Start of survey

I did the first three pairs on my list, and got the following. (All
turned out to be Minkowski reduced according to Tenney height.)

<1728/1715, 2048/2025>

ets: 14, 22, 58, 80

LLL reduced map:

[ 0 2]
[-3 4]
[ 6 3]
[-5 7]

Generators: a = 0.1376381046 = 11.01104837 / 80; b = 1/2

Appromimately 58+22 in the 80-et.

Errors:

3: 2.55
5: 4.68
7: 5.35

Extension of map to the 11-limit:

[ 0 2]
[-3 4]
[ 6 3]
[-5 7]
[ 7 5]

<225/224, 49/48>

ets: 9, 10, 19, 29

LLL-reduced map:

[-1 1]
[-2 -2]
[-2 5]
[-3 1]

Adjusted map:

[ 0 1]
[-4 2]
[ 3 2]
[-2 3]

Generator a = 0.1045573299 = 1.986589268 / 19

This system is closely related to 10+9 in the 19-et, and also related
to 19+10.

Errors:

3: -3.83
5: -9.91
7: -19.76

<245/243, 50/49>

Map:

[-2 -2]
[-1 5]
[-1 9]
[-2 8]

Adjusted map:

[0 2]
[3 1]
[5 1]
[5 2]

Generator: 0.3629853525 = 7.985677755 / 22

Errors:

3: 4.79
5: -8.40
7: 9.09

This one may as well be taken as the generator 8/22 in the 22-et;
this is a supermajor third (9/7), and we have two parallel chains
separated by sqrt(2). This is a unique facet of the 22-et.

--- In tuning-math@y..., genewardsmith@j... wrote:
> I did the first three pairs on my list, and got the following. (All
> turned out to be Minkowski reduced according to Tenney height.)
>
> <1728/1715, 2048/2025>
>
> ets: 14, 22, 58, 80
>
> LLL reduced map:
>
> [ 0 2]
> [-3 4]
> [ 6 3]
> [-5 7]
>
> Generators: a = 0.1376381046 = 11.01104837 / 80; b = 1/2
>
> Appromimately 58+22 in the 80-et.
>
> Errors:
>
> 3: 2.55
> 5: 4.68
> 7: 5.35
>
> Extension of map to the 11-limit:
>
> [ 0 2]
> [-3 4]
> [ 6 3]
> [-5 7]
> [ 7 5]
>
> <225/224, 49/48>
>
> ets: 9, 10, 19, 29
>
> LLL-reduced map:
>
> [-1 1]
> [-2 -2]
> [-2 5]
> [-3 1]
>
> Adjusted map:
>
> [ 0 1]
> [-4 2]
> [ 3 2]
> [-2 3]
>
> Generator a = 0.1045573299 = 1.986589268 / 19
>
> This system is closely related to 10+9 in the 19-et, and also
related
> to 19+10.
>
> Errors:
>
> 3: -3.83
> 5: -9.91
> 7: -19.76
>
> <245/243, 50/49>
>
> Map:
>
> [-2 -2]
> [-1 5]
> [-1 9]
> [-2 8]
>
> Adjusted map:
>
> [0 2]
> [3 1]
> [5 1]
> [5 2]
>
> Generator: 0.3629853525 = 7.985677755 / 22
>
> Errors:
>
> 3: 4.79
> 5: -8.40
> 7: 9.09
>
> This one may as well be taken as the generator 8/22 in the 22-et;
> this is a supermajor third (9/7), and we have two parallel chains
> separated by sqrt(2).

Then shouldn't you have said

a = 0.3629853525 = 7.985677755 / 22, b = 1/2

above, similar to what you did for the first example?

--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:

> Then shouldn't you have said
>
> a = 0.3629853525 = 7.985677755 / 22, b = 1/2
>
> above, similar to what you did for the first example?

I got lazy, but I suppose I'd better do it systematically. I also
left out b=1 when that was a generator.

--- In tuning-math@y..., genewardsmith@j... wrote:
> I did the first three pairs on my list, and got the following. (All
> turned out to be Minkowski reduced according to Tenney height.)
>
> <1728/1715, 2048/2025>
>
> ets: 14, 22, 58, 80
>
> LLL reduced map:
>
> [ 0 2]
> [-3 4]
> [ 6 3]
> [-5 7]
>
> Generators: a = 0.1376381046 = 11.01104837 / 80; b = 1/2
>
> Appromimately 58+22 in the 80-et.
>
> Errors:
>
> 3: 2.55
> 5: 4.68
> 7: 5.35

Complexity 22, max. error 5.35

>
> <225/224, 49/48>
>
> ets: 9, 10, 19, 29
>
> LLL-reduced map:
>
> [-1 1]
> [-2 -2]
> [-2 5]
> [-3 1]
>
> Adjusted map:
>
> [ 0 1]
> [-4 2]
> [ 3 2]
> [-2 3]
>
> Generator a = 0.1045573299 = 1.986589268 / 19
>
> This system is closely related to 10+9 in the 19-et, and also
related
> to 19+10.
>
> Errors:
>
> 3: -3.83
> 5: -9.91
> 7: -19.76

Complexity 7, max. error 19.76.

>
> <245/243, 50/49>
>
> Map:
>
> [-2 -2]
> [-1 5]
> [-1 9]
> [-2 8]
>
> Adjusted map:
>
> [0 2]
> [3 1]
> [5 1]
> [5 2]
>
> Generator: 0.3629853525 = 7.985677755 / 22 [b = 1/2]
>
> Errors:
>
> 3: 4.79
> 5: -8.40
> 7: 9.09
>
> This one may as well be taken as the generator 8/22 in the 22-et;
> this is a supermajor third (9/7), and we have two parallel chains
> separated by sqrt(2). This is a unique facet of the 22-et.

Complexity 10, max. err. 17.49¢