hey Paul

I'm interested in these scales...

>> [4, -3, 2, 13, 8, -14] [[1, 2, 2, 3], [0, 4, -3, 2]]
>> complexity 14.729697 rms 12.188571 badness 2644.480844
>> generators [1200., -125.4687958]
>
>25:24 chroma = -6 - 4 = -10 generators -> 10 note scale
>graham complexity = 7 -> 6 tetrads

Not sure of the significance of the - in -125. I realize
that might have been Gene.

>> [4, 2, 2, -1, 8, -6] [[2, 0, 3, 4], [0, 2, 1, 1]]
>> complexity 10.574200 rms 23.945252 badness 2677.407574
>> generators [600.0000000, 950.9775006]
>
>//
>
>> [2, 6, 6, -3, -4, 5] [[2, 0, -5, -4], [0, 1, 3, 3]]
>> complexity 11.925109 rms 18.863889 badness 2682.600333
>> generators [600.0000000, 1928.512337]
>
>25:24 chroma = 6 - 1 = 5 generators -> 10 note scale
>graham complexity = 3*2 = 6 -> 8 tetrads

I've never noticed "generators" being expressed as larger
than "periods". Why? Can't we just reduce by the periods
here, getting

350.9775006

and

600., 128.512337

resp.?

Again, sorry if this is more of a question for the poster
of the >>'d text (Gene?).

>> [6, -2, -2, 1, 20, -17] [[2, 2, 5, 6], [0, 3, -1, -1]]
>> complexity 19.126831 rms 11.798337 badness 4316.252447
>> generators [600.0000000, 231.2978354]
>
>25:24 chroma = -2 - 3 = 5 generators -> 10 note scale
>graham complexity = 8 -> 4 tetrads

By the way, do these temperaments have names?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> I'm interested in these scales...
>
> >> [4, -3, 2, 13, 8, -14] [[1, 2, 2, 3], [0, 4, -3, 2]]
> >> complexity 14.729697 rms 12.188571 badness 2644.480844
> >> generators [1200., -125.4687958]
> >
> >25:24 chroma = -6 - 4 = -10 generators -> 10 note scale
> >graham complexity = 7 -> 6 tetrads
>
> Not sure of the significance of the - in -125. I realize
> that might have been Gene.

yup. anyway, this is a negri scale, yes?

> >> [4, 2, 2, -1, 8, -6] [[2, 0, 3, 4], [0, 2, 1, 1]]
> >> complexity 10.574200 rms 23.945252 badness 2677.407574
> >> generators [600.0000000, 950.9775006]
> >
> >//
> >
> >> [2, 6, 6, -3, -4, 5] [[2, 0, -5, -4], [0, 1, 3, 3]]
> >> complexity 11.925109 rms 18.863889 badness 2682.600333
> >> generators [600.0000000, 1928.512337]
> >
> >25:24 chroma = 6 - 1 = 5 generators -> 10 note scale
> >graham complexity = 3*2 = 6 -> 8 tetrads
>
> I've never noticed "generators" being expressed as larger
> than "periods". Why? Can't we just reduce by the periods
> here, getting
>
> 350.9775006
>
> and
>
> 600., 128.512337
>
> resp.?
>
> Again, sorry if this is more of a question for the poster
> of the >>'d text (Gene?).

it is. but the answer is yes, you can so reduce by the periods. gene
was just trying to give a "hermite-reduced basis" or some such
abstractly interesting form for the generators.

> >> [6, -2, -2, 1, 20, -17] [[2, 2, 5, 6], [0, 3, -1, -1]]
> >> complexity 19.126831 rms 11.798337 badness 4316.252447
> >> generators [600.0000000, 231.2978354]
> >
> >25:24 chroma = -2 - 3 = 5 generators -> 10 note scale
> >graham complexity = 8 -> 4 tetrads
>
> By the way, do these temperaments have names?

many of them do, thanks to gene . . .

>> >> [4, -3, 2, 13, 8, -14] [[1, 2, 2, 3], [0, 4, -3, 2]]
>> >> complexity 14.729697 rms 12.188571 badness 2644.480844
>> >> generators [1200., -125.4687958]
>> >
>> >25:24 chroma = -6 - 4 = -10 generators -> 10 note scale
>> >graham complexity = 7 -> 6 tetrads
>>
>> Not sure of the significance of the - in -125. I realize
>> that might have been Gene.
>
>yup. anyway, this is a negri scale, yes?

Yep.

>> >> [4, 2, 2, -1, 8, -6] [[2, 0, 3, 4], [0, 2, 1, 1]]
>> >> complexity 10.574200 rms 23.945252 badness 2677.407574
>> >> generators [600.0000000, 950.9775006]
>> >
>> >//
>> >
>> >> [2, 6, 6, -3, -4, 5] [[2, 0, -5, -4], [0, 1, 3, 3]]
>> >> complexity 11.925109 rms 18.863889 badness 2682.600333
>> >> generators [600.0000000, 1928.512337]
>> >
>> >25:24 chroma = 6 - 1 = 5 generators -> 10 note scale
>> >graham complexity = 3*2 = 6 -> 8 tetrads
>>
>> I've never noticed "generators" being expressed as larger
>> than "periods". Why? Can't we just reduce by the periods
>> here, getting
>>
>> 350.9775006
>>
>> and
>>
>> 600., 128.512337
>>
>> resp.?
>>
>> Again, sorry if this is more of a question for the poster
>> of the >>'d text (Gene?).
>
>it is. but the answer is yes, you can so reduce by the periods. gene
>was just trying to give a "hermite-reduced basis" or some such
>abstractly interesting form for the generators.

Tx.

>> >> [6, -2, -2, 1, 20, -17] [[2, 2, 5, 6], [0, 3, -1, -1]]
>> >> complexity 19.126831 rms 11.798337 badness 4316.252447
>> >> generators [600.0000000, 231.2978354]
>> >
>> >25:24 chroma = -2 - 3 = 5 generators -> 10 note scale
>> >graham complexity = 8 -> 4 tetrads
>>
>> By the way, do these temperaments have names?
>
>many of them do, thanks to gene . . .

Is there a way for people to look them up?

-Carl

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

> Is there a way for people to look them up?

Should I put up a web page? Dave, do you have an objection?

>> Is there a way for people to look them up?
>
>Should I put up a web page? Dave, do you have an objection?

Graham's catalog is neither complete or up to date, last I
checked.

The existence of a single resource is a lot to ask, I know...

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Is there a way for people to look them up?
> >
> >Should I put up a web page? Dave, do you have an objection?
>
> Graham's catalog is neither complete or up to date, last I
> checked.
>
> The existence of a single resource is a lot to ask, I know...

I'm perfectly willing to put up web pages of named temperaments.

>> >Should I put up a web page? Dave, do you have an objection?
>>
>> Graham's catalog is neither complete or up to date, last I
>> checked.
>>
>> The existence of a single resource is a lot to ask, I know...
>
>I'm perfectly willing to put up web pages of named temperaments.

Then don't stop 'til the break of dawn!

-Carl