two VERY small 7-limit intervals

I had a little fun with Scala this morning. I searched for intervals with a size similar to | -1054 665 > (the "Satanic comma", or what I prefer to call a "microcomma"), and found....

78125000/78121827 = | 3 -13 10 -2 > ~ 0.0703 cents

645700815/645657712 = | -4 17 1 -9 > ~ 0.1156 cents

I found these by dividing 0.1 cents into a thousand equal divisions (yes, that would be 12,000,000-TET), did a rational approximation and normalized. These were the only two that came up. I also came across these while compiling a list of possible JI values for schisma-level equal temperaments (like 600, 612, 665, 730 and so on).

I'm doing 11-limit now, but it's taking a while. My computer is slower than I thought.

~Danny~

... and now 11-limit.

> 78125000/78121827 = | 3 -13 10 -2 > ~ 0.0703 cents
>
> 645700815/645657712 = | -4 17 1 -9 > ~ 0.1156 cents

781258401/781250000 = | -4 2 -11 2 6 > ~ 0.0186 cents

3294225/3294172 = | -2 2 2 -7 4 > ~ 0.0279 cents

67110351/67108864 = | -26 1 5 3 > ~ 0.0384 cents

199297406/199290375 = | 1 -13 -3 7 2 > ~ 0.0611 cents

14348907/14348180 = | -2 15 -1 -2 -4 > ~ 0.0877 cents

1771561/1771470 = | -1 -11 -1 0 6 > ~ 0.0889 cents

100663296/100656875 = | 25 1 -4 0 -5 > ~ 0.1104 cents

That's enough now. I'm afraid to try 13-limit; it might cause my computer to catch on fire.

~Danny~

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> I had a little fun with Scala this morning. I searched for intervals
with a
> size similar to | -1054 665 > (the "Satanic comma", or what I prefer
to call
> a "microcomma"), and found....
>
> 78125000/78121827 = | 3 -13 10 -2 > ~ 0.0703 cents
>
> 645700815/645657712 = | -4 17 1 -9 > ~ 0.1156 cents

Put them together and you get the 171&3125 temperament. This is
actually in theory a good temperament and a fine way to organize the
notes of 3125, in case you felt the urge to. 4426/18921 is a copop
generator, and the resulting 7 and 9 limit optimized tuning
might be good enough, if getting within 1/200th of a cent will do for
your purposes.

> I'm doing 11-limit now, but it's taking a while. My computer is
slower than
> I thought.

Once you have them, what do you propose to do with them? Incidentally,
there are much faster ways of doing a search like this than the method
you suggest.

From: "Gene Ward Smith" <gwsmith@...>

>> 78125000/78121827 = | 3 -13 10 -2 > ~ 0.0703 cents
>>
>> 645700815/645657712 = | -4 17 1 -9 > ~ 0.1156 cents
>
> Put them together and you get the 171&3125 temperament. This is
> actually in theory a good temperament and a fine way to organize the
> notes of 3125, in case you felt the urge to. 4426/18921 is a copop
> generator, and the resulting 7 and 9 limit optimized tuning
> might be good enough, if getting within 1/200th of a cent will do for
> your purposes.

Oh 171-tone is great for 7-limit. And it's also enneadecal, and I've been working on a 19-nominal naming system.

(The only reason I'd want super-high ETs is for measurement purposes. I probably won't go past 72 in practice.)

>> I'm doing 11-limit now, but it's taking a while. My computer is
> slower than
>> I thought.
>
> Once you have them, what do you propose to do with them? Incidentally,
> there are much faster ways of doing a search like this than the method
> you suggest.

Yeah, but I only know how to use Scala for this purpose. This was all just curiosity.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> Oh 171-tone is great for 7-limit. And it's also enneadecal, and I've
been
> working on a 19-nominal naming system.

I thought about 19 nominals for notating ennealimmal, but I doubt
there would be much enthusiasm for it.

> (The only reason I'd want super-high ETs is for measurement purposes. I
> probably won't go past 72 in practice.)

I'd be interested to hear what you've done with 72.