Re: [tuning] Re:: JI and the listening composer

graham@microtonal.co.uk wrote:

> In-Reply-To: <3D066AF7.EDB6B501@which.net>
> Alison Monteith wrote:
>
> > To clarify: For my current musical project I would rather tune up
> > accurately, say, seven different
> > pelogs, than an ET (in the 30-50 tones per octave range) that
> > approximated them even to within a
> > cent or two. The reason is that I believe I can hear a difference and I
>
> And to clarify what Gene was suggesting, 612-equal gives 5-limit intervals
> to within a 20th of a cent and 9-limit to about a fifth of a cent. So
> that's very different to "within a cent or two". And you only need 10
> notes.
>
> Graham

That is edifying. Thank you Graham.

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.

Regards

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