7-limit temperaments with fifth and octave as generators

Given Paul's comments on the special nature of the fifth as generator,
I thought I would list these.

Meantone
[[1, 2, 4, 7], [0, -1, -4, -10]] [1, 4, 10, 4, 13, 12]
[1200., 503.3520320]

bad 835.864430 comp 15.101806 rms 3.665035

Infraschismic
[[1, 2, -1, 19], [0, -1, 8, -39]] [1, -8, 39, -15, 59, 113]
[1200., 498.2414296]

bad 1159.472962 comp 72.040511 rms .223412

Schismic
[[1, 2, -1, -3], [0, -1, 8, 14]] [1, -8, -14, -15, -25, -10]
[1200., 497.8598384]

bad 1704.355358 comp 24.414474 rms 2.859338

Dominant seventh
[[1, 2, 4, 2], [0, -1, -4, 2]] [1, 4, -2, 4, -6, -16]
[1200., 497.7740225]

bad 1950.956905 comp 9.836560 rms 20.163282

Superpythagorean
[[1, 2, 6, 2], [0, -1, -9, 2]] [1, 9, -2, 12, -6, -30]
[1200., 489.6151808]

bad 2430.162102 comp 19.470320 rms 6.410458

[[1, 2, 1, 1], [0, -1, 3, 4]] [1, -3, -4, -7, -9, -1]
[1200., 532.1557550]

bad 2695.579145 comp 8.756575 rms 35.154715

Pelogic
[[1, 2, 1, 5], [0, -1, 3, -5]] [1, -3, 5, -7, 5, 20]
[1200., 526.8909182]

bad 2828.823659 comp 12.337509 rms 18.584500

Flattone
[[1, 2, 4, -1], [0, -1, -4, 9]] [1, 4, -9, 4, -17, -32]
[1200., 506.5439220]

bad 2965.536792 comp 19.685796 rms 7.652395

[[1, 2, 0, 4], [0, -1, 6, -3]] [1, -6, 3, -12, 2, 24]
[1200., 468.4644943]

bad 4593.171154 comp 15.521698 rms 19.064883

[[1, 2, 9, 17], [0, -1, -16, -34]] [1, 16, 34, 23, 51, 34]
[1200., 500.9569337]

bad 4849.147837 comp 53.592633 rms 1.688322

[[1, 2, 16, 14], [0, -1, -33, -27]] [1, 33, 27, 50, 40, -30]
[1200., 497.3975646]

bad 4988.312470 comp 65.757540 rms 1.153619

[[1, 2, -1, -8], [0, -1, 8, 26]] [1, -8, -26, -15, -44, -38]
[1200., 498.7882616]

bad 5312.978320 comp 41.357685 rms 3.106173

[[1, 2, -1, 2], [0, -1, 8, 2]] [1, -8, -2, -15, -6, 18]
[1200., 498.4152538]

bad 5451.864616 comp 16.648693 rms 19.669112

[[1, 2, -13, -15], [0, -1, 37, 43]] [1, -37, -43, -61, -71, 4]
[1200., 496.9546632]

bad 5627.373521 comp 85.068723 rms .777617

[[1, 2, 8, 2], [0, -1, -14, 2]] [1, 14, -2, 20, -6, -44]
[1200., 486.3802354]

bad 5995.726244 comp 29.525064 rms 6.877967

[[1, 2, 0, 2], [0, -1, 6, 2]] [1, -6, -2, -12, -6, 12]
[1200., 467.9535131]

bad 6466.522095 comp 12.766699 rms 39.674691

[[1, 2, -1, -30], [0, -1, 8, 79]] [1, -8, -79, -15, -128, -161]
[1200., 498.3393014]

bad 6536.767371 comp 127.074856 rms .404803

[[1, 2, -6, -13], [0, -1, 20, 38]] [1, -20, -38, -34, -63, -32]
[1200., 499.1780246]

bad 7239.522633 comp 63.056929 rms 1.820725

[[1, 2, 4, 12], [0, -1, -4, -22]] [1, 4, 22, 4, 32, 40]
[1200., 501.4086553]

bad 7903.032213 comp 33.983455 rms 6.843191

[[1, 2, 11, -10], [0, -1, -21, 31]] [1, 21, -31, 31, -52, -131]
[1200., 495.8167399]

