37-edo: new Tonalsoft Encyclopedia page

over on tuning-math i've been discussing 37-edo a bit,
having recently discovered that it gives really great
approximations of prime-factors 5, 3, 7, 11, and 13
in 13-limit JI ... unfortunately 3 is not so good.
Anyway, here is a copy of a post from tuning-math:

.............

Here is my new Tonalsoft Encyclopedia page about 37-edo:

http://tonalsoft.com/enc/number/37-edo/37edo.aspx

It is not yet included in the index menu, but in case anyone
here wants to see it and use it, there's the URL.

This is really quite a promising EDO tuning!

I'm still hoping to get the ASCII sagittal notation for
this periodicity-block.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> over on tuning-math i've been discussing 37-edo a bit,
> having recently discovered that it gives really great
> approximations of prime-factors 5, 3, 7, 11, and 13
> in 13-limit JI ... unfortunately 3 is not so good.
> Anyway, here is a copy of a post from tuning-math:
>
> .............
>
> Here is my new Tonalsoft Encyclopedia page about 37-edo:
>
> http://tonalsoft.com/enc/number/37-edo/37edo.aspx

oops ... that was supposed to say "... it gives really great
approximations of prime-factors 5, 7, 11, and 13 ..."

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Hi Monz,

In http://sagittal.org/sagittal.pdf (and implemented in Scala) we recommend notating 37-EDO as every third note of 111-EDO, for which we give a notation. This of course treats it as not having a mapping of the prime 3 (only 2, 5, 7, 11, 13).

A native fifth notation could also be devised for it, based on the 11-limit porcupine mapping [<1 2 3 2 4], <0 -3 -5 6 -4]]. Herman Miller may already have devised such a sagittal notation.

-- Dave

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> over on tuning-math i've been discussing 37-edo a bit,
> having recently discovered that it gives really great
> approximations of prime-factors 5, 3, 7, 11, and 13
> in 13-limit JI ... unfortunately 3 is not so good.
> Anyway, here is a copy of a post from tuning-math:
>
> .............
>
> Here is my new Tonalsoft Encyclopedia page about 37-edo:
>
> http://tonalsoft.com/enc/number/37-edo/37edo.aspx
>
> It is not yet included in the index menu, but in case anyone
> here wants to see it and use it, there's the URL.
>
> This is really quite a promising EDO tuning!
>
> I'm still hoping to get the ASCII sagittal notation for
> this periodicity-block.
>
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music software
>

On 4/21/2012 9:33 AM, dkeenanuqnetau wrote:
> Hi Monz,
>
> In http://sagittal.org/sagittal.pdf (and implemented in Scala) we
> recommend notating 37-EDO as every third note of 111-EDO, for which
> we give a notation. This of course treats it as not having a mapping
> of the prime 3 (only 2, 5, 7, 11, 13).
>
> A native fifth notation could also be devised for it, based on the
> 11-limit porcupine mapping [<1 2 3 2 4],<0 -3 -5 6 -4]]. Herman
> Miller may already have devised such a sagittal notation.

My porcupine[37] notation is based on the 7-limit porcupine.

21 A~!) 26 A||\
31 B/|) 36 D~!) 04 D||\
09 E/|) 14 G~!) 19 G||\
24 A/|) 29 B 34 C||\
02 D/|) 07 E 12 F||\
17 G/|) 22 A 27 B\!)
32 C/|) 00 D 05 E\!)
10 F/|) 15 G 20 A\!)
25 B!!/ 30 C 35 D\!)
03 E!!/ 08 F 13 G\!)
18 A!!/ 23 A~|) 28 C\!)
33 D!!/ 01 D~|) 06 F\!)
11 G!!/ 16 G~|)

An 11-limit porcupine notation can substitute /|\ \!/ for /|) \!), but otherwise would be the same.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> My porcupine[37] notation is based on the 7-limit porcupine.

Good work. 7-limit is better, because it's better not to use /|\ for 2 degrees here. We try not to use /|\ when it is not a half-apotome (which would be 3 degrees). Your notation makes good sense (when I do "Show Source" and "Use Monospaced Font").

However I note it lacks an accidental for 3 degrees (8 generators) presumably because there is no core symbol whose primary comma maps to 8 generators, and you can get away without it by using alternative spellings. Now that we have the definitions of the accented symbols in http://sagittal.org/JINotate.xls (at least the single-shaft ones, and we can work out the others as apotome complements), you could use the symbol for 21/20 [-2 1 -1 1> whose untempered size is between those of 36/35 and 135/128 whose symbols you've used for 2 and 4 degrees. 21/20 has the accented symbol .||)
Then we can proceed to drop the accent and use ||) as follows.

21 A~!) 26 B!!)
31 B/|) 36 D~!) 04 E!!)
09 E/|) 14 G~!) 19 A!!)
24 A/|) 29 B 34 D!!)
02 D/|) 07 E 12 G!!)
17 G/|) 22 A 27 B\!)
32 C/|) 00 D 05 E\!)
10 F/|) 15 G 20 A\!)
25 A||) 30 C 35 D\!)
03 D||) 08 F 13 G\!)
18 G||) 23 A~|) 28 C\!)
33 C||) 01 D~|) 06 F\!)
11 F||) 16 G~|)

See:
/tuning-math/message/20570

--George

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> Hi Monz,
>
> In http://sagittal.org/sagittal.pdf (and implemented in Scala) we recommend notating 37-EDO as every third note of 111-EDO, for which we give a notation. This of course treats it as not having a mapping of the prime 3 (only 2, 5, 7, 11, 13).
>
> A native fifth notation could also be devised for it, based on the 11-limit porcupine mapping [<1 2 3 2 4], <0 -3 -5 6 -4]]. Herman Miller may already have devised such a sagittal notation.
>
> -- Dave
>
>
> --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
> >
> > over on tuning-math i've been discussing 37-edo a bit,
> > having recently discovered that it gives really great
> > approximations of prime-factors 5, 3, 7, 11, and 13
> > in 13-limit JI ... unfortunately 3 is not so good.
> > Anyway, here is a copy of a post from tuning-math:
> >
> > .............
> >
> > Here is my new Tonalsoft Encyclopedia page about 37-edo:
> >
> > http://tonalsoft.com/enc/number/37-edo/37edo.aspx
> >
> > It is not yet included in the index menu, but in case anyone
> > here wants to see it and use it, there's the URL.
> >
> > This is really quite a promising EDO tuning!
> >
> > I'm still hoping to get the ASCII sagittal notation for
> > this periodicity-block.
> >
> >
> > -monz
> > http://tonalsoft.com/tonescape.aspx
> > Tonescape microtonal music software
> >
>