Hobbits

I've implemented a new HOBBIT command in Scala so if anyone likes to test it, please download the latest Windows version. The parameter profile is the same as that of the DWARF command. Be aware that it only creates just hobbits. It produces the same results as in Gene's post with "jobbits" on Jan 12, 2011.
However when I try the 22 note hobbit on http://xenharmonic.wikispaces.com/Hobbits using "hobbit 22 2 11" it gives a different result: 33/32 16/15 35/32 8/7 7/6 6/5 5/4 9/7 4/3 11/8 7/5 16/11 3/2 14/9 8/5 5/3 12/7 7/4 64/35 15/8 64/33 2/1. These intervals have a shorter TE length. It looks to me that a different method is described there, but I don't understand it. Why is 16/15 the interval of minimal nonzero size and why isn't it then in the given hobbit?

I've attempted to generalise the method for other periods than 2. If we do "hobbit/full 13 3 7" for example then Bohlen's just scale comes out.
The variant with /FULL uses the full Tenney weighted norm, i.e. including 2 if that's the formal octave. Without this qualifier the seminorm is used. The formal octaves are not restricted to being primes or even integers, although not sure how useful that is. Also the scale size does not have to be equal to one of the val elements. For nonstandard vals the command line has to be used.

The time complexity has the order of number of notes raised to the number of primes so it tends gets out of hand quickly with more than a few primes.

Manuel

--- In tuning-math@yahoogroups.com, "kleisma" <manuel.op.de.coul@...> wrote:

> However when I try the 22 note hobbit on http://xenharmonic.wikispaces.com/Hobbits using "hobbit 22 2 11" it gives a different result: 33/32 16/15 35/32 8/7 7/6 6/5 5/4 9/7 4/3 11/8 7/5 16/11 3/2 14/9 8/5 5/3 12/7 7/4 64/35 15/8 64/33 2/1. These intervals have a shorter TE length.

Then perhaps we should adopt that definition. For hobbits with an even number of notes, it wasn't clear to me what the best definition was.

I'll download it and have a look; thanks Manuel for your work on this.

--- In tuning-math@yahoogroups.com, "kleisma" <manuel.op.de.coul@...> wrote:
>
> I've implemented a new HOBBIT command in Scala so if anyone likes to test it, please download the latest Windows version. The parameter profile is the same as that of the DWARF command. Be aware that it only creates just hobbits.

Are you planning to extend to tempered hobbits? That's pretty much the whole point.

Simply use PROJECT/TEMPER, PROJECT/VAL, QUANTIZE, etc to change the just hobbit into a tempered hobbit.

Manuel

> Are you planning to extend to tempered hobbits? That's pretty much the whole point.
>

--- In tuning-math@yahoogroups.com, "kleisma" <manuel.op.de.coul@...> wrote:
>
> Simply use PROJECT/TEMPER, PROJECT/VAL, QUANTIZE, etc to change the just hobbit into a tempered hobbit.
>
> Manuel
>
> > Are you planning to extend to tempered hobbits? That's pretty much the whole point.

The point I was trying to make is to ask if you were intending to feed in a list of commas or a mapping matrix or a multival, and then output a hobbit with respect to the resulting temperament.

It's not completely clear to me yet how to do that. In the hobbits you've posted I understand how to go from the transversal hobbit to the tempered hobbit. But how to produce the transversal hobbits? They look different from just hobbits. Are their Tenney lengths not measured from the origin? Is the method different?

Manuel

> > Simply use PROJECT/TEMPER, PROJECT/VAL, QUANTIZE, etc to change the just hobbit into a tempered hobbit.
> >
> > Manuel
> >
> > > Are you planning to extend to tempered hobbits? That's pretty much the whole point.
>
> The point I was trying to make is to ask if you were intending to feed in a list of commas or a mapping matrix or a multival, and then output a hobbit with respect to the resulting temperament.
>