bad 8049.514486 comp 77.870556 rms 1.327465

[[1, 2, -5, 2], [0, -1, 18, 2]] [1, -18, -2, -31, -6, 46]
[1200., 488.4529600]

bad 8056.407803 comp 36.781140 rms 5.955127

[[1, 2, 4, 15], [0, -1, -4, -29]] [1, 4, 29, 4, 43, 56]
[1200., 504.6434851]

bad 8172.009202 comp 45.418971 rms 3.961451

[[1, 2, 11, 9], [0, -1, -21, -15]] [1, 21, 15, 31, 21, -24]
[1200., 495.7080636]

bad 8383.389707 comp 40.527877 rms 5.104015

[[1, 2, -8, 9], [0, -1, 25, -15]] [1, -25, 15, -42, 21, 105]
[1200., 495.4499387]

bad 8498.205838 comp 64.879485 rms 2.018889

[[1, 2, -6, -18], [0, -1, 20, 50]] [1, -20, -50, -34, -82, -60]
[1200., 499.3603580]

bad 8661.804640 comp 79.600666 rms 1.367020

[[1, 2, 9, 12], [0, -1, -16, -22]] [1, 16, 22, 23, 32, 6]
[1200., 501.3431135]

bad 8800.446366 comp 38.667369 rms 5.885935

[[1, 2, -18, -3], [0, -1, 49, 14]] [1, -49, -14, -80, -25, 105]
[1200., 497.6823538]

bad 9506.298851 comp 95.772428 rms 1.036407

[[1, 2, -3, 11], [0, -1, 13, -20]] [1, -13, 20, -23, 29, 83]
[1200., 491.4400621]

bad 9539.393884 comp 49.549142 rms 3.885514

[[1, 2, 28, 26], [0, -1, -62, -56]] [1, 62, 56, 96, 86, -44]
[1200., 496.9820268]

bad 11549.825230 comp 127.430034 rms .711266

[[1, 2, 6, -7], [0, -1, -9, 24]] [1, 9, -24, 12, -41, -81]
[1200., 490.4322040]

bad 12799.334640 comp 49.681423 rms 5.185604

[[1, 2, 14, 27], [0, -1, -28, -58]] [1, 28, 58, 42, 89, 56]
[1200., 500.5566262]

bad 13078.169160 comp 92.349249 rms 1.533487

[[1, 2, 7, -4], [0, -1, -11, 16]] [1, 11, -16, 15, -28, -68]
[1200., 510.4083259]

bad 13307.986690 comp 40.474090 rms 8.123780

[[1, 2, -4, -9], [0, -1, 15, 28]] [1, -15, -28, -26, -47, -23]
[1200., 505.8354701]

bad 13412.109770 comp 46.922728 rms 6.091589

[[1, 2, 13, 18], [0, -1, -26, -37]] [1, 26, 37, 39, 56, 13]
[1200., 492.6818432]

bad 13887.938240 comp 64.729582 rms 3.314608

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Given Paul's comments on the special nature of the fifth as
>generator,

pajara and injera both qualify.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> wrote:
> > Given Paul's comments on the special nature of the fifth as
> >generator,
>
> pajara and injera both qualify.

If you allow 1/2 octave, it's more like having a half-fourth or half-
fifth as generator.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...>
> > wrote:
> > > Given Paul's comments on the special nature of the fifth as
> > >generator,
> >
> > pajara and injera both qualify.
>
> If you allow 1/2 octave, it's more like having a half-fourth or
half-
> fifth as generator.

nonsense. neither the half-fourth nor the half-fifth are anywhere near
any of the possible generators for pajara or injera.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > If you allow 1/2 octave, it's more like having a half-fourth or
> half-
> > fifth as generator.
>
> nonsense. neither the half-fourth nor the half-fifth are anywhere near
> any of the possible generators for pajara or injera.

You missed my point, which was about complexity.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > > If you allow 1/2 octave, it's more like having a half-fourth or
> > half-
> > > fifth as generator.
> >
> > nonsense. neither the half-fourth nor the half-fifth are anywhere
near
> > any of the possible generators for pajara or injera.
>
> You missed my point, which was about complexity.

ah, ok, now that i've seen what you posted after that, this makes
perfect sense! sorry for taking "more like" too literally . . .