got my script at <http://x31eq.com/temper/> to work on the
> 1.7.11.13.17.19 limit. It came up with these consistent ETs:
>
> 11 16 20 37 43 46 50 56 57 62 67 80 93 94 100 104 111 113 121 124
>
> The top three linear temperaments are really the same, a combination of
> 46, 57 and 11, with a complexity of 18 and a worst error of 4.7 cents.
> It's got a generator of 547.4 cents, so it may be pelog-like. The
> simplest MOS with complete chords has 24 notes.
>
> Here are some more consistent ETs if you want closer to microtempering:
>
> 129 137 146 150 157 161 170 181 186 187 204 207 217 218 224 227 230 250
> 261 274
>
> For a better than 2 cent error, it's giving a mighty strange temperament
> with two keyboards tuned to 50-equal, 9.1 cents apart. That's good to 1.2
> cents.
>
> If you remind me of your URL I can see how relevant it is to the scales
> you're using. A 100 note scale probably isn't at all useful for
> containing 7 note scales. It may be possible to temper out a single
> comma, which is more Gene's thing.
>
> Graham

My URL:-

>
> http://www.unsork.info

That was quick. It'll take me a while to get my head round all this but thanks for your time in
looking all this out.

Kind Regards

Alison Monteith wrote:

> My URL:-
>
> >
> > http://www.unsork.info

None of the pelogs or slendros use 11, so that shouldn't have been
included. Until you get to the 8 course zithers, they only involve 3, 7
and 19.

For the 1.3.7.19-limit I get a temperament with a generator of 234 cents,
a complexity of 12 and a worst error of 2.4 cents. The simplest ET is 16,
so it might be pelog-like. 3:2 is 3 generators, 8:7 is 1 generator and
32:19 is 9 generators with octave adjustment. It involves 5, 26 and
31-equal.

So this is a kind of septimal slendro. Paul mentioned it recently, I
can't remember why. It might have something to do with this. One JI
version is the "Pygmie scale" from Manuel's archive

1/1 8/7 21/16 3/2 7/4 2/1

which is your "unnamed" but with a different fourth. Later on, you allow
17/12 instead of 4/3, so this might be in the spirit. If not, you'll have
to get three fourths to approximate the 19:8, which will need a lot more
notes.

The more precise temperament has a 586 generator, which is like one that
came up before. Worst error of 0.9 cents and a complexity of 28 so I
don't know if it'll be good for anything.

Oh, here are some efficient equal temperaments

36 41 77 166 193 202 234 270 306 311

> That was quick. It'll take me a while to get my head round all this
> but thanks for your time in
> looking all this out.

That's the advantage of using a computer. It doesn't take at all long to
work these things out.

Graham

graham@microtonal.co.uk wrote:

> Alison Monteith wrote:
>
> > My URL:-
> >
> > >
> > > http://www.unsork.info
>
> None of the pelogs or slendros use 11, so that shouldn't have been
> included. Until you get to the 8 course zithers, they only involve 3, 7
> and 19.
>

My mistake.

>
> For the 1.3.7.19-limit I get a temperament with a generator of 234 cents,
> a complexity of 12 and a worst error of 2.4 cents. The simplest ET is 16,
> so it might be pelog-like. 3:2 is 3 generators, 8:7 is 1 generator and
> 32:19 is 9 generators with octave adjustment. It involves 5, 26 and
> 31-equal.
>
> So this is a kind of septimal slendro. Paul mentioned it recently, I
> can't remember why. It might have something to do with this. One JI
> version is the "Pygmie scale" from Manuel's archive
>
> 1/1 8/7 21/16 3/2 7/4 2/1
>
> which is your "unnamed" but with a different fourth. Later on, you allow
> 17/12 instead of 4/3, so this might be in the spirit. If not, you'll have
> to get three fourths to approximate the 19:8, which will need a lot more
> notes.
>
> The more precise temperament has a 586 generator, which is like one that
> came up before. Worst error of 0.9 cents and a complexity of 28 so I
> don't know if it'll be good for anything.
>
> Oh, here are some efficient equal temperaments
>
> 36 41 77 166 193 202 234 270 306 311
>
> > That was quick. It'll take me a while to get my head round all this
> > but thanks for your time in
> > looking all this out.
>
> That's the advantage of using a computer. It doesn't take at all long to
> work these things out.
>
> Graham

> It's still bloody clever... : - )

Regards