top23

Paul's Dave-approved list of 23 7-limit temperaments...

>1. Huygens meantone
>2. Pajara
>3. Magic
>4. Semisixths
>5. Dominant Seventh
>6. Tripletone
>7. Negri
>8. Hemifourths
>9. Kleismic/Hanson
>10. Superpythagorean
>11. Injera
>12. Miracle
>13. Biporky
>14. Orwell
>15. Diminished
>16. Schismic
>17. Augmented
>18. 1/12 oct. period, 25 cent generator (we discussed this years ago)
>19. Flattone
>20. Blackwood
>21. Supermajor seconds
>22. Nonkleismic
>23. Porcupine

This looks reasonable. Let's go back to the top 23 from Gene's 114...

>Number 1 Ennealimmal
>Number 2 Meantone
>Number 3 Magic
>Number 4 Beep
>Number 5 Augmented
>Number 6 Pajara
>Number 7 Dominant Seventh
>Number 8 Schismic
>Number 9 Miracle
>Number 10 Orwell
>Number 11 Hemiwuerschmidt
>Number 12 Catakleismic
>Number 13 Father
>Number 14 Blackwood
>Number 15 Semisixths
>Number 16 Hemififths
>Number 17 Diminished
>Number 18 Amity
>Number 19 Pelogic
>Number 20 Parakleismic
>Number 21 {21/20, 28/27}
>Number 22 Injera
>Number 23 Dicot

...also reasonable. Assuming names are synchronized (hemififths=
hemifourths?, meantone=huygens?, etc), here's the intersection of
these lists in Paul order...

>1. Huygens meantone
>2. Pajara
>3. Magic
>4. Semisixths
>5. Dominant Seventh
>11. Injera
>12. Miracle
>14. Orwell
>15. Diminished
>16. Schismic
>17. Augmented
>20. Blackwood

Here's the intersection in Gene order...

>Number 2 Meantone
>Number 3 Magic
>Number 5 Augmented
>Number 6 Pajara
>Number 7 Dominant Seventh
>Number 8 Schismic
>Number 9 Miracle
>Number 10 Orwell
>Number 14 Blackwood
>Number 15 Semisixths
>Number 17 Diminished
>Number 22 Injera

Agreement is on 12 temperaments, and fairly well on order.
Schismic, augmented and Blackwood seem to be the greatest
order disputes. Ennealimmal, beep, tripletone, negri and
kleismic seem to be the greatest omission disputes.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Paul's Dave-approved list of 23 7-limit temperaments...
>
> >1. Huygens meantone
> >2. Pajara
> >3. Magic
> >4. Semisixths
> >5. Dominant Seventh
> >6. Tripletone
> >7. Negri
> >8. Hemifourths
> >9. Kleismic/Hanson
> >10. Superpythagorean
> >11. Injera
> >12. Miracle
> >13. Biporky
> >14. Orwell
> >15. Diminished
> >16. Schismic
> >17. Augmented
> >18. 1/12 oct. period, 25 cent generator (we discussed this years
ago)
> >19. Flattone
> >20. Blackwood
> >21. Supermajor seconds
> >22. Nonkleismic
> >23. Porcupine
>
> This looks reasonable. Let's go back to the top 23 from Gene's
114...
>
> >Number 1 Ennealimmal
> >Number 2 Meantone
> >Number 3 Magic
> >Number 4 Beep
> >Number 5 Augmented
> >Number 6 Pajara
> >Number 7 Dominant Seventh
> >Number 8 Schismic
> >Number 9 Miracle
> >Number 10 Orwell
> >Number 11 Hemiwuerschmidt
> >Number 12 Catakleismic
> >Number 13 Father
> >Number 14 Blackwood
> >Number 15 Semisixths
> >Number 16 Hemififths
> >Number 17 Diminished
> >Number 18 Amity
> >Number 19 Pelogic
> >Number 20 Parakleismic
> >Number 21 {21/20, 28/27}
> >Number 22 Injera
> >Number 23 Dicot
>
> ...also reasonable. Assuming names are synchronized (hemififths=
> hemifourths?,

That can't be the same, but it looks like you didn't assume they were
the same below.

> here's the intersection of
> these lists in Paul order...
>
> >1. Huygens meantone
> >2. Pajara
> >3. Magic
> >4. Semisixths
> >5. Dominant Seventh
> >11. Injera
> >12. Miracle
> >14. Orwell
> >15. Diminished
> >16. Schismic
> >17. Augmented
> >20. Blackwood
>
> Here's the intersection in Gene order...
>
> >Number 2 Meantone
> >Number 3 Magic
> >Number 5 Augmented
> >Number 6 Pajara
> >Number 7 Dominant Seventh
> >Number 8 Schismic
> >Number 9 Miracle
> >Number 10 Orwell
> >Number 14 Blackwood
> >Number 15 Semisixths
> >Number 17 Diminished
> >Number 22 Injera
>
> Agreement is on 12 temperaments, and fairly well on order.
> Schismic, augmented and Blackwood seem to be the greatest
> order disputes. Ennealimmal, beep, tripletone, negri and
> kleismic seem to be the greatest omission disputes.

Sure, and remember, I might have included Ennealimmal but Gene didn't
provide enough data to locate where a moat might go in that vicinity.
When I have time, I'll do my own 7-limit linear temperament search,
though I haven't implemented the linear programming needed (?) to
calculate TOP error yet.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> This looks reasonable. Let's go back to the top 23 from Gene's
>114...

Gene was using the L_infinity norm of the wedgie there, but never
explained why. I used the L_1 norm because that gives you the (hyper)
taxicab cross-sectional area of the periodicity unit of the
temperament in the Tenney lattice. I'll assume that Gene had some
reason for using L_infinity . . . It seems that in all the cases
we've looked at, only 7-limit linear's wedgie is "rich" enough so
that L_infinity and L_1 don't give virtually identical results . . .

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > This looks reasonable. Let's go back to the top 23 from Gene's
> >114...
>
> Gene was using the L_infinity norm of the wedgie there, but never
> explained why.

It was one of the two obvious choices, and since a linear temperament
is always two vals wedged together, I picked a val-based definition.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> > > This looks reasonable. Let's go back to the top 23 from Gene's
> > >114...
> >
> > Gene was using the L_infinity norm of the wedgie there, but never
> > explained why.
>
> It was one of the two obvious choices, and since a linear
temperament
> is always two vals wedged together, I picked a val-based definition.

I don't get it. Why would a val-based definition lead you to use the
L_infinity norm?