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¢