Re:13 limit tuning for justin white

Paul wrote

>Using the unison vector 196:195, we can change
>14/13 to 15/14
>84/65 to 9/7
>65/42 to 14/9
>7/6 to 65/56

I have a better understanding of perodicity blocks now [thanks to your
papers] I have a few questions though.

When you transpose various intervals by unison vectors is it a) just a
pick and choose method [ie. "I'd prefer to have this note than this
one..."] or b) must you transpose only those intervals along the edges of
the Fokker parallelogram or else c) all intervals within the periodicity
block ? Or is it e) some other method ?

If it is option a) is the only criterion for swapping intervals their
distance from one another ?

I really like the scale and will definitley use it or a slight variation
[using the above method once clarified] on one of the interchageable
fretboards.

Thanks for your help it has been much appreciated.

Justin White

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--- In tuning@egroups.com, "Justin White" <justin.white@d...> wrote:

>
> When you transpose various intervals by unison vectors is it a) just a
> pick and choose method [ie. "I'd prefer to have this note than this
> one..."]

Pretty much . . . although if you take this too far, you get disconnected bits of lattice -- hardly what
is meant by "block".

> If it is option a) is the only criterion for swapping intervals their
> distance from one another ?

No -- though I did make sure that there were no steps smaller than a syntonic comma (which is
already very tight on the guitar), the main criterion was trying to maximize the number of
consonant intervals and otonal chords (such as 4:5:6:7:9:11 and 4:5:6:7:9:11:13, which I take it
you're interested in using). I'm hoping Manuel and others will continue analyzing this scale and
perhaps other improvements will present themselves.