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.