Temperaments with a 7/5 generator

Linear temperaments with a generator which is itself a consonant interval
seem to me of particular interest, so I thought I would explore what is
out there for generators of about 7/5. While nothing dramatic turned up,
these systems might be of interest.

[3, -5, -6, -1, -15, -18, -12, 0, 15, 18]
<56/55, 64/63, 77/75>
badness = 326 rms = 13.78

[3, -5, -6, 0, 18, -15]
<64/63, 392/375>
badness = 532 rms = 14.78

7/15 < 15/32 < 8/17

15/32 is a nearly exact 11-limit generator; 11/8 is closer than 7/5 to
this generator, which is convenient.

[3, 12, 11, -1, 12, 9, -12, -8, -44, -41]
<56/55, 81/80, 540/539>
badness = 404 rms = 12.62

[3, 12, 11, -8, -9, 12]
<81/80, 686/675>
badness = 634 rms = 9.05

8/17 < 17/36 < 9/19

17/36 is nearly exact 11-generator; again, 11/8 is closer. These two are
the same in the 17-et.

[5, -11, -12, -3, -29, -33, -22, 3, 31, 33]
<121/120, 225/224, 441/440>
badness = 355 rms = 5.15

[5, -11, -12, 3, 33, -29]
<225/224, 50421/50000>
badness = 376 rms = 2.68

15/31 generator

[7, -15, -16, -3, -40, -45, -29, 5, 45, 47]
<225/224, 441/440, 1344/1331>
badness = 485 rms = 4.19

[7, -15, -16, 5, 45, -40]
<225/224, 2500000/2470629>
badness = 491 rms = 1.91

20/41 < 61/125 < 41/84

20/41 generator, or 61/125 if you are really picky.

[7, 26, 25, -3, 25, 20, -29, -15, -97, -95]
<540/539, 896/891, 1375/1372>
badness = 318.5 rms = 2.58

[7, 26, 25, -15, -20, 25]
<4000/3969, 10976/10935>
badness = 641 rms = 1.89

39/80 < 59/121 < 79/162 < 20/41

59/121 generator; 20/41 makes this the same as the previous.

[30, 13, 14, 3, -49, -62, -99, -4, -38, -40]
<385/384, 2401/2400, 4000/3993>
badness = 372 rms = 1.18

[30, 13, 14, -4, 62, -49]
<2401/2400, 390625/387072>
badness = 443 rms = 1.48

generator 35/72

--- In tuning-math@yahoogroups.com, Gene W Smith <genewardsmith@j...>
wrote:
> Linear temperaments with a generator which is itself a consonant
interval
> seem to me of particular interest, so I thought I would explore
what is
> out there for generators of about 7/5. While nothing dramatic
turned up,
> these systems might be of interest.
>
>
> [3, -5, -6, -1, -15, -18, -12, 0, 15, 18]
> <56/55, 64/63, 77/75>
> badness = 326 rms = 13.78
>
> [3, -5, -6, 0, 18, -15]
> <64/63, 392/375>
> badness = 532 rms = 14.78
>
> 7/15 < 15/32 < 8/17
>
> 15/32 is a nearly exact 11-limit generator; 11/8 is closer than 7/5
to
> this generator, which is convenient.
>
>
>
> [3, 12, 11, -1, 12, 9, -12, -8, -44, -41]
> <56/55, 81/80, 540/539>
> badness = 404 rms = 12.62
>
> [3, 12, 11, -8, -9, 12]
> <81/80, 686/675>
> badness = 634 rms = 9.05
>
> 8/17 < 17/36 < 9/19
>
> 17/36 is nearly exact 11-generator; again, 11/8 is closer. These
two are
> the same in the 17-et.

17/36 or 19/36. Gawel.