Complete Rank 2 Temperament Searches

I'm working on a PDF about my proof of completeness of certain searches for rank 2 temperaments. I explained it here a couple of years ago but I don't think anybody understood. It's on my website at

http://x31eq.com/complete.pdf

There are things I want to add or change so if you want a stable document wait until the new moon.

To go with this I've also updated the source bundle for temperament searches:

http://x31eq.com/temper/regular.zip

That's stable now. There's a new file with only code for complete searches and some other refinements. This includes equal temperament and mapping searches that really are watertight (but only from complete.py).

Graham

At 06:41 AM 3/3/2008, you wrote:
>I'm working on a PDF about my proof of completeness of
>certain searches for rank 2 temperaments. I explained it
>here a couple of years ago but I don't think anybody
>understood. It's on my website at
>
> http://x31eq.com/complete.pdf
>

"this is generally true for all rank
2 temperament."

Did you mean "temperaments" there?

-Carl

Carl Lumma wrote:

> "this is generally true for all rank
> 2 temperament."
> > Did you mean "temperaments" there?

Yes. Or maybe "any" and I got the two phrases mixed up.

Graham

Graham Breed wrote:
> I'm working on a PDF about my proof of completeness of > certain searches for rank 2 temperaments. I explained it > here a couple of years ago but I don't think anybody > understood. It's on my website at
> > http://x31eq.com/complete.pdf
> > There are things I want to add or change so if you want a > stable document wait until the new moon.
> > To go with this I've also updated the source bundle for > temperament searches:
> > http://x31eq.com/temper/regular.zip
> > That's stable now. There's a new file with only code for > complete searches and some other refinements. This includes > equal temperament and mapping searches that really are > watertight (but only from complete.py).

For the 11-limit temperament
|<1, -5, 0, -3, -7|, <0, 17, 6, 15, 27|>

I don't know a specific name, but the 7-limit version has been called "semisept". Of the other 11-limit "semisept" temperaments, [<1, -5, 0, -3, 5], <0, 17, 6, 15, -4]> is more complex and has a larger error, and [<1, -5, 0, -3, 0], <0, 17, 6, 15, 9]> is less complex but has a much larger error. The earliest refrence to the name that I can locate is in "A table of 7-limit MOS" from 7/4/2005.

The 13-limit temperament
|<2, 4, 7, 7, 9, 11|, <0, -6, -17, -10, -15, -26|>
is identified as "Harry" in the message "13-limit hexany hole ball scales" from Gene Ward Smith, 3/26/2005.

Herman Miller wrote:

> For the 11-limit temperament
> |<1, -5, 0, -3, -7|, <0, 17, 6, 15, 27|>
> > I don't know a specific name, but the 7-limit version has been called > "semisept". Of the other 11-limit "semisept" temperaments, [<1, -5, 0, > -3, 5], <0, 17, 6, 15, -4]> is more complex and has a larger error, and > [<1, -5, 0, -3, 0], <0, 17, 6, 15, 9]> is less complex but has a much > larger error. The earliest refrence to the name that I can locate is in > "A table of 7-limit MOS" from 7/4/2005.

I take it the "sept" refers to the 7-limit. In that case would an 11-limit extension be "semiundec"?

> The 13-limit temperament
> |<2, 4, 7, 7, 9, 11|, <0, -6, -17, -10, -15, -26|>
> is identified as "Harry" in the message "13-limit hexany hole ball > scales" from Gene Ward Smith, 3/26/2005.

Thank you! No temperament class is too obscure to have a name! Are these tuning-math references?

Graham

Graham Breed wrote:
> Herman Miller wrote:
> >> For the 11-limit temperament
>> |<1, -5, 0, -3, -7|, <0, 17, 6, 15, 27|>
>>
>> I don't know a specific name, but the 7-limit version has been called >> "semisept". Of the other 11-limit "semisept" temperaments, [<1, -5, 0, >> -3, 5], <0, 17, 6, 15, -4]> is more complex and has a larger error, and >> [<1, -5, 0, -3, 0], <0, 17, 6, 15, 9]> is less complex but has a much >> larger error. The earliest refrence to the name that I can locate is in >> "A table of 7-limit MOS" from 7/4/2005.
> > I take it the "sept" refers to the 7-limit. In that case > would an 11-limit extension be "semiundec"?

You'd have to ask Gene about the "sept". It could be that the generator is half of the tempered interval 12/7.

>> The 13-limit temperament
>> |<2, 4, 7, 7, 9, 11|, <0, -6, -17, -10, -15, -26|>
>> is identified as "Harry" in the message "13-limit hexany hole ball >> scales" from Gene Ward Smith, 3/26/2005.
> > Thank you! No temperament class is too obscure to have a > name! Are these tuning-math references?

Yes, and both are from Gene Ward Smith.

Herman Miller wrote:
> Graham Breed wrote:
>> Herman Miller wrote:
>>
>>> For the 11-limit temperament
>>> |<1, -5, 0, -3, -7|, <0, 17, 6, 15, 27|>
>>>
>>> I don't know a specific name, but the 7-limit version has been called >>> "semisept". Of the other 11-limit "semisept" temperaments, [<1, -5, 0, >>> -3, 5], <0, 17, 6, 15, -4]> is more complex and has a larger error, and >>> [<1, -5, 0, -3, 0], <0, 17, 6, 15, 9]> is less complex but has a much >>> larger error. The earliest refrence to the name that I can locate is in >>> "A table of 7-limit MOS" from 7/4/2005.
>> I take it the "sept" refers to the 7-limit. In that case >> would an 11-limit extension be "semiundec"?
> > You'd have to ask Gene about the "sept". It could be that the generator > is half of the tempered interval 12/7.

Unfortunately he's out playing with his science fiction friends. At least that's the last I heard.

>>> The 13-limit temperament
>>> |<2, 4, 7, 7, 9, 11|, <0, -6, -17, -10, -15, -26|>
>>> is identified as "Harry" in the message "13-limit hexany hole ball >>> scales" from Gene Ward Smith, 3/26/2005.
>> Thank you! No temperament class is too obscure to have a >> name! Are these tuning-math references?

I was a bit dismissive of Harry. Maybe it is a 13-limit stand-out.

> Yes, and both are from Gene Ward Smith.

And I take it numerical dates are all in American form, so 7/4/2005 is the 4th of July.

Graham

The PDF in question is now finished bar corrections.

http://x31eq.com/complete.pdf

I've also compiled a version that puts everything in one column which you may prefer. The font's also larger and it has an unlucky number of pages.

http://x31eq.com/complete_onecol.pdf

Graham