Bingo Card Lattices

When I first started out on my generalised diatonic stuff, I arranged my
grids like the Balzano (which is why they are like that in the PNM article).

I also laid them out like the bingo card lattice, as it does away with the
left-handed tonalities that Balzano mentions. But I draw my lattices in
other vectors that the prime vectors, and in all cases what operates
analogously to the 'minor third' structurally goes straight up, and the
'major third' goes down and off to the right at 120 deg.

the 19 and 31 systems can be arranged at least 2 ways each using either
square or haxagonal grids.

Mark

> From: tuning@yahoogroups.com
> Reply-To: tuning@yahoogroups.com
> Date: 28 Oct 2002 20:55:31 -0000
> To: tuning@yahoogroups.com
> Subject: [tuning] Digest Number 2286
>
> Message: 13
> Date: Mon, 28 Oct 2002 19:43:52 -0000
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> Subject: Re: hexagonal bingo-card-lattice for 31edo
>
> --- In tuning@y..., "monz" <monz@a...> wrote:
>> i've adapted one of paul erlich's hexagonal
>> bingo-card lattices, and included it in the
>> Tuning Dictionary bingo-card-lattice definition:
>>
>> http://sonic-arts.org/dict/bingo.htm#31
>>
>>
>>
>>
>> -monz
>> "all roads lead to n^0"
>
> nice stuff, monz! i love it 'cuz you know i prefer this "hexagonal"
> distance measure to the rectangular one . . .
>
> the main advantage of these hexagonal bingo cards, though, is that
> each unison vector points in exactly the same direction as it does
> (that is, as the line corresponding to the linear temperament that
> tempers out that unison vector does) on xoomer.gif! please take a
> moment to verify this property for yourself. this could be very
> useful in a presentation on equal temperaments that runs along the
> same lines as the one you have in your dictionary . . .